Elastic Elements with Embedded Actuation and
Sensing for Use in Self-Transforming Robotic Planetary Explorers
by
Emily Katherine Andrews
B.S., Mechanical Engineering
Northwestern University, 1998
Submitted to the Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
at the
Massachusetts Institute of Technology
September 2000
©Massachusetts Institute of Technology
All Rights Reserved
Signature of Author:
Department of Mechanical Engineering
August 18, 2000
Certified by:
Profes
Accepted by:
Steven Dubowsky
of Mechanical Engineering
Thesis Supervisor
-
Ain
Amn A. Sonin
Chairman, Department Committee on Graduate Students
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
BARKER
SEP 2 0 2000
1
LIBRARIES
Elastic Elements with Embedded Actuation and
Sensing for Use in Self-Transforming Robotic Planetary Explorers
by
Emily Katherine Andrews
Submitted to the Department of Mechanical Engineering
on August 18, 2000 in Partial Fulfillment of the
Requirements for the Degree of
Master of Science in Mechanical Engineering
ABSTRACT
The content of this thesis addresses two separate, but related areas of research. The first
part of the thesis will present the findings of a feasibility study conducted on the topic of
Self-Transforming Robotic Planetary Explorers. The study focused on defining the
overall concept of Self-Transforming Planetary Explorers, researching the state of those
enabling technologies that would be required for the concept development, and
formulating a research plan for meeting the development objectives. This includes a
discussion of the two system architectures developed as well as a technology readiness
assessment. The second part of the thesis will present preliminary work conducted into
Elastic Robotic Elements with Embedded Actuation and Sensing. The objective of this
research was to bound the capabilities of elastic structures for use in robotics as well as to
understand the fabrication complexities related to embedding the actuation and sensing
systems. The motivation behind this preliminary work was the design of a new series of
mechanical components for use as robotic structures for planetary robotics. This is one
of the requisite enabling technologies under development in the pursuit of the SelfTransforming Robotic Planetary Explorer Concept.
Thesis Supervisor: Steven Dubowsky
Title: Professor of Mechanical Engineering
2
Acknowledgements
This work was conducted at the Field and Space Robotics Laboratory at The
Massachusetts Institute of Technology under the sponsorship of The NASA Institute for
Advanced Concepts.
I'd like to thank The NIAC for giving me the opportunity to
conduct work on this exciting, far-sighted research.
The feasibility study, which
comprises the first portion of this thesis, was, in part, a collaborative effort. I'd like to
thank those primary collaborators Professor Steven Dubowsky, Professor Gregory
Chirikjian, Karl Iagnemma, Vivek Sujan, Sharon Lin, Rob Pinder, and Guillermo
Oropeza, without whose help the study would not have been possible. I'd also like to
thank John Madden for his assistance with conducting polymer actuator characterization.
I'd also like to acknowledge the assistance I received from the Dick Fenner and his staff
in the Pappalardo Laboratory.
I'd like to thank my advisor, Professor Steven Dubowsky for his assistance and guidance
throughout my research. His support and insights were greatly appreciated.
Finally, I'd like to thank my family and friends for all their support throughout the past
two years.
.3
Table of Contents
T itle P age .............................................................................................
1
A bstract ............................................................................................
2
Acknowledgements ..............................................................................
3
Table of Conents...................................................................................4
Table of Figures and Tables.......................................................................6
7
Chapter 1 Introduction ..............................................................................
1.1 Introduction .............................................................................
7
1.2 Motivation............................................................................7
1.3 Background and Literature Review..............................................12
1.4 Research Overview................................................................15
1.5 Thesis Overview....................................................................16
Chapter 2 Self-Transforming Robotic Planetary Explorers...................................18
2.1 Introduction.............................................................................18
2.2 The Future of Planetary Space Robotics..........................................18
2.3 The STX Concept..................................................................20
2.4 The CTX Concept..................................................................24
Chapter 3 Enabling Technologies.............................................................25
3.1 Overview of Technologies............................................................25
3.2 The Physical System................................................................25
3.3 Embedded Active Binary Muscles..........................................29
3.4 Reconfigurable Information and Power Networks.............................32
3.5 Motion Control......................................................................34
36
3.6 Physical System Configuration Planning ........................................
Chapter 4 Elastic Elements with Embedded Actuation And Sensing........................39
4.1 Introduction.........................................................................39
4.2 Elastic Mechanism Study............................................................39
4.2.1 Finite Element Approach............................................40
4.2.2 Beam Elements.........................................................41
4.2.3 Elbow Elements........................................................48
4.2.4 Rhomboid Elements..................................................50
4.2.5 Hexagon Elements....................................................52
4.3 Lattice Structure - Hyper Degrees of Freedom................................54
4.4 Fabrication Techniques............................................................54
4.4.1 Materials Selection....................................................55
4.4.2 Mold Fabrication....................,.................................57
4.4.3 Idealized Fabrication Techniques...................................59
4.5 Embedded Actuators.............................................................60
4.5.1 Actuator Placement......................................................62
4.6 Embedded Sensors..................................................................64
4.6.1 Passive Sensors Design...............................................64
4
Chapter 5 Conclusions and Future Work....................................................
67
5.1
C onclusions........................................................................67
5.2
Future Work........................................................................70
References ........................................................................................
72
Appendix A The NIAC............................................................................76
Appendix B ProMechanica Finite Element Results..........................................78
Appendix C Shape Memory Alloys.............................................................100
.5
Table of Figures
and Tables
Figure 1 Sample Martian Terrain Map; Sojourner Traversing Martian Terrain.............8
Figure 2 Planetary Colony Concept...............................................................8
Figure 3 STX concept..........................................................................16
Figure 4 STX Constructing a Ground Facility; STX Traversing a Boulder Field.........16
Figure 5 Planetary Robot Progression..........................................................21
Figure 6 The STX Concept.....................................................................21
Figure 7. STX Constructing a Ground Facility; STX Traversing a Boulder Field........23
Figure 8 (a) Compliant SMA Gripper with no bearings; (b) Conceptual Model of
a 3DOF Compliant Leg..........................................................................27
Figure 9. (a) Articulated Binary Element, ABE; (b) SMA "Squatting" Suspension......28
30
Figure 10 Embedded Actuation ..................................................................
Latch
with
Electronic
of
a
Bi-stable
Compliant
Figure 11 Conceptual Model
34
H andshake........................................................................................
Figure 12 A 3 Bit Stewart Platform Manipulator..............................................35
38
Figure 13 Genetic Crossover Methods .........................................................
Figure 14 Load Diagram for Beam Buckling...............................................42
Figure 15 Eccentrically Loaded Beam...........................................................44
Figure 16 Beam with Truss-like Voids......................................................46
Figure 17 Eccentrically Loaded Beam with Truss Voids.................................47
Figure 18 Elbow under External Load..........................................................49
Figure 19 Rhombus Closed Form...............................................................51
Figure 20 Hexagonal Closed Form Element....................................................53
Figure 21 Element Network Structure and Mechanism Example............................54
Figure 22 FlexCast Beam Elements...........................................................57
Figure 23 Machined Aluminum and Cast RTV Silicone Molds..........................58
65
Figure 24 Experimental Photo-Detector Setup.............................................
Figure 25 Passive Embedded Optical Sensor Array........................................66
Figure C1 Transformation Between High and Low Temperature Structures.............100
56
Table 1 FlexCast Material Properties ............................................................
Table C1 Flexinol Muscle Wire Properties....................................................101
6
Chapter 1
Introduction
1.1
Introduction
The content of this thesis addresses two separate, but related areas of research. The first
part of the thesis will present the findings of a feasibility study conducted on the topic of
Self-Transforming Robotic Planetary Explorers.
The study focused on defining the
overall concept of Self-Transforming Planetary Explorers, researching the state of those
enabling technologies that would be required for the concept development, and
formulating a research plan for meeting the development objectives. This work was a
cooperative effort in the Field and Space Robotics Laboratory at MIT, of which a major
portion was completed by this author.
The second part of the thesis will present
preliminary work conducted into Elastic Robotic Elements with Embedded Actuation and
Sensing. This is one of the requisite enabling technologies under development in the
pursuit of the Self-Transforming Robotic Planetary Explorer Concept.
1.2
Motivation
In order to understand the motivation driving research of Elastic Robotic Elements with
Embedded Actuation and Sensing, it is first necessary to understand the overall research
objective. Research into Self-Transforming Robotic Planetary Explorers is sponsored by
the NASA Institute for Advanced Concepts (The NIAC, see Appendix A) and conducted
at MIT's Field and Space Robotics Laboratory. The concept represents a paradigm shift
in the design of robotic planetary explorers. Today's planetary robots, Sojourner, Rocky,
7
Fido, [Bickler, 1992] for example, are fixed configuration systems composed of discrete
mechanical and electrical components. Their abilities include traversing benign terrain,
specific surveying and small sample collection. (See Figure 1.)
(H. Das, Jet Propulsion Laboratory, 1998)
In the future, planetary robots will need to perform more ambitious tasks. In the next 10
to 40 years, it is possible to imagine robots that can explore and help prepare the way for
human exploration and even habitation of planetary surfaces. In order to accomplish
these goals, planetary robots will have to be able to scout, mine, conduct science
experiments, construct ground facilities and aid human planetary explorers and settlers,
(see Figure 2.)
Figure 6 Planetary Colony Concept (Slawek Wojtowicz)
R
These tasks necessitate robots that are extremely flexible and adaptive to varying terrain,
environments and duties.
One may imagine robots that can assume any shape and
therefore accomplish many field objectives. These types of "flexible" or "shape-shifting"
robots have thus far been confined to the domain of science fiction writers (Terminator 2
- Cameron, J.; Deep Space 9 - Piller, M., et al.; etc.) There is, however, validity in the
idea of moving from a paradigm of fixed configuration robots with discrete components
to one of continuous systems and components (Chirikjian '94, Kawauchi, et al. '92,
Kotay, et al. '97, '98, Murata, eta 1. '94, Rus '98, Yim '95). Fixed configuration systems
are suited for a narrow range of simple tasks. As the tasks grow in complexity, the robot
complexity also increases.
The overall objectives of this research are to explore the
notions of continuous mechanical and electrical elements and sub systems, simplified
control architectures and configuration planning that would potentially allow robots to be
self-transforming.
The goal of designing and building Self-Transforming Robotic Planetary Explorers is not
a trivial one. The fulfillment of the goal relies heavily on the parallel development of
many technologies that will improve the selection of mechanical and electrical
components which roboticists use in robot design.
Currently, robots are built with
discrete, heavy motors and gear trains, rigid mechanical links for "arms", a myriad of
bearings and fasteners, a rats' nest of wiring, and a relatively large computing stack
comprised of hundreds of electronic components. All of these components are heavy,
failure prone, and have limited capabilities due to their fixed configurations.
They
represent conservative, tried and true methods that do not approach the state of the art in
component technology. While many advances have been made in the control, planning
9
and intelligence of today's robots, mechanical and electrical component design
advancements have been left behind. The case has been made, in the previous chapter,
that until these mechanical and electrical hindrances are lifted, the advancement of space
robotics is extremely limited.
Today's robots are constructed from strong, heavy, metal elements. Rigid structures are
well understood and when fortified with extra material, can be modeled as undergoing
very little deflection under load. This is advantageous from a position control point of
view that seeks to know exactly where the endpoint of a manipulator is at any given time
so that it can appropriately accomplish its assigned task. In the context of space robotics,
however, this design presents a number of problems that act, ultimately, to limit the
robot's capabilities. The first, and perhaps most obvious, problem is that these structures
are extremely heavy. Not only are the rigid metal links themselves heavy, but they are
actuated by necessarily heavy motors, adding to their weight. Fundamentally, in NASA
terms, weight is expense. As this is no longer the Space Age of the 1960's, NASA's
budget limits the payload it can send to a planet. The ramifications of this problem are
that only small robots of limited and fixed configuration are currently sent to Mars. For
example, a robot that would be very effective with dual manipulators, may be limited to a
single manipulator due to the weight envelope. From this perspective of weight alone, it
can be seen that space robotics would be served by finding an alternative paradigm for
their mechanical design.
There is, additionally, the issue of rigid mechanical robotic structures having, inherently,
limited capabilities. It was mentioned that these robotic structures are positioned with
heavy, rotary motors. These motors, along with heavy gear trains, are located at the
10
robots joints between rigid links. The workspace of the robot, the range of points it can
reach, is defined by the size of these rigid links and the number of motors, or degrees of
freedom, it possesses.
Clearly, having one rotary motor on a manipulator limits the
robot's reach to a circle of points. It would seem the clear solution, then, would be to
have a large number of motors and therefore, many degrees of freedom. If the comments
of the previous paragraph are to be heeded, that number of motors would far exceed any
acceptable weight envelope. Ultimately, under this current design paradigm, there must
be a trade-off between the robot's weight and it's capabilities. It is therefore time to start
looking at designing mechanical structural components for use in robotics that have
increased capabilities and minimized weight.
The proposed method for meeting such seemingly conflicting demands is to utilize
elasticity and flexibility in space robotic structures.
Instead of using discrete, rigid
components that slide on bearing surfaces to create motion, more natural flexural pivots
and distributed elasticity would be used.
It has been attempted to introduce some
compliance into rigid structures by using force controls and other control algorithms for
the purposes of controlling "soft" motions. This work is aimed at creating more sensitive
robotic limbs rather than at actually using compliance for its motion advantages.
Much
work has been done in the area of designing and optimizing compliant mechanisms
{Frecker, , Howell, Kota, Sigmund.] These are mechanisms that gain their force and
motion characteristics from discrete flexural hinge points. It is the ultimate goal of the
CTX (Continuously Transforming Explorer) that is the motivation for this work into
elastic elements, however. Recall that the vision for the CTX was of a robot comprised
largely of one material that is capable of morphing into different shapes and
11
configurations depending on the task at hand. If this ambitious vision is some forty to
fifty years down the road, elastic elements research represents the first step down that
road.
Elastic Elements are structural robotic elements that gain some or all of their motion and
force characteristics from actuators embedded inside of their elastic structure. Instead of
having discrete hinge points of localized motion, their motions are achieved continuously
throughout the entire structure. Their design precludes the use of mechanical elements
such as gears, bearings, motors, etc. which are mechanically complex and prone to
mechanical failures. The embedded actuators and sensors in these elements are binary in
nature and thus allow for a far simpler, "digital" control architecture than conventional
mechanical actuators and sensors.
These elastic elements may achieve close to
continuous motion by using many of these binary degrees of freedom or hyper degrees of
freedom. This continuous motion is the foundation of the Self-Transforming Robotic
Planetary Explorer Concept.
1.3
Background and Literature Review
Current planetary robots and robots under development for use in unstructured
environments, such as space, in the next 5 to 10 years are designed to perform a small set
of tasks in relatively benign terrain. In order to achieve higher functionality, new robotic
concepts are being pursued. Such research includes reconfigurable robots. The term
reconfigurable applied to robots includes both topological and geometric changes in a
robot.
Among the concepts that have been proposed are modular robotics, cellular
robotics, morphing robotics, and cooperative robotics. Modular or cellular robotics refer
12
to those robotic systems that are composed of a set of similar units [Farritor et al, 19961.
By changing the placement or topology of these modules, the overall shape of the robot is
altered. The workspace encompassed by the system of modules is determined by the
number of modules and the number of ways that they can recombine.
Research in
modular robotics includes the development of a system of self-reconfiguring molecules
[Kotay and Rus, 1997] and a metamorphic system of hexagonal planar modules
[Pamecha, et al., 1997]. Research into the complexities involved with designing systems
with a high degree of redundancy ("hyper-redundancy") has also been completed
[Chirikjian and Burdick, 1995].
Interaction among similar robots or cells has been
studied in relation to autonomy in robots [Kawauchi et al, 1992].
Motion control of discrete, binary actuation has been addressed [Chirikjian, 1997].
Binary motion action planning using Genetic Algorithms has also been studied [Farritor
and Dubowsky, 1997]. The Concept of discretely actuated manipulators is actually quite
an old idea. The concept can be traced back to work done in the Stanford robotics group
more than a quarter of a century ago [Pieper, 1968 and Roth, 1973]. Research in the
former Soviet Union along these lines was also performed more than a decade ago
[Koliskor, 1986]. A model that relates joint accuracy to end effecter accuracy has also
been described [Kumar, 1980]. Despite these efforts, two important tools did not exist:
(1.) A framework to handle the combinatorially explosive nature of the inverse
kinematics problem; and (2.) A means for designing discretely actuated manipulators so
that they could reach a finite set of specified frames in space. The absence of these tools
had been a major impediment to the use of discrete actuators in robotic motion until
recent years.
13
In addition to the issues of reconfigurability and motion control, a major challenge in this
research has been in the area of mechanisms and actuation. There has been much work
done in the area of deployable structures for space applications [Huang and Pelligrino,
1996]; however, because of their complexity and weight, they do not represent a realistic
direction for planetary robotics.
In the field of compliant mechanisms, design
optimization for small deflection structures has been studied [Frecker et al., 1996]. Work
has also been done in creating bi-stability in compliant mechanisms [Opdahl et al., 1998].
Physical, electrical and information connector prototypes have been developed from
discrete mechanical and electrical components [Okhami, 1999].
Researchers in
conducting polymers have demonstrated physical and theoretical evidence of the
polymer's abilities to outperform biological muscles [Baughman, 1996; Madden et al.,
1995]. Work has also been done in embedding actuators into materials for the purpose of
damping and vibration control [Janos and Hagood, 1998]. Work in both fields of active
materials and compliant mechanisms have been related to achieving small, quick
displacements. In order to use these technologies in planetary, robotic applications, they
will have to be developed to achieve large motions over longer periods of time.
Preliminary studies conducted with SMAs suggest that active materials will play an
important role in self-transforming robotic planetary explorers.
While the research community has yet to address the feasibility of self-transforming or
reconfigurability to future planetary exploration robotics, the work that has been done
provides an excellent foundation for developing continuously transformable robotic
systems for planetary exploration purposes. Concepts related to reconfigurability and the
development of continuous components and systems offers promise in overcoming the
14
limitations of conventional robot design for future planetary exploration. The study of
the concepts of self-transforming systems for planetary exploration has been the
application focus of this research.
1.4
Research Overview
This research has begun with studying the feasibility of Self-Transforming Robotic
Planetary Explorers. The physical design of such systems would be based on the use of
Active Binary Elements (ABEs) which are compliant, elastic members with embedded
actuators, sensors, and information and power networks.
This research study sets its initial focus on studying the design of the physical system and
its control of self-transforming systems. It addresses the underlying fundamental physics
of this class of system in attempting to assess the concept feasibility. Such systems also
present important technical challenges in a number of areas, such as sensor technologies,
communications and artificial intelligence, which, while important, were beyond the
scope of this initial study. First, working with NASA experts from JPL, a set of potential
missions for planetary exploration, and for precursor human missions that might occur in
the next 10 to 15 years, were formulated.
Concepts for a class of self-transforming
robotic planetary explorers, called STXs, which could meet the objectives of these
representative missions will be investigated.
An STX system is a hybrid system
composed of a combination of conventional system components and elements that can be
fabricated from elastic materials with embedded actuators, sensors and information and
power networks, ABEs. As discussed below, the binary nature of the articulation results
in a significant reduction of system complexity, while maintaining a high degree of
15
. .........
functionality. The move to ABEs can be thought of as being analogous to the landmark
replacement of analog electronic circuits by digital circuits that occurred twenty years
ago. Figure 3 shows a representation of an STX system with an idealization of a system
composed entirely of a very large number of highly integrated, non-conventional binary
elements. Figure 4 presents two STX topological configurations of an STX performing
future tasks.
/ABU
Nodes
Figure 7 STX concept
Figure 8 STX Constructing a Ground Facility; STX Traversing a Boulder Field
(Pinder, R.)
16
1.5
Thesis Outline
This thesis will encompass both the general topic of Self-Transforming Robotic Planetary
Explorers as well as the specific research conducted under the topic of Elastic Elements
with Embedded Actuation and Sensing. Chapter 2 will include an overview of the SelfTransforming Robotic Planetary Explorer system concepts generated during the
feasibility study.
Chapter 3 will present the major enabling technologies that were
researched including their current state of development and how they will each play a
critical role in achieving the system concept. In Chapter 4, the structural design, analysis
and experiments of elastic elements developed for this work, and the research into
embedded actuation and will be presented. The final chapter, Chapter 5, will discuss
conclusions that can be drawn from this research as well as future work to be conducted
in this field.
17
Chapter 2
Self-Transforming Robotic Planetary Explorers
2.1
Introduction
This chapter will present the concepts generated for Self-Transforming Robotic Planetary
Explorers system architectures. This work was done in collaboration with researchers in
the Field and Space Robotics Laboratory, namely Professor Stven Dubowsky, Karl
Iagnemma, Vivek Sujan, Sharon Lin and Guillermo Oropeza.
The feasibility study
conducted for The NASA Institute for Advanced Concepts (NIAC) was aimed at
developing both concepts for the system architectures as well as the requisite enabling
technologies. This chapter will focus on the architectures, including an architecture for a
hybrid system with a ten year horizon and a completely continuous system with a forty
year horizon.
2.2
The Future of Planetary Space Robotics
Planetary Rovers are robots such as Sojourner, Rocky IV and Fido that have been
developed largely at NASA's Jet Propulsion Laboratory (JPL). These robots have been
designed with the specific purpose of exploring the surfaces of planets such as Mars.
These rovers are all wheeled vehicles of a fixed configuration with one or more
manipulators and mono or stereovision. They are controlled via tele-operation from the
earth's surface. Given these design constraints, their capabilities are limited. They are
capable of traversing limited feature size terrain; generally no larger than half of their
wheel diameter.
They can take and transmit photographs of the surface they are
exploring. Some of the rovers are capable of gathering samples from the loose rocks they
encounter on the planet's surface.
Given the relative novelty of planetary surface explorations, these are accomplishments,
indeed. However, in the context of the NIAC charter that gives a ten to forty year time
horizon for research, it is clear that far greater capabilities will be required of planetary
robots. Some of these capabilities include the ability to roam over large distances; the
ability to vary and adapt their mode of locomotion depending on the terrain; the ability to
core into the planet for samples and raw materials; and the ability to build infrastructure
such as communications towers, extraction and processing sites, and habitats as a
precursor to HEDS (Human Exploration and Development of Space) missions.
It is clear that solutions to some of these tasks and others may naturally evolve in ten to
forty years. However, it is also clear that the rover-model architecture will not ever allow
for some of these tasks to be completed. The rover-model, as mentioned earlier, is of a
fixed configuration, mechanically, electronically as well as at the software level. Its
workspace is, therefore, limited to the "reach" of each of these systems at the time it is
designed. A robot capable of adapting to its surroundings and to the task at hand can be
imagined.
Indeed, the artificial intelligence community is already demonstrating a
computer's ability to learn from experience and dynamically change its software. Why
should this adaptability be limited to the software domain? It should not.
19
The premise of this feasibility study is the exploration of building analogous adaptability
into the design of the mechanical and electrical systems of planetary robots.
This
necessitates the development of new mechanical and electrical "components" that have an
innate flexibility that motors, gears, bearings, and wires, etc. do not. The aim of this work
into Self-Transforming Robotic Planetary Explorers is the development of a robot
analogous the morphing "robot" depicted in Terminator 2 in a timeframe of forty years.
This ambitious goal necessitates some intermediary steps that will be discussed in the
following sections.
2.3
STX Concept
The stated aim of creating an adaptable, continuously self-transforming robot in forty
years is ambitious and must begin with more humble objectives. In order to realistically
approach such a farsighted goal, it is necessary to set some goals at intermediary time
intervals.
The near term goal of designing and building a STX, Self-Transforming
Explorer in a ten year timeframe is the driving motivation behind this feasibility study.
The premise of the STX is that it represents a hybridized bridge between planetary space
robots of today and the ultimate, farsighted goal of developing a CTX, Continuously
Transformable Explorer, robot that will be able to morph its shape and adapt to its
surroundings and tasks. To look at the spectrum between these extremes (see Figure 5),
current robots are characterized by their fixed, rigid configurations that won't allow for
topological changes. Moreover, they are comprised entirely of discrete mechanical and
20
electrical components that, due to their diversity and individual complexity, limit the
adaptability of the structure.
2000
2010
ROVERS
STX
CTX
Discrete
Compo0ents
Hibrltib
CotInous
Sstem
S'stem
2040
Figure 5. Planetary Robot Progression
The STX would be a robot that has some discrete components and other, more
generalized components that may be used and reused. Specifically, the envisioned STX
is composed of nodal computing centers connected by generalized Active Binary
Elements (ABEs). A visual concept model for the STX can be seen in Figure 6.
Nodes
Figure 6. The STX Concept
21
The nodes would serve as computing centers as well as storage and transport units. As
can be seen in figure 6, these nodes are envisioned as having many sides to which the
ABEs could be connected. In this model they are shown as rhombic dodecahedrons, the
merit of which lies in their twelve identical sides, close packing structure and the subtle
dihedral angle of 1200. All of these characteristics improve the ease of reconfiguration
for the robot. The identical sides means that the same size and shape of connectors may
be used. Having twelve sides instead of four, as in the case of a cube or pyramid, gives
many more places for the ABEs to attach, increasing the number of configurations the
system can achieve. It also means that the robot has many more options for finding a
statically stable configuration. By using a closed-packed geometric element as the basis
for the node design, the shipping footprint could be mimized.
It is envisioned that, in militaristic fashion, each node would have a specialized task.
Such specialized nodules will include a scout, a General or primary computing center, a
power hub, storage and a communications node, for example. In this way, each node
would contribute to the overall mission of the system, but each would not have to carry
all of the requisite subsystems. While the power hub would store all of the power for the
network, all of the nodes would be capable of collecting solar power via panels on each
of their faces.
These nodes would be connected by ABEs in a number of different, though finite,
configurations.
The ABEs, Active Binary Elements, are continuous, flexible, self-
contained appendages. They are designed to be generalized so that they may be used for
manipulation, connecting the nodes as well as legs or wheels for transportation. The
ABEs would have all actuation and structure contained internally and would be able to
22
act as conduits of power and information between the nodes. The actuation is binary in
nature in order to simplify motion control.
Their structure would be composed of
compliant mechanisms allowing the required freedom of motion while minimizing the
weight as well as the number of discrete components. The ABEs will be discussed in
further detail in Chapter 3.
Figure 7. STX Constructing a Ground Facility; STX Traversing a Boulder Field
(Pinder, R.)
This physical structure would allow the STX to reconfigure itself for any given task.
Two such tasks, construction and traversing a rocky terrain, are demonstrated in figure 7.
The "General" node would be responsible for path planning.
This includes global
planning of how to move around its environment but also local planning of how to
reconfigure the ABEs for the specific task. Genetic algorithms would be the basis of its
decision-making processes.
GAs involves an iterative process of cross-pollinating
different action sequences, adding mutations into the code until a particular threshold
evaluation term is met. It has proven to be a computationally efficient tool for such
planning issues [Farritor, 1998.]
The physical design of the STX was the focus of this feasibility. The use of discrete
nodes and ABEs is in keeping with the physical structures of today while utilizing some
23
of the advances being made in mechanical design.
Its advantages over convention
systems is in its generalized design that allows for reconfiguration as well as in the selfcontained flexibility and motion of the ABEs.
2.4
CTX Concept
The STX is a hybrid of today's robotic components and of tomorrow's long range vision
for a shift in robotic component design. It represents an intermediary step on the way to
the realization of a Continuously Transformable Explorer, CTX. Where the STX has
some generalized and continuous elements capable of changing the reconfiguration of the
robot, the CTX strives for a robot that will be almost universally generalized. It would be
constructed entirely of a single family of plastics that will provide the structure, the
motion, the computing, the sensing and the power.
With this generalized material
approach, the ultimate goal is for the CTX to be able to shift its shape to meet the
changing demands of a hostile planetary surface. The goal of achieving the CTX has
been given a forty year time horizon as it requires a complete and radical change in the
way robots are physically designed. This CTX concept is the basis for elastic elements
research and therefore will be discussed in greater detail in Chapter 4.
24
Chapter 3
Enabling Technologies
3.1
Overview of Technologies
In order to achieve the objective of hybrid self-transforming planetary robots, STXs, in
the next 10 to 15 years, and true, continuously transforming robots, CTXs, in the 15-40
year time frame, some key technologies will need to be developed. The feasibility study
included a technology assessment of the following areas:
1.
Physical System:
The Structure of the System (Elastic Elements and Compliant Mechanisms)
Active Binary Muscles (SMAs, conducting polymers)
Reconfigurable Information and Power Networks
2. Discrete, Binary Motion Control
3. Physical System Configuration Planning
The following sections present each of these enabling technologies, their current state of
development as well as the future work required to implement these technologies in the
STX concept.
3.2
Physical System
Consider, first, the physical structure of the self-transforming robotic planetary explorer
(STX), see Figures 6 and 7. The body of the STX is composed of a network of node
25
elements. The role of these nodes is multifunctional. They act as connection points for
the system. They also house the system intelligence, power storage and carry science
apparatus and geological samples.
Conceptually, they are many faceted (possibly
rhombic dodecahedrons) each face representing a different point of connection, for the
ABEs.
These connection points allow the STX to change its topology.
With this
increased number of connection points, the possible number of topological configurations
expands from that of the basic fixed configuration shapes used today.
Each robotic
system is a set of multiple nodes. The larger the number of nodes available to the system,
the more configurations and, therefore, the larger the effective workspace of the robot.
Each node may have a specific task or responsibility. This network of nodes would rely
on Articulated Binary Elements, ABEs, for connection to each other as well as for
mobility and manipulation. The following sections will explain how these ABEs will be
realized based on emerging technologies.
ABEs will allow the topological changes
necessary for completing a wide and varying range of tasks in systems in the 10-15 year
time frame, see Figures 3 through 5. In the 15-40 year time frame, many of the functions
of robotic systems will become distributed throughout these ABEs, and the ABEs
themselves will evolve into more generalized members.
In the STX concept, the nodes are joined by Articulated Binary Elements, ABEs, which
are composed of compliant mechanisms and contain their own internal actuation. The
actuation methods will be discussed below. ABEs are capable of accomplishing many
diverse tasks, such as mobility and manipulation. They also form the skeleton of the
system. Whereas today's robots are structurally rigid (and heavy), the ABEs will exploit
26
their flexibility, eliminating the need for bearings and traditional joints. In addition to
simplifying some of the mechanical complexity of today's robots, the ABEs will allow
the STX to undergo topological changes through connecting and reconnecting to different
nodes, in different configurations, see Figure 7. Favoring compliance over rigidity is, in
fact, the way of nature [Vogel, 1995].
As discussed in section 2.4, ABEs are lightweight structures, made from non-metallic
materials, which achieve points of relative motion through optimized material
minimization. Thus forming compliant joints. Figure 8(a) shows a prototype compliant
gripper, that is mechanically simple but capable of lifting geological samples. Figure 8(b)
shows a model of a 3DOF compliant leg, also demonstrating the simplicity of compliant
joints.
Figure 8 (a) Compliant SMA Gripper with no bearings (Lin, S., 1999);
(b) Conceptual Model of a 3DOF Compliant Leg
Instead of having two rigid links coupled by a complex rotary actuator and bearing,
compliant joints provide relative motion with minimal complexity.
Ideally, each
compliant machine is a continuous structure, manufactured from a single piece of
material, and designed to have multiple points of flexure, or joints. Because of the
simplicity of compliant joints, it is possible to construct members (ABEs) with many of
27
these joints that are actuated in a simple binary fashion. The advantage of this type of
structure over rigid manipulators, is that they are lightweight, simple to control (see
section 3.5), and multifunctional. They would be used not only for manipulation but also
for mobility, walking, climbing and rolling for example, and in the STX, as a skeletal
structure for connecting the various node bodies.
In the Field and Space Robotics Laboratory, a first generation ABE has been built
[Oropeza, G., 1999] (Figure 9(a)). It consists of five stages, each composed of two discs
interconnected by three flexure-hinged links. The links were made out of Ultra High
Molecular Weight (UHMW) polyethylene and the discs were machined out of Delrin.
The links were press-fit to the discs and the stages were connected to each other with
nylon screws. The structure is actuated by shape memory alloy (SMA) wires (see section
3.3) Also built at the FSRL and shown in Figure 9(b) is a prototype of a "squatting"
suspension that can change its geometric configuration by activating antagonistic SMAs.
Figure 9. (a) Articulated Binary Element (Oropeza, G., and Sujan, V., 1999), ABE;
(b) SMA "Squatting" Suspension (Burns, R., 1998)
During the Phase II study period, research will be conducted in order to find a material
for the skeletal structure that is optimally strong and elastic.
Research will also
concentrate on addressing the issues of how these materials will perform in space
environments, including microgravity, temperature and contamination issues. In a 10 to
15 year timeframe, it is believed that this work in compliant structures will grow to
represent an entirely new family of engineering components for terrestrial as well as
space applications. This group of mechanical materials will be an integral step toward
the realization of a continuously transformable planetary explorer. In the 15-40 year
timeframe, the number of compliant joints will increase, approaching the very large scale
binary actuation (VLSBA) systems with more distributed functions.
3.3
Embedded Active Binary Muscles
The concept of ABEs, as discussed above, requires actuators that have only two states. In
a sense they will be artificial muscles, but with less complexity. Control is achieved by
having many of these binary actuators (see section 3.5.) There have been many advances
in recent years in active materials for artificial muscles. Among these materials are shape
memory alloys, conducting polymers, polymer gels, piezoelectrics, magnetostrictives,
and many more. As most of these materials are still in their infancy, extensive use of
them in practical robotic systems has not been realized. A limitation of some of active
materials is that they can only be used for small deflections in short periods of time. For
robotic systems such as the STX, active materials will have to be able to achieve large
29
'Ad
motions. Since these robots will be used in space exploration, fast action is not expected
to be a critical performance criterion on most missions.
The path that this research will follow is governed by the available technology. Initial
work includes using bundles of these muscles attached to the skeleton, similar to
mammalian musculature. This segment of the research is amenable to the current state of
technology and will be pursued in the 10-15 year timeframe, as discussed further in
Chapter 4. Central to the research for the 15-40 year time frame will be on the idea of
embedding matrices of these muscles within the material of the skeletal structure itself, as
shown in Figure 10. This idea contributes to the development of the active mechanical
material family mentioned in the last section.
By embedding the muscles, a clear
development path from embedded discrete actuators in mechanical materials to
continuously adaptable materials will be established.
As discussed, below, two very
promising actuator technologies for self-transforming robots are SMAs and conducting
polymers. The study of the feasibility of these actuators for robots used for exploration is
one focus of this research.
comrfite
c r~a;-lo
Inte'zons Comrunicaon
Avceiect-c
-cs
S~
R TURE
.AM.1 NAtE~
Leacis
se so's
and
Sg-a Proce-snt-cC1atEc
A
A
Ectctes
Sensi4. Laye
Pv- PScyiricse 8ase
riocAC
Modifec
Layer
W AIGNr
AINA
nte-agsatec
Firers
1EWAT
E[
flerog,*:atec Eiecrode
Figure 10 Embedded Actuation [Hagood]
30
Conducting Polymers. Conducting polymers are a class of materials that can be used as
electromechanical
actuators
by
achieving
large
dimensional
changes
through
electrochemical doping. Applying a voltage across two conducting polymer electrodes of
similar electrochemical potential generates a strain. For a few volts, conducting polymer
actuators can achieve linear dimensional changes on the order of 10%. This can be
compared with piezoelectric and electrostrictive actuators which require on the order of
30 volts to achieve a 0.1% dimensional change [Baughman, 1996].
Conducting polymer response time is an order of magnitude faster than the fastest natural
muscles; ant jaw closure: 0.3 ms and flea jumping: lms [Baughman, 1996].
The
maximum force of conducting polymers is 80-100 times that of natural muscles
(790kgf/cm2 compared with 8kgf/cm2 for crawfish muscle [Baughman, 1996]). Given
these metrics, it is likely that conducting polymers will be an integral part of robotics in
the coming century. They would allow robotic actuation to reach, and surpass, that of
biological systems. Together with the compliant mechanical skeleton, these conducting
polymer actuators will be fundamental in the development of adaptable generalized
appendages. Bundles of conducting polymers, used in parallel but controlled individually
would be able to adjust the force and compliance of the appendage, similar to the
adjustable rigidity of the human ankle that can be achieved by contracting multiple
muscles [Baughman, 1996]. This idea of controllable compliance, studied in connection
with ABEs, would be used by embedding conducting polymers into the compliant
mechanical skeleton of the self-transforming robotic planetary explorers.
Conducting
polymer actuators promise to be very useful to robotics in the long-run [Madden, 1995],
31
however, in the next 15 years SMA may prove to be a more feasible option for binary
actuation in the ABEs.
Shape Memory Alloys. Another class of actuators, which are considered in the study of
self-transforming robotic planetary explorers, are shape memory alloys.
Whereas
conducting polymers are in their infancy in terms of development, SMAs have been well
studied and are commercially available.
SMAs are important to the study of self-
transforming robotic planetary explorers for several reasons. First, SMAs represent a
substantial improvement in strength to weight ratio over traditional hydraulic and
electromechanical actuators, (600Mpa/3.166E-4kg/m). They can be actuated in a binary
fashion that simplifies the control aspect, as will be discussed in section 3.5.
While
SMAs are considered inefficient for most applications, it is believed that for planetary
and space applications, where fast action is not critical, SMAs will exhibit better
efficiency when well insulated and actuated slowly. Finally, they are readily available
and low cost. They have been used to actuate the compliant mechanical structure and a
clear progression from early work done with SMAs on the ABEs to later development of
conducting polymer musculature can be seen.
3.4
Reconfigurable Information and Power Networks
In order for the STX to be able to topologically transform, the information and power
networks will, themselves, have to be reconfigurable. The idea of hard wiring does not
32
work within the context of this application because it limits the system to a fixed
configuration. There are several issues that require research in this area. These include:
1.
Determining if these information and power pathways that make up these
networks can be consolidated.
2. Determining if the same muscles used for actuation can be used to carry
signals.
3. Addressing the issues related to reconnecting the information and power
pathways to allow reconfiguration of the STX.
Possible solutions to these issues that are under study include:
1.
Establishing a "Bus" structure for the networks or "multiplexing" the
pathways.
2. Developing a methodology for an electronic handshake.
As the physical
systems mate, the power and information re-connections would be made as
well, as shown conceptually in Figure 11.
The physical mating will be
accomplished through the releasing and locking of bistable compliant
mechanisms at the ends of the ABEs and on the node faces. For the sake of
visualization, view these links as gripping "hands". On the "palm" of each
"hand" would be an electrical grid pad. When these two pads come together
and are locked in place by the physical grip, they would meet up in some
arbitrary configuration. Some portions of each grid would have counterparts
on the other grid and some would not. Once the physical connection is in
place, the system intelligence would query the point of connection. It would
be able to establish its new connectivity by detecting which grid point
33
..........
....
received which signal. Through an "electronic handshake" the very electrical
system itself becomes transformable
3. Exploring new ways to actuate ABEs at a distance, such as magnetic field,
lasers, eddycurrents.
Mdingrintemecting
Ccndcting"Pad"
Pcins d Electricd
Connection
Mca~gned TcV
ABE 2
ABE I
Open Position
ABE IABE
Locked Position
Figure 11 Conceptual Model of a Bi-stable Compliant Latch with Electronic
Handshake
3.5
Motion Control
Binary Actuated Robotics. Binary actuation constitutes a new paradigm that may have
an impact for mechanical and robotic systems as profound as the impact that digital
devices have had for electronic systems.
In traditional approaches to robotics, relatively heavy continuous-motion actuators such
as electric motors and hydraulic cylinders are used. While such actuation is reasonable in
the context of factory automation, the weight requirements are prohibitive for missions in
space. On the other hand, technologies such as micro electrostatic combs, shape memory
alloy (SMA), and electro-polymer gels have very good force to weight ratios, but are
rather difficult to control using traditional PID and/or adaptive control schemes.
By
34
driving these actuators from one hard stop to another, a cost (and weight) effective
actuator results.
As an example of a mechanical device constructed from binary
actuators, consider the platform manipulator shown below.
o
o 0o
01
000
010
1
01
101
001
0
11110
0
100
01l
Figure 12 A 3 Bit Stewart Platform Manipulator (Chirikjian, G., 1997)
Here each leg has two states, and so the platform has
2A 3
= 8 configurations. In general,
if there are N actuators, 2AN states result. Hence, as N becomes large, a binary robot can
perform the vast majority of tasks that a continuous-motion robot can. For planetary
surface the following operations are possible: (1)
docking and locking of self-
transforming robotic modules; (2) discrete-step locomotion of a collection of selftransforming modules.
For such applications as discrete-state robotic devices have several advantages over
traditional continuous-motion robots. These include:
1.
Reduced need for feedback control and its associated computation and
hardware;
35
2. Reduced need for high bandwidth communications for remotely controlled
robots.
Previous work has focused on the design, workspace properties, and motion planning of
binary-actuated manipulator arms ranging from 3 to 36 bits.
Present work
[Chirikjian,1997] includes:
1.
Simulation of discrete-state locomotion processes;
2. Analysis of self-transforming maneuvers for discrete-state
mechanical
modules;
3. Investigation of control strategies for self-transforming binary robots;
The metrics for demonstrating how this technology is an improvement over conventional
robotics include: (1)
quantitative comparison of the discrete-state locomotion scheme
with other modes of locomotion used in practice (e.g., wheels, tracks, legs, and
continuous snake-like robots), and (2) comparison of the communications bandwidth
requirements for remote control of continuous-motion vs. discrete-state robots.
3.6
Physical System Configuration Planning
Physical system configuration planning applies to both reconfiguration and path planning
that are determined by the system intelligence of the STX. First, consider the problem of
reconfigurability.
The goal is for the self-transforming robotic planetary explorer to
reconfigure itself as to achieve the optimal configuration for accomplishing any given
task. A physical system can change its configuration in two ways. The first is through
36
geometric changes; that is, changes to the dimensionality of the existing physical system
such that the system appears to "grow" or "shrink" or shift its center of mass. The ABE
shown in Figure 9(a) is capable of undergoing geometric reconfiguration through
extension or contraction of itself.
The second way to make physical changes of
configuration is to change the topology of the system; that is, how the individual
elements of the system are connected such that the entire shape and functionality of the
system change. The arrangement of the nodes and ABEs in the STX are subject to
topological configuration changes. The question for the system intelligence is how to
come up with the optimal configuration. One way is to "program" the many different
configurations into the system, initially. While this would appear to be a relatively easy
task, it would be impossible and impractical to preprogram all of the possible
eventualities the robot might encounter. What is more realistic, is to somehow train the
robot to come up with its own solutions to the problems and tasks it faces. The feasibility
of using genetic algorithms to accomplish these goals will be studied. The inventory of
nodes and ABEs make up the set of usable assets for accomplishing any task. These
assets are represented by chromosomes in the genetic algorithm.
Each possible
configuration is described by a script of these chromosomes. The intelligence initially
picks several candidate scripts arbitrarily and runs them through a simulation of the task
to see how proficiently the task is accomplished.
The quantitative measure of this
proficiency is termed the performance measure. If the performance measure does not
meet some predetermined value for any of the candidate configurations, this generation is
sent back to the GA. At this point, the GA performs cross breeding from the parent
generation to establish a new generation of candidate designs to be evaluated (Figure 13).
37
In addition to crossbreeding, mutations are randomly introduced to speed the selection
process.
This cycle continues until the performance measure is met by one of these
candidates.
Before Crossover
Before Crossover
AClC
ClC
B
D
After Crossover
C2
After Crossover
A
C
Pa 4
Tail Crossover
Cris-Crossover
Figure 13 Genetic Crossover Methods [Farritor,S., 1998]
Once the optimal configuration is found, the STX must physically reconfigure. This is a
path planning issue, which can also be addressed with genetic algorithms.
In this
application, each possible action is considered a chromosome, and each representative
plan is a script or a series of these chromosomes. The same iterative process is followed
until the system intelligence finds the optimal way to physically change from its current
configuration to the chosen configuration. After this transformation is completed, the
system intelligence uses the same path planning genetic algorithm to choose a path to
accomplish the given reconfiguration.
conducted by Professor Shane Farritor.
Significant research in this field has been
Chapter 4
Elastic Elements with Embedded
Actuation and Sensing
4.1
Introduction
This research involves an attempt to understand the complexities associated with elastic
elements with distributed flexibility, actuated by embedded muscles used for robotic
applications. This represents a vast break from traditional design methodologies in this
field and, as such, must be approached from simplistic models. The analysis of several
types of elastic elements as mechanisms will be discussed in the next section. This will
be followed by a discussion of structures that may be made from networks of these
elements. A materials selection overview will then be given followed by fabrication
techniques. A presentation of Embedded Actuation and Sensing concepts will complete
the chapter
4.2
Elastic Mechanism Study
It was proposed in the previous chapters that elastic elements be used in place of rigid
structures and joints in planetary robots of the future. The term "elements" is being used
as it is the ultimate aim of this work to design entities that have characteristics of both
structures and mechanisms. That is, they can support and transmit loads as well as move
those loads when actuated. Individual elements would be linked together in a network
creating part of the structure through symmetry.
Before assembling these networks,
39
however, it is first necessary to understand the mechanics and capabilities of several
different geometries of individual elements.
The following analysis seeks to consider the motion capabilities inherent in elements with
distributed elasticity.
Instead of these elements deforming solely at discrete flexural
pivot points, as is the case with compliant mechanisms, their overall motion is achieved
by the entire element deforming.
The advantages of such elements may not, at first
glance, appear obvious. It is only taken in the context of the global goal of eliminating
discrete mechanisms and building more general networked structures capable of behaving
mechanically that this initial research step has applicability. Clearly, by concentrating the
motion at discrete points, larger overall local deformations are achieved in a single
element than by distributing the motions across an entire element.
However, these
motion advantages are accomplished at the loss of structural capabilities, as will be
demonstrated in the analysis and construction of the "elbow" element. In order to create
mechanisms from structures, it is necessary to exploit the inherent instabilities in the
structure. The internal loads applied by the embedded actuators are designed to do just
this, as will be discussed in the next chapter.
4.2.1 Finite Element Approach
The following analysis was conducted on the PTC finite element package
ProMechanicag. The elements were first designed in ProEngineer@, another PTC Tool,
and then the integrated ProMechanica@ package was used to model the load conditions,
material properties and constraints. The element meshes were automatically generated
with the following settings the element limits:
40
Edges: min: 50,
max: 1750
Face: min: 50,
max: 175'
Maximum Allowable Edge Turn: 950
Maximum Allowable Aspect Ratio: 30
Both GDP and SQP AGEM Alogorithms were used in the analysis. The convergent
method used was a multi-pass adaptive approach with a 10% convergence based on local
displacements and local strain energies. The details of each of the following analyses are
included in Appendix B.
The material properties used were taken from those for FlexCast@ and have the following
characteristics:
*
Young's Modulus:
E - 3 MPa = .44 ksi
" Thermal Expansion Coefficient:
" Poisson's Ratio:
a - 100 pm/m= 53 pin/in0 F
1 ~.4
In each case, one edge of the elastic element was grounded and a longitudinal load on the
order of 1-2N was applied which was a basic model of the load case imposed by the
embedded actuators.
4.2.2 Beam Elements
The first element considered is the basic beam. As the fundamental element of structural
mechanics, the mechanical characteristics of the beam are well understood. It therefore
represents an acceptable starting point for the study of elasticity and deformation induced
by internal forces. The largest deflection that can be achieved in a beam is achieved
when it is cantilevered under a significant force at the free end. This force, however,
41
necessarily must be perpendicular to the longitudinal axis. As the innovations related to
these mechanisms are based on embedded actuation, the load set is limited by the
capabilities of those actuators. Initially, due to limitations in the strain rate of current
state of the art actuators, all actuation schemes must run along the length of the element.
That is, Shape Memory Alloys (SMAs) have an effective strain rate of 6%. Therefore the
longer the wire, the greater the net deflection achieved. The longest path, then, is along
the entire length of the element; as opposed to shorter wires placed in the transverse
direction.
The first load scheme approached, then, is that of buckling under an axial load, shown in
figure 14.
This is more appropriate given the constraints inflicted by the embedded
actuation.
Actuator Path
Pcrit
.
na
--
--
.......
........................
- - -
Pcrit
- - -
L
Figure 14 Load Diagram for Beam Buckling
Pcrit
Critical Buckling Load
E
Young's Modulus
na
Neutral Axis
e
Eccentricity
L
Beam Length
8
Tip Deflection
I
Moment of Inertia, I = b4/12
b
Width and height of beam
42
Under the standard column buckling model (assuming pinned ends), if an axial load
greater than the critical load [Gere and Timoshenko, 1997]
Pcrit = it2 El/L 2
is applied the column becomes unstable and will buckle in the presence of an external
disturbance.
This buckling instability can be imposed by applying the axial load
eccentrically, thus deliberately causing the column to deflect in a predictable way [Gere
and Timoshenko, 1997.].
6
= -vx=L/2=
e(tan (kL/2) sin(kL/2) + cos(kL/2) -1),
k=4(P/EI)
This highly nonlinear relationship may be better observed through a graphic depiction of
the finite element analysis for this case in Figure 15.
Both the displacement and the
strain states are shown in the figure.
43
Figure 15 Eccentrically Loaded Beam
44
Two analytical approaches were used in the analysis of these elements based on modeling
assumptions made about the actuators. The first method was to apply an external axial
load that would approximate the internal forces supplied by the embedded actuator. For a
single 250 pum Shape Memory Alloy SMA wire, the load would be approximately ION in
axial contraction.
The purpose of this approach was to demonstrate the maximum
deflections achievable by these actuators. The above diagram demonstrates that for a
beam with a nominal length of 10 cm and square 1cm cross section, the maximum
deflection was 17mm.
The second approach taken was to predetermine the internal
strain state and demonstrate the overall deflection characteristics. The strain diagram on
the right side of figure 15 demonstrates a strain state that achieves comparable maximum
deflections to the previous approach with a strain field ranging from 0% to -7%. This is
the strain range for SMA actuators. It can be seen that for the buckling model, the strain
fields run the length of the element in parallel sheets. A discussion of strain fields will
follow in the next chapter as it pertains to the placement of the embedded actuators.
Another beam element examined was a beam of similar aspect ratio to the previous
example with the added aspect of having some material removed from the interior of the
beam. The voids were chosen heuristically to resemble a truss structure as shown in
figure 16. With such a patterns of voids in the material, the flexural rigidity is decreased.
The actuators may then, strained at the same rate, achieve larger maximum deflections in
the element. The trade-off, of course is a loss of structural rigidity, the effects of which
may be accounted for in the larger structural networks.
45
Figure 16 Beam with Truss-like Voids
Figure 17 demonstrates the analytical results of the voided beam under an eccentrically
applied axial load of 1ON,
46
Figure 17 Eccentrically Loaded Beam with Truss Voids
47
4.2.3 Elbow Elements
In order to demonstrate the difference between distributed and localized compliance, the
next example is presented.
The elbow element follows the compliant mechanism far
more closely than that of the elastic element. In this analysis, external load pairs were
placed at intervals along the length of the arm. Each pair was "actuated" individually to
demonstrate the capabilities of actuators placed at these intervals.
As expected, the
largest motions were achieved by the external load pair located at the furthest distance
from the hinge.
The corresponding strain state, however, was entirely in tension as
shown in figure 18. As Shape Memory Alloys exert their forces in compression, there
would be no possible internal placement of the actuators that would permit the designated
range of motion. The element could be, and was, constructed with the actuators external
to the structure. While this allowed the elbow to deflect the predicted amount (18 mm),
the SMA wires were located externally.
This does not follow in the proposed new
paradigm that suggests a move away from external, discrete actuators and localized
motion.
There is an addition problem with this design related, again, to the motion being localized
at the elbow hinge. This hinge is too narrow to support any load, even itself under
gravity, without deflecting. These elastic structures are required to be stiff enough to act
as a spring to deflect the SMA wires when not deflected. Clearly, this element can not
meet this specific requirement.
48
Figure 18 Elbow under External Load
49
4.2.4 Rhomboid Elements
It is possible to salvage some of the advantages from the elbow element.
Its major
shortcoming was related to its lack of stiffness. If two of these elements are combined, in
closed form, the symmetry of the union adds structural rigidity, while still allowing for a
small range of motion. This resembles, in some ways, a classic four bar linkage. The
difference is related to the distribution of compliance in the structure.
While the
actuators undergo the greatest strains at the corner points, due to increase geometric
advantage, the deformations of the structure are distributed evenly through the lengths of
the sides.
50
Figure 19 Rhombus Closed Form
51
4.2.5 Hexagonal Elements
The advantages gained from the rhombus shape can be extended further. One may unite
three, elbow elements in closed form to create a hexagonal shape.
To further simplify,
the hexagon is the first introduction to a structural element created by joining six of the
fundamental beam elements. Each side has its own set of actuators, providing a local,
eccentric, axial compressive load under command.
When the various actuators are
contracted, alone or in combination, the hexagon moves in different, prescribed motions.
The actuators contracted all at once, however, will cancel out the net motion, creating,
effectively, a hoop stress state. Figure 20 demonstrates the displacement, stress and strain
states that result from actuating two, opposite sides.
52
Figure 20 Hexagonal Closed Form Element
53
4.3
Lattice Structure - Hyper Degrees of Freedom
The purpose of the previous discussion of these small elements with relatively small
deformations, has been to set the stage for systems or networks of these elements which
can be combined to amplify the small motions. The result of amplifying these motions is
that these structures may be used to accomplish actual tasks faced by robots. Consider
figure 21. This network or lattice of hexagonal shapes represents a molecular approach
to robotic motion. Each of the six sides of each actuator is commanded separately. The
result is a multi-degree of freedom structure.
between the individual beam elements.
There is, of course, strong coupling
While they constrain each other, they are
providing the necessary structure for load bearing tasks. When actuated, the controller
commands the entire structure to move in some designated fashion. The structure, when
actuated, behaves as a mechanism and moves.
Figure 21 Element Network Structure and Mechanism Example
4.4
Fabrication Techniques
In order to verify the analytical results of the previous section, it was necessary to
fabricate these elements for the purposes of experimental validation.
Fabrication
54
planning was a two step process involving first extensive material selection research and
second the design and production of positive and negative molds and castings. Both of
these areas will be discussed including a discussion of idealized fabrication techniques.
4.4.1
Materials Selection
There were several constraints driving the selection of a material that would be
appropriate for this application. First, it had to be extremely flexible, having a tensile
elongation between 200% and 400%. The class of materials that are described by these
large elongation percentages are known as elastomers and include materials such as
rubber, isoprene, isobutylene, butadiene styrene, silicones, etc.
Elastomers may be
deflected by these large percentages and still return to their undeformed state without any
permanent yielding. They do, eventually, start to creep under a prolonged load. This
problem is not immediately applicable as these elements will only be deformed for short
periods of time. This is the case as the focus of initial research is on the motion and
mechanism aspects of these elements and not on the structural, load bearing aspects.
The other constraint placed on the material selection process was that the elastomer
needed to be castable.
This constraint arises from the practical necessity of building
experimental, bench top prototypes. In order to be able to embed the actuators, it was
necessary to find a castable elastomer.
A suitable material was found made by
Goldenwest Mfg. Inc. The trade name of the material is FlexCast@ and it is a urethane
elastomer.
There are two grades of FlexCast@, SA90 and SA50.
They are both
.55
comprised of a two part mixture that is blended just prior to casting. Their material
properties are included below in Table 1.
TEST DATA
SA90
SA50
Hardness: Shore A
90
50
Viscosity (cps)
A:60, B:130
A:350, B:150
Mix Ratio (by Volume)
50/50
50/50
Mix Time (minutes)
2
2
Gel Time (minutes)
4-7
4-7
Demold Time (minutes)
20-30
20-30
Exotherm can Reach... (*F)
250
200
Specific Gravity
A:1.12, B:1.03
A:1.10, B:1.02
Tensile Strength (psi)
2000
1000
Tensile Elongation (%)
170
350
Die-c Tear (pli)
160
60
Split Tear (pli)
40
20
Color
Opaque light amber
Translucent Amber
Table 2 FlexCast Material Properties [Goldenwest Mfg Co., 1999]
Based on its greater elongation percentage, SA50 was chosen for prototyping purposes.
Further comparison of FlexCast® SA50 with other similar elastomers, BayFlex W20 and
APA Alcryn 4060 data from MatWeb, provided the following material properties
estimates
* Young's Modulus:
E ~ 3 MPa =.44 ksi
" Thermal Expansion Coefficient:
a - 100 gm/m= 53
sin/in*F
56
e
Poisson's Ratio:
u ~.4
These estimates were used in the earlier analysis to predict, accurately, the actual reaction
and performance of elements made of this material. The figure below is a picture of a
FlexCast@ beam with embedded Shape Memory Alloys.
Figure 22 FlexCast Beam Elements
4.4.2
Mold Fabrication
Due to the requirement of these elements being able to be cast from an elastomer, a
significant portion of the fabrication technique is related to the production of suitable
molds. The unique properties of FlexCast® require secondary processes in its conversion
into a viable element. It has high reactivity with many substances, such as waxes and
many mold releases. Additionally, it fills and bonds to any imperfections in metals. It is,
therefore, quite difficult to use molds constructed from metals to achieve satisfactory
results. FlexCast@ can be cast in a RTV Silicone mold, however. RTV Silicone is a
flexible, castable material used in commercial mold making. Its properties are a good
deal weaker than those of FlexCast®, disallowing the use of it as the ultimate elastomer
57
material used in the elements. For example, RTV Silicone has the tendency to tear and
break apart after several uses.
Given these capabilities and fabrication requirements for FlexCast® and RTV Silicone, a
series of Aluminum molds were machined. These molds were "positives" from which the
"negative" RTV silicone molds were cast. Figure 23 shows three examples of these
Figure 23 Machined Aluminum and Cast RTV Silicone Molds
positive and negative molds. The curing time for the RTV Silicone is approximately 24
hours. After these molds had cured, the pre-strained shape memory alloys were laid in
place and the mixed FlexCast® was poured around the SMAs, cementing them in place.
More details about the pre-straining of the SMAs as well as their specific placement in
the molds will be discussed in the next chapter.
58
4.4.3
Idealized Fabrication Techniques
This lengthy and involved fabrication process would not be practical for the large-scale
production of elements. Alternative manufacturing processes, then, are being considered.
A cue may be taken from the electronics industry in terms of their automated
"embedding" of IC chips onto boards. Analogous processes may be explored for the
production of elastic elements with embedded actuators and sensors. Advances in the
past 10 years in the field of rapid prototyping and 3D printing have been significant. The
machines are affordable and are capable of producing parts quickly, regardless of
complexity. Particularly, Stereo Lithography (SLA) and Selective Laser Sintering (SLS)
are two technologies at the forefront of these developments. The capabilities for building
up parts a single layer at a time exist and lend themselves to the production of elastic
elements with embedded actuators and sensors.
The bottleneck to this manufacturing process for this particular application is material
based.
The parts made produced through traditional rapid prototyping methods are
usually extremely brittle.
This usually limits the applicability of this process to the
production of visual prototypes. Also, machines in the past have been limited to using a
single type of material on an individual part.
The initial stages of breaking these
manufacturing limitations are currently underway. For example, ZCorp, a company at
the forefront of 3D printing technology, has recently announced a new material for use in
their machines as well as a new color 3D printer. Their primary printer, the Z402, can be
used with ZPI 1 material. ZP 1I is a starch cellulose combination that is spread in layers,
.59
and is hardened in places where there is part volume. Parts made with ZP II are fragile
when removed from the printer and require an additional infiltrant to determine the
material properties of the final product. One such infiltrant is an elastomer that lends its
flexible, rubber-like properties to the part.
Another company, 3D Systems Inc., has also announced breakthroughs in SLA
technology. They have recently announced the development of a material that allows the
designer to "tune" the physical properties of the final product. On their SLA machines, it
is possible to create solid objects of varying material properties from a single material.
One part of the component may be flexible, while another is rigid. This exciting new
technology may bridge the gap between the today's concepts of elastic elements and
tomorrow's Continuously Transforming Explorer.
4.5 Embedded Actuators
The previous sections were devoted to the discussion of how elasticity may be used as a
basis for a new space robotic mechanical design paradigm.
The elastic elements
introduced provided the mechanistic approach to this stepping stone technology.
For
these mechanisms to function robotically, they require "muscles" and "nerves" as well.
These actuators and sensors are the topic under discussion in this chapter.
The CTX robot would be able to morph into different shapes by changing not only its
local shape, but also by changing its entire topology. In order to have the freedom to
transform into these different shapes, it will require many degrees of freedom. These
60
degrees of freedom are a function of the actuators, or muscles, that move the structure.
As the number of actuators is increased, so too is the degree of freedom of the entire
system. Consider the distributed elasticity model introduced previously. If the nominal
structure may be deformed continuously at any localized area due to its structural and
mechanistic design, a distributed network of actuators may be placed throughout the
structure. Each actuator would be attached to a point on the structure and therefore be
responsible for the motion of only that one point. The cumulative effect of a network of
thousands or millions of these actuated local points moving, then, would be to generate
large, global motions and therefore morphing capabilities.
This network of actuators would be mirrored by an array of distributed sensors. Again,
each sensor would be responsible for reporting the state or position of a given point. This
would be something analogous to the network of nerve endings distributed throughout the
human system, just beneath the skin. The effect is the ability for the brain to determine
exactly where and when it feels a sensation of contact.
Traditionally, and in the majority of cases to date, the motion of robots is controlled with
large rotary motors.
Their characteristics are well understood, they are capable of
moving large masses, and their positioning, for the most part, is predictable. For all of
these reasons they are excellent for use in industrial robotics. They do have drawbacks,
however, which preclude them from being considered the most effective actuators in a
space robotics context.
Primary among these detriments is their weight and the
complexity of their control.
The space robotics community has recognized the
61
limitations of these actuators and is pursuing alternative actuator technologies including
piezoelectric, magnetostrictive, electrorheological, pneumatic, conducting polymer and
shape memory actuators.
As part of the CTX development, conducting polymers (CPs)
are being pursued. As CPs are still in their infancy, however, Shape Memory Alloys
(SMAs) will serve as place holders in the parallel development of elastic elements with
embedded actuation and sensing.
Details on the mechanical, electrical and thermal
characteristics of SMAs is included in Appedix C.
Embedding actuators and sensors into structures is a relatively new field, certainly to
roboticists. Significant work has been completed embedding actuators for the purposes
of vibration and noise control in aircraft and other structures, [Baz, Chen, Jolly.]
Vibration and noise control, however, are a somewhat different application. This is due to
the fact that only small strain rates are required to cancel out vibrations. That is, strains
on the order of 0.10%. The application of embedding actuators for robotics applications
is a different domain as the required strains are on the order of 10%. These two orders of
magnitude represent a large gap in research domains.
4.5.1 Actuator Placement
One key aspect of the concept of embedding actuators and sensors is the question of how
to place them. The placement should allow a uniformly strained set of actuators to be
placed at strategic locations throughout the base element. Desired deflections would then
be the result of actuating these actuators alone or in pairs.
Each pair of opposing
actuators would represent one complete degree of freedom for the element. A pair of
62
actuators would be necessary as Shape Memory Alloys can only perform work in
compression. These pairs are not quite antagonistic, as it is not required to actuate one to
stretch out the other.
restoring force.
The inherent stiffness of the elastic element will provide this
These actuators, in the beam model, would act to provide pseudo-
external forces along eccentric longitudinal axes. Under a load of this nature applied
externally, the deflection of the entire beam would increase as small deflections were
registered. This is due to the fact that beam buckling under an external axial load is
inherently unstable, and this fact may be exploited. In the case of the embedded SMAs,
the line of action of the force never varies from the eccentricity value, e; the distance
from the neutral axis.
This reality motivated the study of placing the actuators throughout the elements such
that they act as strain drivers instead of direct pseudo-external loads.
The analysis
conducted in the previous chapter demonstrated what the necessary strain distribution
would have to be to deform the element analogously to an external load. It was found
that the strain deformation mode can only replicate the deflection results of the exterior
load deformation mode when a field of strains is applied. For a single beam element, for
example, to duplicate beam buckling would require that the SMA actuators were layered
parallel to the neutral axis.
The array of these actuators would have to represent a
spectrum of different pre-actuation strain rates. Instead of having a single pair of SMAs
to control one degree of freedom, several pairs would be required. These pairs would
range in strain rate from 1% to 7% compression. This is a complication of the initial
intent of these elements.
Conversely, the SMAs may all be strained by the same amount
63
if an analogue controller were present to send different currents to each actuator
depending on the desired motion.
This complex controller, however, would violate the
premise of using binary control.
4.6
Embedded Sensors
The previous section mentioned the need for a distributed array of embedded sensors in
these hyper degree of freedom structures. The sensors are necessary to provide overall
system motion feedback to the controller. In the CTX concept, these sensors would be
constructed from the same family of materials as the rest of the structure, namely,
plastics. For simplicity, it is also proposed that these sensors be passive and not require
their own controller/command architecture. They would be integrated into the system as
a whole. The following section describes a passive sensor design that could be embedded
in to the elastic structure.
4.6.1 Passive Sensors Design
The aim of designing passive sensors embedded into elastic structures is to gather some
position feedback information without having to separately power and collect data about
the state of the system. This passive sensor design is based on photo-optics and takes
advantage of the translucent and birefringence properties of the FlexCast elastic material.
When two aligned sheets of polarizing material are placed on either side of the elastic
element and this setup is held up to the light, it is possible to see a pattern of strain waves
when the elastic element is deformed.
This property of the material is called its
64
birefringence. By adding an infrared light emitting diode and receiver pair on opposite
sides of the polarizing sheets as in figure 24, a simple sensor has been produced.
Flexible Element
Motion is out of plcne)
Emitter
Photo
Detector
Polarizers
Figure 24 Experimental Photo-Detector Setup
There are two modes in which this sensor can detect motion. The first is to have an array
of LED/detector pairs, of sufficiently high resolution, distributed along the length of the
elastic element. As each successive strain wave passes between the sensor pair, the
voltage output on the detector changes, tracking the light and dark shadows. The time
and distance between the shadows, corresponding to a pattern of low and high voltage
outputs, gives the controller the necessary position feedback information.
A simpler technique that employs the same setup lends itself to binary motion detection.
That is, one of the polarizing sheets is fixed to the element while the other is fixed to
ground. As the element deflects out of plane, the two sheets that started out aligned,
change their relative angles to each other. With polarizers, all light is allowed through
65
when the two sheets are aligned and all light is blocked out when they are arranged
orthogonal to each other.
Therefore, in an element with binary positions, the light
intensities detected by the photo-detector at the two positions are different.
The
differential would depend on the calibration of the polarizers and any amplification of the
detectors output signal to the controller.
Figure 25 is a diagram of how an array of
optical sensor pairs would be integrated into the elastic element, a beam in this case.
A
Polarizer
Sheets
LEDA rray
Photo Detector
Array
Aout
Ain
Controller
AGND
SMA Wiri
e
Elastic Element
Figure 25 Passive Embedded Optical Sensor Array
66
Chapter 5
Conclusions and Future Work
5.1
Conclusions
This thesis provided an overview of the results of a feasibility study conducted into SelfTransforming Robotic Planetary Explorers.
This included an overview of the system
architecture concepts as well as the enabling technologies that will need to be developed
in order for the system concept to be realized. It also introduced the area of elastic
elements with embedded actuation and sensing as one of these enabling technologies.
The feasibility study focused on developing a new paradigm for planetary space robotics.
The aim of this work is to move away from robots of fixed configurations comprised of
discrete mechanical and electrical components.
The constraints placed on planetary
exploration by conventional rovers are related to their inherent limitations in the context
of space missions. Due to the finite weight envelope of missions to Mars, traditional
robots that are constructed with many, heavy components will only be equipped with
minimal Capabilities; a dual rocker-bogie suspension and a single manipulator, for
example.
The focus of missions to date, then, has been on the tele-operations and
navigation aspects of exploring a distant planet. In order to accomplish more ambitious
mission scenarios, the robots sent to explore will have to have exploratory capabilities.
These capabilities might include things such as long range travel, surface and subsurface
sample return, mining for minerals and refining atmospheric gases, building in situ
infrastructure to support these tasks as well as creating habitats for future human
explorers. It is clear that these tasks would not be within the capabilities of a fixed
67
configuration rover. Accomplishing these goals while staying within the weight envelope
of the launch vehicle calls for a new approach to explorer design.
The envisioned paradigm emphasizes planetary explorers that are lightweight, robust, and
comprised of generalized components that allow for inherent reconfiguration flexibility.
Due to the weight envelope, it is not feasible to envision a system that is capable of
performing every task in its launch configuration. The robot should be able to use a fixed
set of physical components to reconfigure itself any time it is required to accomplish a
different task. Conventional gears, motors, bearings, wires, IC chips, etc. do not lend
themselves to such reconfiguration. They depend on being installed into rigidly fixed
systems so that they function properly. They also require a large set of fasteners of
varying type and size.
The STX, Self-Transforming Explorer, concept is based on assembling a robot that
achieves many degrees of freedom from a few lightweight component types. In addition
to general computing modules, a general appendage is the cornerstone of this concept.
This appendage is a self-contained entity capable of being used as a manipulator, a leg, a
connector between modules and even as a wheel. All actuation and sensing will be
embedded into the structure and it will achieve reconfiguration by disconnecting and
reconnecting its ends via a universal mechanical and electrical connector. The planning
of which topology the STX should take and the planning of the path of how to construct
that topology will be decided via genetic algorithms.
68
The STX concept is the near term embodiment of this NIAC funded research.
The
Continuously Transforming Explorer, CTX, is the distant vision. Where the planetary
robots of today are composed entirely of heavy, fixed configuration components, and the
STX of ten years from now is a hybrid system consisting of some generalized, multi
degree of freedom components and some conventional components, the CTX would be
It is the aim of CTX research to develop smart structures and
entirely generalized.
materials that will allow the CTX to be made entirely from one material or family of
materials.
It will have morphing capabilities allowing it to assume a wide range of
shapes and topologies and therefore complete the largest set of tasks among these robots
under discussion. The goal of building the CTX in forty years is ambitious and therefore
requires intermediate development steps.
The CTX is the motivation for work conducted in the area of elastic elements with
embedded actuation. This research represents an introductory look at applying elasticity
to robotic structures in order to capitalize on the low weight and motion characteristics of
elastic materials.
By considering elasticity and discretely embedded actuators and
sensors, a direct development path would lead to the CTX in the future. This thesis has
considered some of the basic shapes that may be considered for use as structuralmechanical elements.
These elements would hen be assembled into hyper degree of
freedom structures that would amplify the small deformations of the elements into the
large displacements required of planetary robotics applications. A major focus of this
work has been on characterizing the fabrication process for making these elements and
69
embedding the actuation and sensor architectures.
Large-scale fabrication techniques
have also been considered including a discussion of rapid-prototyping options.
The other aspect of this work was the design and implementation of embedded actuators
and sensors. Shape Memory Alloy wire is serving as a place-holder actuator technology
while tandem work in conducting polymer actuators is taking place.
SMAs have a
maximum strain rate of 8%, although 6% is a better working strain rate. Included in
Chapter Four was a discussion of how these wires may be placed to use these small strain
rates to achieve larger motions. Also discussed in Chapter Four was the design and
development of passive, all-plastic embedded sensors. These sensors are based on an
emitter-detector pair that uses polarizing sheets to sense motions in the elastic elements.
By embedding the actuators and sensors directly into the structure of the robot, a step is
taken away from discrete, heavy mechanical and electrical components, and towards a
robotic design paradigm based on continuous, flexible motion that allows the structure to
reconfigure itself. The work recorded here represents an introduction to these topics and
lays the groundwork for future development of planetary robots with elastic structure
embedded with actuation and sensing.
5.2
Future Work
Future work in this area will focus on developing the area of Elastic Elements with
Embedded Actuation and Sensing. First, since these robotic systems will be large, having
hyper degrees of freedom, it will be necessary to develop a methodology for their design.
70
This preliminary work used heuristics and basic geometric shapes in the design process.
An automated methodology would include three aspects. The first would be an Elastic
Element Shape Optimization Algorithm.
Such an algorithm would be capable of
exploring more complex element shapes including shapes with unusual voids and threedimensional shapes. The second aspect of future work would be the development of an
Actuator Placement Algorithm. That is, how to place binary actuators of limited strain
rate optimally so that their motions are amplified by the elastic structure.
The third
aspect of the methodology would be the development of an Elastic Element Hyper DOF
Structural Optimization Algorithm. Once the forces and displacements of the building
block elements are understood, the next step would be to design hyper DOF structures
that utilize these elements to achieve large deflections.
These three areas are
interdependent and will therefore be part of an iterative solver.
Once the design methodology is completed, the objective would be to use it to design a
robotic structure for prototyping. This structure should be able to demonstrate large-scale
motions and accomplish a simple task under operator control. Once such a prototype
could be built the focus of research would shift to experimental studies including the
design and prototyping of embedded sensor chips and controllers.
71
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Polypod Website, http://www.parc.xerox.com/spl/members/yim/polypod
74
Parkinson, M., et al., "A Parametric Approach to the Optimization-based Design of
Compliant Mechanisms", Proc. of the 1997 ASME Design EngineeringTechnical
Conference, Sacramento, CA.
Roth, B, et al., "'On the Design of Computer Controlled Manipulators," First CISMIFTMM Symp. on Theory andPracticeof Robots and Manipulators,1973.
Roytburd, A. L., "Theory of Adaptive Composites", SPIE Vol. 3039, 1997.
Rus, D., "Self-Reconfiguring Robots", IEEE Inteligent Systems, July/August 1998.
Saggere, L., and Kota, S., "Synthesis of Distributed Compliant Mechanisms for Adaptive
Structures Application: An Elasto-kinematic Approach", Proc. of 1997 ASME
Design EngineeringTechnical Conference, Sacramento, CA.
Salamon, B., and Midha, A., "An Introduction to Mechanical Advantage in Compliant
Mechanisms," Advances in DesignAutomation, DE- Vol. 44-2, 1 8e ASM E Design
Automation Conference, 1992.
Schenker, P., et al., "Lightweight Rovers for Mars Science Exploration and Sample
Return", SPIE Proc. Intelligent Robots and Computer Vision XVI, 1997.
Sigmund, 0., "On the Design of Compliant Mechanisms Using Topology Optimization",
Mechanics ofStructures andMachines, November 1997, Vol. 24 No. 4.
Skelton, R. E., and Sultan, C., "Controllable Tensigrity, A New Class of Smart
Structures", SPIE Vol 3039, 1997.
SMA Inc.: www.sma-inc.com
Srinivasan, A.V., et al., "Biomimetics: Advanced Man-Made Materials through Guidance
from Nature", Applied Mechanics Review, Vol. 44, No. 11, November 1991.
Srinivasan, A.V., "Smart Biological Systems as Models for Engineering Structures",
JournalofMaterialsScience andEngineering,C99, 1995.
Suzumori, K., "Elastic Materials Producing Compliant Robots", Robotics and
Autonomous Systems 18, 1996.
Toth-Fejel, T., "LEGOTMs to the Stars: Active MesoStructures, Kinetic Cellular
Automata, and Parallel nanomachines for Space Applications", The Assembler, Vol.
4, No. 3, 1996.
Troisfontaine, N., et al., "Optimal Design of Micro-Actuators based on SMA Wires",
Smart Materialsand Structures, 1999.
Vogel, S., "Better Bent Than Broken", Discovery, April 1994.
Waram, T., Actuator Design Using Shape Memory Alloys. 2nd Edition, T. C. Waram
Publisher, Hamilton Onterio, Canada, 1993.
Warkentin, D.J., et al., "The Feasibility of Embedded Electronics for Intelligent
Structures", Journalof Intelligent MaterialSystems and Structures, Vol. 3, July
1992.
Yim, M., "Locomotion with a Unit Modular Reconfigurable Robot," PhD Thesis,
Stanford Univ, Palo Alto, 1995.
Z Corp: www.zcorp.com
75
Appendix A
The NIAC
In order to understand the unique purpose and goal of research conducted under the
auspices of the NIAC (NASA Institute for Advanced Concepts), it is necessary to grasp
the mission of the NIAC. The NIAC was created in the spring of 1998 as a freestanding
agency under the Universities Space Research Association (USRA).
It is intended to
support NASA initiatives yet remain functionally independent. It exists to "provide an
independent, open forum for the external analysis and definition of space and aeronautics
advanced concepts to complement the advanced concepts activities conducted within the
NASA Enterprises."'
The NIAC's charter is based on the idea of sponsoring research that will dramatically
impact the aeronautics and space industries in a ten to forty year timeframe.
Such
sponsored research must give the promise of "leapfrogging" current state-of-the-art
technologies through the development of non-conventional technologies.
"NIAC
continues to seek revolutionary concepts and particularly wishes to inspire innovative and
visionary concepts from the scientific disciplines that are not normally focused on the
challenges of our aerospace endeavors." 2 These "revolutionary" concepts are intended to
be a means of starting down alternative paths to aerospace objectives that are at some
distant time into the future.
1 The
2The
NIAC 1998 Annual Report, p. 2.
NIAC website. www.niac.usra.edu
76
"We are looking for a new direction in science, we must look for scientific
revolutions.
When no scientific revolution is underway, science continues to
move ahead along old directions. It is impossible to predict scientific revolutions,
but it may sometimes be possible to imagine a revolution before it happens."3
These revolutionary concepts must, of course, comply with the fundamental laws of
nature, as known, but this is the only constraint. The NIAC is in place to fund ideas and
dreams into realities.
3 Dyson, F. Imagined Worlds, as quoted in the NIAC's Grand Challenges
77
Appendix B
ProMechanica Finite Element Analysis
B.1
Eccentrically Loaded Beam
LOAD: -1.5N Eccentric Longitudinal Compression
Pro/MECHANICA STRUCTURE Version 20.0(72)
Summary for Design Study "bucklingstudy"
Run Settings
Memory allocation for block solver: 64.0
Generate elements automatically.
Excluded elements may be required near one or more
loads due to concentrated stresses.
No errors were found in the model.
Pro/MECHANICA Structure Model Summary
Principal System of Units:
Length:
m
kg
Mass:
sec
Time:
Temperature: K
Model Type: Three Dimensional
Points:
Edges:
Faces:
10
26
26
Springs:
Masses:
Beams:
Shells:
Solids:
0
0
0
0
9
Elements:
9
Standard Design Study
Description:
buckling under eccentric load
Static Analysis "buckling":
Convergence Method: Multiple-Pass Adaptive
78
Plotting Grid:
7
Convergence Loop Log:
(08:44:58)
>>Pass 1 <<
Calculating Element Equations
(08:44:58)
Total Number of Equations:
18
Maximum Edge Order:
1
Solving Equations
(08 :44:58)
Calculating Disp and Stress Results (08:44:58)
Checking Convergence
(08:44:59)
Elements Not Converged:
9
Edges Not Converged:
26
Local Disp/Energy Index: 100.0 : :
Global RMS Stress Index: 100.0
(08::44:59)
Resource Check
Elapsed Time (sec):
7.17
(sec):
4.17
CPU Time
Memory Usage
(kb):
82005
Wrk Dir Dsk Usage (kb):
0
>> Pass 2 <<
(08:44:59)
Calculating Element Equations
81
Total Number of Equations:
2
Maximum Edge Order:
(08:44:59)
Solving Equations
Calculating Disp and Stress Results (08:44:59)
(08:44:59)
Checking Convergence
9
Elements Not Converged:
21
Edges Not Converged:
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 87.3%
(08:44:59)
Resource Check
7.64
Elapsed Time (sec):
4.53
(sec):
CPU Time
82018
(kb):
Memory Usage
0
Wrk Dir Dsk Usage (kb):
>> Pass 3 <<
(08:44:59)
Calculating Element Equations
Total Number of Equations: 252
4
Maximum Edge Order:
(08:45:00)
Solving Equations
Calculating Disp and Stress Results (08:45:00)
(08:45:00)
Checking Convergence
7
Elements Not Converged:
0
Edges Not Converged:
Local Disp/Energy Index: 29.5%
Global RMS Stress Index: 16.0%
(08:45:00)
Resource Check
8.22
Elapsed Time (sec):
5.06
(sec):
CPU Time
82044
(kb):
Memory Usage
0
Wrk Dir Dsk Usage (kb):
>> Pass 4 <<
79
Calculating Element Equations
(08:45:00)
Total Number of Equations: 507
Maximum Edge Order:
5
Solving Equations
(08:45:00)
Calculating Disp and Stress Results (08:45:00)
Checking Convergence
(08:45:01)
Elements Not Converged:
0
Edges Not Converged:
0
Local Disp/Energy Index:
9.5%
Global RMS Stress Index: 27.0%
Resource Check
(08:45:01)
9.13
Elapsed Time (sec):
5.89
(sec):
CPU Time
82081
(kb):
Memory Usage
0
Wrk Dir Dsk Usage (kb):
RMS Stress Error Estimates:
Load Set
Eccentload
Stress Error % of Max Prin Str
3.42e+04
5.7% of 6.04e+05
The analysis converged to within 10.0% on
edge displacement and element strain energy.
Total Mass of Model: 2.048256e-03
Total Cost of Model: 0.000000e+00
Mass Moments of Inertia about WCS Origin:
lxx: 1.78652e-06
Ixy: 1.84343e-08 Iyy: 1.78652e-06
lxz: -1.56077e-07 Iyz: 1.56077e-07 Izz: 4.91581e-08
Principal MMOI and Principal Axes Relative to WCS Origin:
Max Prin
1.80495e-06
Mid Prin
1.79597e-06
WCS X: 7.07107e-01
WCS Y: 7.07107e-01
WCS Z: 0.00000e+00
Min Prin
2.12673e-08
7.01528e-01
-7.01528e-01
-1.25363e-01
8.86447e-02
-8.86447e-02
9.92111e-0I
Center of Mass Location Relative to WCS Origin:
( 3.000OOe-03, -3.000OOe-03, 2.54000e-02)
Mass Moments of Inertia about the Center of Mass:
Ixx: 4.46629e-07
Ixy: 0.00000e+00 Iyy: 4.46629e-07
Ixz: -2.64698e-23 Iyz: -2.64698e-23 Izz: 1.22895e-08
Principal MMOI and Principal Axes Relative to COM:
Max Prin
Mid Prin
Min Prin
90
4.46629e-07
4.46629e-07
WCS X: 0.00000e+00
WCS Y: 1.00000e+00
WCS Z: 0.00000e+00
1.22895e-08
1.00000e+00
0.00000e+00
0.00000e+00
0.00000e+00
0.00000e+00
1.00000e+00
Constraint Set: wall
Load Set: Eccentload
Resultant Load on Model:
in global X direction: 3.458356e-14
in global Y direction: 5.990182e-13
in global Z direction: -1.500000e+00
Measures:
Name
Value
Convergence
max_beambending: 0.------e+00
0.0%
maxbeam_tensile: 0.000000e+00
0.00/0
max beamtorsion: 0.000000e+00
0.0%
max beantotal: 0.000000e+00
0.0%
4.4%
max dispmag:
1.752542e-02
max dispx:
-1.281556e-04
6.1%
max disp_y:
1.727595e-02 4.4%
maxdispz:
-2.946123e-03
3 .7%
maxprn mag: -6.039205e+05 31.4%
max_rot_mag:
0.000000e+00
0.0%
maxrotx:
0.000000e+00
0. 0%
0.0%
0.000000e+00
max-rot-y:
max rot z:
0.000000e+00
0.0%
maxstress_prin: 1.950021e+05 39.9%
maxstressvm: 6.853940e+05 31.4%
maxstress xx: -1.556735e+05 11.4%
maxstressxy: -3.834213e+04
50.9%
maxstress xz: 1.030638e+05 37.2%
maxstressyy: -1.547901e+05 3 0.5%
maxstressyz: -2.644876e+05
3.1%
3
maxstress zz: -4.975723e+05 2.1%
minstress_prin: -6.039205e+05 3 1.4%
strainenergy: 2.186693e-03
3. 6%
Displacement:
1.727595e-02 4 .4%
Strain:
0.C00000e+00
0.0%
Stress:
0.0 00000e+00 0.0%
Analysis "buckling" Completed (08:45:01)
Memory and Disk Usage:
Machine Type: Windows NT/x86
RAM Allocation for Solver (megabytes): 64.0
Total Elapsed Time (seconds): 9.44
81
Total CPU Time (seconds): 6.17
Maximum Memory Usage (kilobytes): 82091
Working Directory Disk Usage (kilobytes): 0
Results Directory Size (kilobytes):515 .\buckling_study
B.2 Eccentrically Loaded Beam with Triangular Voids
LOAD: -.75N Eccentric Longitudinal
Pro/MECHANICA STRUCTURE Version 20.0(72)
Summary for Design Study "bucklingstudy"
Run Settings
Memory allocation for block solver: 64.0
Generate elements automatically.
Excluded elements may be required near one or more
loads due to concentrated stresses.
No errors were found in the model.
Pro/MECHANICA Structure Model Summary
Principal System of Units:
m
Length:
kg
Mass:
sec
Time:
Temperature: K
Model Type: Three Dimensional
Points:
Edges:
Faces:
10
26
26
Springs:
Masses:
Beams:
Shells:
Solids:
0
0
0
0
9
Elements:
9
Standard Design Study
Description:
buckling under eccentric load
Static Analysis "buckling":
Convergence Method: Multiple-Pass Adaptive
82
Plotting Grid:
7
Convergence Loop Log:
(08:44:58)
>>Pass 1 <<
Calculating Element Equations
(08:44:58)
18
Total Number of Equations:
Maximum Edge Order:
I
Solving Equations
(08:44:58)
Calculating Disp and Stress Results (08:44:58)
(08:44:59)
Checking Convergence
Elements Not Converged:
9
Edges Not Converged:
26
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 100.0%
(08:44:59)
Resource Check
7.17
Elapsed Time (sec):
CPU Time
(sec):
4.17
82005
(kb):
Memory Usage
Wrk Dir Dsk Usage (kb):
0
>> Pass 2 <<
(08:44:59)
Calculating Element Equations
81
Total Number of Equations:
2
Maximum Edge Order:
(08:44:59)
Solving Equations
Calculating Disp and Stress Results (08:44:59)
(08:44:59)
Checking Convergence
9
Elements Not Converged:
21
Edges Not Converged:
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 87.3%
(08:44:59)
Resource Check
7.64
Elapsed Time (sec):
4.53
(sec):
CPU Time
82018
(kb):
Memory Usage
0
Wrk Dir Dsk Usage (kb):
>>Pass 3<<
(08:44:59)
Calculating Element Equations
Total Number of Equations: 252
4
Maximum Edge Order:
Solving Equations
(08:45:00)
Calculating Disp and Stress Results (08:45:00)
(08:45:00)
Checking Convergence
7
Elements Not Converged:
Edges Not Converged:
0
Local Disp/Energy Index: 29.5%
Global RMS Stress Index:
16.0%
(08:45:00)
Resource Check
8.22
Elapsed Time (sec):
5.06
(sec):
CPU Time
(kb):
82044
Memory Usage
0
Wrk Dir Dsk Usage (kb):
>> Pass 4 <<
8-3
Calculating Element Equations
(08:45:00)
Total Number of Equations:
507
Maximum Edge Order:
5
Solving Equations
(08:45:00)
Calculating Disp and Stress Results (08:45:00)
Checking Convergence
(08:45:01)
Elements Not Converged:
0
Edges Not Converged:
0
Local Disp/Energy Index:
9.5%
Global RMS Stress Index: 27.0%
Resource Check
(08:45:01)
Elapsed Time (sec):
9.13
CPU Time
(sec):
5.89
Memory Usage
(kb):
82081
Wrk Dir Dsk Usage (kb):
0
RMS Stress Error Estimates:
Load Set
Eccent-load
Stress Error % of Max Prin Str
3.42e+04
5.7% of 6.04e+05
The analysis converged to within 10.0% on
edge displacement and element strain energy.
Total Mass of Model: 2.048256e-03
Total Cost of Model: 0.000000e+00
Mass Moments of Inertia about WCS Origin:
lxx: 1.78652e-06
Ixy: 1.84343e-08 Iyy: 1.78652e-06
Ixz: -1.56077e-07 Iyz: 1.56077e-07 Izz: 4.91581e-08
Principal MMOI and Principal Axes Relative to WCS Origin:
Max Prin
1.80495e-06
Min Prin
Mid Prin
1.79597e-06
2.12673e-08
WCS X: 7.07107e-01
WCS Y: 7.07107e-01
WCS Z: 0.00000e+00
7.01528e-01
-7.01528e-01
-1.25363e-01
8.86447e-02
-8.86447e-02
9.92111 e-0I
Center of Mass Location Relative to WCS Origin:
( 3.000OOe-03, -3.000OOe-03, 2.54000e-02)
Mass Moments of Inertia about the Center of Mass:
lxx: 4.46629e-07
Ixy: 0.00000e+00 Iyy: 4.46629e-07
Ixz: -2.64698e-23 Iyz: -2.64698e-23 Izz: 1.22895e-08
Principal MMOI and Principal Axes Relative to COM:
Max Prin
Mid Prin
Min Prin
84
4.46629e-07
4.46629e-07
WCS X: 0.00000e+00
WCS Y: 1.00000e+00
1.22895e-08
1.00000e+00
0.00000e+00
0.00000e+00
WCS Z: 0.00000e+00
0.00000e+00
0.00000e+00
1.00000e+00
Constraint Set: wall
Load Set: Eccentload
Resultant Load on Model:
in global X direction: 3.458356e-14
in global Y direction: 5.990182e-13
in global Z direction: -1.500000e+00
Measures:
Name
Value
Convergence
maxbeam_bending: 0.000000e+00
0.0%
max beamtensile: 0.000000e+00
0.0%
maxbeam-torsion: 0.000000e+00
0.0%
max beamntc : 0.000000e+00
0.0%
max-disp me
1.752542e-02
4.4%
-1.281556e-04
maxdispx:
6.1%
1.727595e-02
max-disp_y:
4.4%
-2.946123e-03
max-disp-z:
3.7%
-6.039205e+05 31.4%
max_prin-ma
0.000000e+00
maxrotmag
0.0%
max rotx:
0.000000e+00
0.0/o
0.000000e+00
maxroty:
0.0%
0.000000e+00
0.0%
max rotz:
max-stressJp : 1.950021e+05 39.9%
6.853940e+05 31.4%
maxstressv
-1.556735e+05 11.4%
maxstress_x
-3.834213e+04 50.9%
maxstress x
1.030638e+05 37.2%
maxstress_x
max-stressy
-1.547901e+05
10.5%
-2.644876e+05 33.1%
max stressy:
-4.975723e+05 32.1%
maxstress_7z
-6.039205e+05 31.4%
min stresspi
strain energy
2.186693e-03
3.6%
Displacement
1.727595e-02
4.4%
Strain:
0.000000e+00
0.0%
0.000000e+00
Stress:
0.0%
Analysis "buckling" Completed (08:45:01)
Memory and Disk Usage:
Machine Type: Windows NT/x86
RAM Allocation for Solver (megabytes): 64.0
Total Elapsed Time (seconds): 9.44
9.5
Total CPU Time (seconds): 6.17
Maximum Memory Usage (kilobytes): 82091
Working Directory Disk Usage (kilobytes): 0
Results Directory Size (kilobytes): 515 .\buckling_study
B.3 Elbow
Load: 2N Along interior length of Elbow
Pro/MECHANICA STRUCTURE Version 20.0(72)
Summary for Design Study "elbow"
Run Settings
Memory allocation for block solver: 64.0
Generate elements automatically.
No errors were found in the model.
Pro/MECHANICA Structure Model Summary
Principal System of Units:
mm
Length:
N
Force:
Time:
sec
Temperature: C
Model Type: Three Dimensional
Points:
Edges:
Faces:
37
120
133
Springs:
Masses:
Beams:
Shells:
Solids:
0
0
0
0
49
Elements:
49
Standard Design Study
Static Analysis "elbow":
Convergence Method: Multiple-Pass Adaptive
8
Plotting Grid:
Convergence Loop Log:
>> Pass
(10:05:24)
1 <<
86
Calculating Element Equations
(10:05:24)
Total Number of Equations:
99
Maximum Edge Order:
1
Solving Equations
(10:05:24)
Calculating Disp and Stress Results (10:05:25)
Checking Convergence
(10:05:26)
Elements Not Converged:
49
Edges Not Converged:
120
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 100.0%
Resource Check
(10:05:27)
Elapsed Time (sec):
10.05
CPU Time
(sec):
6.30
Memory Usage
(kb):
83378
Wrk Dir Dsk Usage (kb):
0
>> Pass 2 <<
Calculating Element Equations
(10:05:27)
Total Number of Equations: 444
Maximum Edge Order:
2
Solving Equations
(10:05:27)
Calculating Disp and Stress Results (10:05:27)
Checking Convergence
(10:05:28)
Elements Not Converged:
27
Edges Not Converged:
94
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 94.1%
Resource Check
(10:05:29)
Elapsed Time (sec):
12.11
CPU Time
(sec):
7.98
Memory Usage
(kb):
83464
Wrk Dir Dsk Usage (kb):
0
>> Pass 3 <<
Calculating Element Equations
(10:05:29)
Total Number of Equations: 1470
4
Maximum Edge Order:
Solving Equations
(10:05:29)
Calculating Disp and Stress Results (10:05:29)
Checking Convergence
(10:05:32)
Elements Not Converged:
23
Edges Not Converged:
32
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 71.7%
Resource Check
(10:05:32)
Elapsed Time (sec):
15.26
CPU Time
(sec):
10.62
Memory Usage
(kb):
83656
Wrk Dir Dsk Usage (kb):
1024
>> Pass 4 <<
Calculating Element Equations
(10:05:32)
Total Number of Equations: 2292
Maximum Edge Order:
5
Solving Equations
(10:05:32)
Calculating Disp and Stress Results (10:05:33)
87
Checking Convergence
(10:05:36)
Elements Not Converged:
13
Edges Not Converged:
1
Local Disp/Energy Index: 73.5%
Global RMS Stress Index: 46.4%
Resource Check
(10:05:36)
Elapsed Time (sec):
19.45
(sec):
14.36
CPU Time
Memory Usage
(kb):
83826
Wrk Dir Dsk Usage (kb):
2048
>> Pass 5 <<
(10:05:36)
Calculating Element Equations
Total Number of Equations: 3207
6
Maximum Edge Order:
(10:05:38)
Solving Equations
Calculating Disp and Stress Results (10:05:39)
(10:05:43)
Checking Convergence
Elements Not Converged:
3
0
Edges Not Converged:
Local Disp/Energy Index: 15.1%
4.0%
Global RMS Stress Index:
(10:05:43)
Resource Check
27.01
Elapsed Time (sec):
20.37
(sec):
CPU Time
Memory Usage
(kb):
83998
5120
Wrk Dir Dsk Usage (kb):
>>Pass 6 <<
Calculating Element Equations
(10:05:44)
Total Number of Equations: 3777
Maximum Edge Order:
7
Solving Equations
(10:05:47)
Calculating Disp and Stress Re sults (10:05:49)
(10:05:55)
Checking Convergence
Elements Not Converged:
0
Edges Not Converged:
0
Local Disp/Energy Index:
5.0%
Global RMS Stress Index:
4.2%
Resource Check
(10:05:55)
Elapsed Time (sec):
38. 36
CPU Time
(sec):
29.1 2
Memory Usage
(kb):
84 143
8192
Wrk Dir Dsk Usage (kb):
RMS Stress Error Estimates:
Load Set
loadi
Stress Error % of Max Prin Str
4.60e-01
8.7% of 5.26e+00
The analysis converged to within 10.0% on
edge displacement and element strain energy.
Total Mass of Model: 5.002642e-06
88
Total Cost of Model: 0.000000e+00
Mass Moments of Inertia about WCS Origin:
lxx: 5.80582e-03
Ixy: 2.18222e-05 Iyy: 6.17184e-03
Ixz: 2.82106e-09 Iyz: -3.82003e-10 Izz: 4.52092e-04
Principal MMOI and Principal Axes Relative to WCS Origin:
Max Prin
6.17314e-03
Min Prin
Mid Prin
4.52092e-04
5.80452e-03
WCS X: 5.93045e-02
WCS Y: 9.98240e-01
WCS Z: -3.74108e-08
9.98240e-01
-5.93045e-02
5.30367e-07
-5.27215e-07
6.8798le-08
1.00000e+00
Center of Mass Location Relative to WCS Origin:
(-1.71738e+00, 2.54000e+00, 2.42635e-05)
Mass Moments of Inertia about the Center of Mass:
Ixx: 5.77354e-03
Ixy: -4.85043e-1I Iyy: 6.15709e-03
Ixz: 2.61260e-09 Iyz: -7.36937e-l I Izz: 4.05063e-04
Principal MMOI and Principal Axes Relative to COM:
Max Prin
6.15709e-03
Mid Prin
5.77354e-03
WCS X: -1.26463e-07
WCS Y: 1.00000e+00
WCS Z: -1.28118e-08
Min Prin
4.05063e-04
1.00000e+00
1.26463e-07
4.86656e-07
-4.86656e-07
1.281 18e-08
1.00000e+00
Constraint Set: constraintl
Load Set: loadi
Resultant Load on Model:
in global X direction: -2.828400e+00
in global Y direction: 1.061696e-11
in global Z direction: 8.400029e-12
Measures:
Name
Value
Convergence
0.0%
max beam bending: 0.000000e+00
0.0%
max beam tensile: 0.000000e+00
0.0%
maxbeam torsion: 0.000000e+00
max_beamtotal: 0.000000e+00
0.0%
max dispmag:
1.146926e+00
0.5%
0.5%
-1.030249e+00
max dispx:
2.7%
1.778927e-02
max disp-y:
-5.044528e-01
0.7%
max-dispz:
99
5.264012e+00
maxprinmag:
0.000000e+00
max_rot_mag:
maxrot x:
0.000000e+00
0.000000e+00
maxroty:
maxrotz:
0.000000e+00
max_stressprin 5.264012e+00
maxstressvm: 4.840824e+00
max stress xx: 3.292248e+00
maxstress_xy: -7.051359e-01
maxstress xz: 2.448102e+00
maxstress yy: 1.154303e+00
maxstress yz: 5.258212e-01
maxstresszz: -4.213816e+00
minstressprin: -4.862247e+00
strainenergy: 2.369590e-01
6.0%
0.0%
0.0%
0.0%
0.0%
6.0%
1.2%
26.4%
29.6%
0.8%
20.9%
5.8%
11.9%
3.5%
0.2%
Analysis "elbow" Completed (10:05:57)
Memory and Disk Usage:
Machine Type: Windows NT/x86
RAM Allocation for Solver (megabytes): 64.0
Total Elapsed Time (seconds): 40.53
Total CPU Time (seconds): 31.14
Maximum Memory Usage (kilobytes): 84162
Working Directory Disk Usage (kilobytes): 8192
Results Directory Size (kilobytes):
2359 .\elbow
Maximum Data Base Working File Sizes (kilobytes):
4096 .\elbow.tmp\kblkl .bas
4096 .\elbow.tmp\kell .bas
B.4
RHOMBUS
LOAD: 2N on 2 adjacent interior surfaces; other sides unloaded
Pro/MECHANICA STRUCTURE Version 20.0(72)
Summary for Design Study "elbow"
Run Settings
Memory allocation for block solver: 64.0
Generate elements automatically.
No errors were found in the model.
Pro/MECHANICA Structure Model Summary
Principal System of Units:
90
Length:
mm
Force:
N
sec
Time:
Temperature: C
Model Type: Three Dimensional
Points:
Edges:
Faces:
37
120
133
Springs:
Masses:
Beams:
Shells:
Solids:
0
0
0
0
49
Elements:
49
Standard Design Study
Static Analysis "elbow":
Convergence Method: Multiple-Pass Adaptive
Plotting Grid:
8
Convergence Loop Log:
(10:05:24)
>>Pass 1 <<
Calculating Element Equations
(10:05:24)
Total Number of Equations:
99
1
Maximum Edge Order:
Solving Equations
(10:05:24)
Calculating Disp and Stress Results (10:05:25)
Checking Convergence
(10:05:26)
49
Elements Not Converged:
120
Edges Not Converged:
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 100.0%
(10:05:27)
Resource Check
Elapsed Time (sec):
10.05
CPU Time
(sec):
6.30
Memory Usage
(kb):
83378
Wrk Dir Dsk Usage (kb):
0
>> Pass 2 <<
Calculating Element Equations
(10:05:27)
Total Number of Equations: 444
Maximum Edge Order:
2
Solving Equations
(10:05:27)
Calculating Disp and Stress Results (10:05:27)
Checking Convergence
(10:05:28)
Elements Not Converged:
27
91
Edges Not Converged:
94
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 94.1%
Resource Check
(10:05:29)
Elapsed Time (sec):
12.11
CPU Time
(sec):
7.98
Memory Usage
(kb):
83464
Wrk Dir Dsk Usage (kb):
0
> Pass 3 <<
Calculating Element Equations
(10:05:29)
Total Number of Equations: 1470
Maximum Edge Order:
4
Solving Equations
(10:05:29)
Calculating Disp and Stress Results (10:05:29)
Checking Convergence
(10:05:32)
23
Elements Not Converged:
Edges Not Converged:
32
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 71.7%
Resource Check
(10:05:32)
Elapsed Time (sec):
15.26
CPU Time
(sec):
10.62
Memory Usage
(kb):
83656
Wrk Dir Dsk Usage (kb):
1024
> Pass 4 <<
Calculating Element Equations
(10:05:32)
Total Number of Equations: 2292
Maximum Edge Order:
5
Solving Equations
(10:05:32)
Calculating Disp and Stress Results (10:05:33)
Checking Convergence
(10:05:36)
Elements Not Converged:
13
Edges Not Converged:
1
Local Disp/Energy Index: 73.5%
Global RMS Stress Index: 46.4%
Resource Check
(10:05:36)
Elapsed Time (sec):
19.45
CPU Time
(sec):
14.36
Memory Usage
(kb):
83826
Wrk Dir Dsk Usage (kb):
2048
> Pass 5 <<
Calculating Element Equations
(10:05:36)
Total Number of Equations: 3207
Maximum Edge Order:
6
Solving Equations
(10:05:38)
Calculating Disp and Stress Results (10:05:39)
Checking Convergence
(10:05:43)
Elements Not Converged:
3
Edges Not Converged:
0
Local Disp/Energy Index: 15.1%
Global RMS Stress Index:
4.0%
Resource Check
(10:05:43)
Elapsed Time (sec):
27.01
92
CPU Time
(sec):
20.37
Memory Usage
(kb):
83998
Wrk Dir Dsk Usage (kb):
5120
>> Pass 6 <<
Calculating Element Equations
(10:05:44)
Total Number of Equations: 3777
Maximum Edge Order:
7
Solving Equations
(10:05:47)
Calculating Disp and Stress Results (10:05:49)
Checking Convergence
(10:05:55)
Elements Not Converged:
0
Edges Not Converged:
0
Local Disp/Energy Index:
5.0%
Global RMS Stress Index:
4.2%
Resource Check
(10:05:55)
Elapsed Time (sec):
38.36
CPU Time
(sec):
29.12
Memory Usage
(kb):
84143
Wrk Dir Dsk Usage (kb):
8192
RMS Stress Error Estimates:
Load Set
loadi
Stress Error %of Max Prin Str
4.60e-01
8.7% of 5.26e+00
The analysis converged to within 10.0% on
edge displacement and element strain energy.
Total Mass of Model: 5.002642e-06
Total Cost of Model: 0.000000e+00
Mass Moments of Inertia about WCS Origin:
lxx: 5.80582e-03
Ixy: 2.18222e-05 Iyy: 6.17184e-03
Ixz: 2.82106e-09 Iyz: -3.82003e-10 Izz: 4.52092e-04
Principal MMOI and Principal Axes Relative to WCS Origin:
Max Prin
6.17314e-03
WCS X: 5.93045e-02
WCS Y: 9.98240e-01
WCS Z: -3.74108e-08
Mid Prin
5.80452e-03
Min Prin
4.52092e-04
9.98240e-01
-5.93045e-02
5.30367e-07
-5.27215e-07
6.87981e-08
1.00000e+00
Center of Mass Location Relative to WCS Origin:
(-1.71738e+00, 2.54000e+00, 2.42635e-05)
Mass Moments of Inertia about the Center of Mass:
lxx: 5.77354e-03
Ixy:-4.85043e-11 Iyy: 6.15709e-03
93
Lxz: 2.61260e-09 Iyz: -7.36937e-1 1 Izz: 4.05063e-04
Principal MMOI and Principal Axes Relative to COM:
Max Prin
6.15709e-03
Mid Prin.
5.77354e-03
WCS X: -1.26463e-07
WCS Y: 1.00000e+00
WCS Z: -1.28118e-08
Min Prin
4.05063e-04
1.00000e+00
1.26463e-07
4.86656e-07
-4.86656e-07
1.28118e-08
1.00000e+00
Constraint Set: constraintI
Load Set: loadi
Resultant Load on Model:
in global X direction: -2.828400e+00
in global Y direction: 1.061696e-1 1
in global Z direction: 8.400029e-12
Measures:
Name
Value
Convergence
max..beam bending: 0.000000e+00
0.0%
max_ beamtensile: 0.000000e+00
0.0%
maxbeamtorsion: 0.000000e+00
0.0%
0.0%
maxbeamtotal: 0.000000e+00
maxdispmag:
1.146926e+00
0.5%
maxdispx:
-1.030249e+00
.5%
max dispy:
1.778927e-02
2..7%
maxdispz:
-5.044528e-01
0.7%
maxprinmag:
5.264012e+00
6.0%
max rotmag:
0.000000e+00
0.0%
max rotx:
0.000000e+00
0.0%
max roty:
0.000000e+00
0. 0%
0. 0%
0.000000e+00
max rotz:
max stress_prin: 5.264012e+00
6.0%
max stressvm: 4.840824e+00
1.2%
max stressxx: 3.292248e+00 26.4%
max stress-xy: -7.051359e-01 29.6%
max-stress xz: 2.448102e+00
0.8%
max stressyy: 1.154303e+00 2 0.9%
max stressyz: 5.258212e-01
5.8%
max stress zz: -4.213816e+00
11.9%
min_stress_prin: -4.862247e+00
3.5%
strainenergy: 2.369590e-01 0. 2%
Analysis "elbow" Completed (10:05:57)
Memory and Disk Usage:
Machine Type: Windows NT/x86
RAM Allocation for Solver (megabytes): 64.0
94
Total Elapsed Time (seconds): 40.53
Total CPU Time (seconds): 31.14
Maximum Memory Usage (kilobytes): 84162
Working Directory Disk Usage (kilobytes): 8192
Results Directory Size (kilobytes):
2359 .\elbow
Maximum Data Base Working File Sizes (kilobytes):
4096 .\elbow.tmp\kblkl.bas
4096 .\elbow.tmp\kell .bas
B.5
HEXAGON
Load: Combined Load Set: 2 of 3 Loads were actuated; each of the active loads was
centered on a joint with each side directing approximately 2N toward the joint.
Pro/MECHANICA STRUCTURE Version 20.0(72)
Summary for Design Study "elbow"
Run Settings
Memory allocation for block solver: 64.0
Generate elements automatically.
No errors were found in the model.
Pro/MECHANICA Structure Model Summary
Principal System of Units:
mm
Length:
Force:
N
Time:
sec
Temperature: C
Model Type: Three Dimensional
Points:
Edges:
Faces:
37
120
133
Springs:
Masses:
Beams:
Shells:
Solids:
0
0
0
0
49
Elements:
49
-----------------------------------------------------------Standard Design Study
9.5
Static Analysis "elbow":
Convergence Method: Multiple-Pass Adaptive
Plotting Grid:
8
Convergence Loop Log:
(10:05:24)
>>Pass l <<
Calculating Element Equations
(10:05:24)
Total Number of Equations:
99
Maximum Edge Order:
1
Solving Equations
(10:05:24)
Calculating Disp and Stress Re sults (10:05:25)
Checking Convergence
(10:05:26)
Elements Not Converged:
49
Edges Not Converged:
120
Local Disp/Energy Index: I 00.0%
Global RMS Stress Index: 100.0%
(10:05:27)
Resource Check
Elapsed Time (sec):
10. 05
CPU Time
(sec):
6.3 0
Memory Usage
(kb):
83 378
Wrk Dir Dsk Usage (kb):
0
>>Pass 2<<
(10:05:27)
Calculating Element Equations
Total Number of Equations: 444
2
Maximum Edge Order:
(10:05:27)
Solving Equations
Calculating Disp and Stress Results (10:05:27)
(10:05:28)
Checking Convergence
27
Elements Not Converged:
94
Edges Not Converged:
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 94.1%
Resource Check
(10:05:29)
12.11
Elapsed Time (sec):
(sec):
7.98
CPU Time
83464
(kb):
Memory Usage
Wrk Dir Dsk Usage (kb):
0
>>Pass 3 <<
Calculating Element Equations
(10:05:29)
Total Number of Equations: 1470
Maximum Edge Order:
4
(10:05:29)
Solving Equations
Calculating Disp and Stress Results (10:05:29)
Checking Convergence
(10:05:32)
Elements Not Converged:
23
Edges Not Converged:
32
Local Disp/Energy Index: 100.0%
Global RMS Stress Index: 71.7%
Resource Check
(10:05:32)
15.26
Elapsed Time (sec):
CPU Time
(sec):
10.62
96
Memory Usage
(kb):
Wrk Dir Dsk Usage (kb):
83656
1024
>> Pass 4 <<
Calculating Element Equations
(10:05:32)
Total Number of Equations: 2292
Maximum Edge Order:
5
Solving Equations
(10:05:32)
Calculating Disp and Stress Results (10:05:33)
Checking Convergence
(10:05:36)
Elements Not Converged:
13
Edges Not Converged:
1
Local Disp/Energy Index: 73.5%
Global RMS Stress Index: 46.4%
Resource Check
(10:05:36)
Elapsed Time (sec):
19.45
(sec):
14.36
CPU Time
Memory Usage
(kb):
83826
Wrk Dir Dsk Usage (kb):
2048
>Pass 5<<
Calculating Element Equations
(10:05:36)
Total Number of Equations: 3207
Maximum Edge Order:
6
Solving Equations
(10:05:38)
Calculating Disp and Stress Results (10:05:39)
Checking Convergence
(10:05:43)
Elements Not Converged:
3
Edges Not Converged:
0
Local Disp/Energy Index: 15.1%
Global RMS Stress Index:
4.0%
Resource Check
(10:05:43)
Elapsed Time (sec):
27.01
CPU Time
(sec):
20.37
Memory Usage
(kb):
83998
Wrk Dir Dsk Usage (kb):
5120
Pass 6 <<
Calculating Element Equations
(10:05:44)
Total Number of Equations: 3777
Maximum Edge Order:
7
Solving Equations
(10:05:47)
Calculating Disp and Stress Results (10:05:49)
Checking Convergence
(10:05:55)
Elements Not Converged:
0
Edges Not Converged:
0
Local Disp/Energy Index:
5.0%
Global RMS Stress Index:
4.2%
Resource Check
(10:05:55)
Elapsed Time (sec):
38.36
CPU Time
(sec):
29.12
Memory Usage
(kb):
84143
Wrk Dir Dsk Usage (kb):
8192
RMS Stress Error Estimates:
97
Load Set
Stress Error % of Max Prin Str
loadi
4.60e-01
8.7% of 5.26e+00
The analysis converged to within 10.0% on
edge displacement and element strain energy.
Total Mass of Model: 5.002642e-06
Total Cost of Model: 0.000000e+00
Mass Moments of Inertia about WCS Origin:
Lxx: 5.80582e-03
Ixy: 2.18222e-05 Iyy: 6.17184e-03
Ixz: 2.82106e-09 Iyz: -3.82003e-10 Izz: 4.52092e-04
Principal MMOI and Principal Axes Relative to WCS Origin:
Max Prin
6.17314e-03
Mid Prin
5.80452e-03
Min Prin
4.52092e-04
9.98240e-01
-5.93045e-02
5.30367e-07
WCS X: 5.93045e-02
WCS Y: 9.98240e-01
WCS Z: -3.74108e-08
-5.27215e-07
6.87981e-08
1.00000e+00
Center of Mass Location Relative to WCS Origin;
(-1.71738e+00, 2.54000e+00, 2.42635e-05)
Mass Moments of Inertia about the Center of Mass:
Ixx: 5.77354e-03
Ixy: -4.85043e-11 Iyy: 6.15709e-03
Ixz: 2.61260e-09 Iyz: -7.36937e-11 Izz: 4.05063e-04
Principal MMOI and Principal Axes Relative to COM:
Max Prin
6.15709e-03
Mid Prin
5.77354e-03
WCS X: -1.26463e-07
WCS Y: 1.00000e+00
WCS Z: -1.28118e-08
Min Prin
4.05063e-04
1.00000e+00
1.26463e-07
4.86656e-07
-4.86656e-07
1.28118e-08
1.00000e+00
Constraint Set: constrainti
Load Set: loadi
Resultant Load on Model:
in global X direction: -2.828400e+00
in global Y direction: 1.061696e-1 1
in global Z direction: 8.400029e-12
Measures:
Name
Value
Convergence
98
maxbeambending: 0.000000e+00
0.0%
maxbeamtensile: 0.000000e+00
0.0%
max beamtorsion: 0.000000e+00
0.0%
max beamtotal: 0.000000e+00
0.0%
max dispmag:
1.146926e+00
0.5%
max dispx:
-1.030249e+00
0.5%
max dispy:
1.778927e-02
2.7%
max dispz:
-5.044528e-01
0.7%
maxjprinmag:
5.264012e+00
6.0%
max rot mag:
0.000000e+00
0.0%
maxrotx:
0.000000e+00
0.0%
max-rot-y:
0.000000e+00
0.0%
maxrotz:
0.000000e+00
0.0%
maxstress_prin: 5.264012e+00
6.0%
maxstressvm: 4.840824e+00
1.2%
maxstressxx:
3.292248e+00 26.4%
-maxstress_ xy: -7.051359e-01 29.6%
0.8%
max stressxz: 2.448102e+00
1.154303e+00 20.9%
maxstressyy:
5.8%
5.258212e-01
maxstressyz:
max stresszz: -4.213816e+00 11.9%
3.5%
min_stress_prin: -4.862247e+00
0.2%
strain_energy: 2.369590e-01
Analysis "elbow" Completed (10:05:57)
Memory and Disk Usage:
Machine Type: Windows NT/x86
RAM Allocation for Solver (megabytes): 64.0
Total Elapsed Time (seconds): 40.53
Total CPU Time (seconds): 31.14
Maximum Memory Usage (kilobytes): 84162
Working Directory Disk Usage (kilobytes): 8192
Results Directory Size (kilobytes):
2359 .\elbow
Maximum Data Base Working File Sizes (kilobytes):
4096 .\elbow.tmp\kblkl .bas
4096 .\elbow.tmp\kell .bas
99
Appendix C
Shape Memory Alloy Actuators
Shape Memory Alloy Actuators
Shape Memory Alloys (SMAs) are actuators that gain their motion capabilities from
changes in their microstructure that transforms upon heating and under load. At low or
room temperatures, the material is in its Martensite phase. In this material phase, the
SMA may be deformed or stretched by an external load. Through stretch alignment of
the Martensitic molecules under a deformation load, the material actually elongates by a
significant amount, 5-8% strain. This elongation is not permanent and can be recovered
through heating the SMA material above its transformation temperature, AF.
A
simplified 2D diagram of these transformations is included in Figure C1.
High Temperature
Cubic Structure
COOL
HEAT
DEFORM
Low Temperature
Twinned Monoclinic Structure
Low Temperature
Deformed
Figure C1 Transformation Between High and Low Temperature Structures4
As the material is heated, the molecules that had been aligned in the strained Martensite
phase regain their preferred cubic structure of Austenite.
4
When the temperature is again
T. Waram. Actuator Design Using Shape Memory Alloys. p.5, C1993.
100
dropped below the Martensite transformation temperature, MF, the shape memory. alloys
will return to its deformed state. Work may be done by applying a load to the SMA
while in its Martensite phase and then heating it to Austenite. As the SMA effectively
shrinks, it lifts the load against gravity.
4.5.1.1
Characteristics of NiTi
The Shape Memory Alloys used in this work are Nickle Titanium (NiTi). SMAs are
available in sheets, ribbons, rings and wires. The wires tend to be the most widespread
shape in use. These wires are commercially available from Mondotronics and, while they
are referred to as "muscle wires", their trade name is Flexinol. They come in a variety of
diameters ranging from 25tm to 500pm.
The material and actuator properties for
Flexinol 150 and 250 are included in table Cl.
PROPERTIES5
Wire Diameter (pm)
Physical
Min. Bend Radius (mm)
X-Sectional Area (pm 2 )
Linear Resitance (Q.m)
Electrical
Recommended Current (mA)
Rec'd Power (W/m)'
Max Recovery Wt @ 600MPa (g)
Strength
Rec'd Recovery Wt @190Mpa (g)
Rec'd Deformation Wt @35Mpa (g)
Max Contraction Speed (sec)
Speed
Relaxation Speed (sec)
Typical Cycle Rate (cyc/min)
Thermal& Activation Start Temperature (*C)
Activation Finish Temp (*C)
Material
Relaxation Start Temp ('C)
Relaxation Finish Temp (*C)
Thermal
Annealing Temp (*C)
&
Melting Temp (*C)
5
Flexinol 150
150
7.50
17,700
50
400
8.0
1056
330
62
0.1
2
20
68
78
52
42
540
1300
Flexinol 250
250
12.50
49,100
200
1000
20.0
2933
930
172
0.1
5.5
9
Modotronics. Muscle Wires Project Book. Mondontronics, p2-5, C1994.42
101
0.077
Latent Heat (J/g)
24.2
Resistivity (ptn)
76 (low temp)/82 (hi temp)
Young's Modulus (Gpa)
28/75
2.5/3.8
Magnetic Susceptability (jemu/g)
Thermal Conductivity (W/cmoC)
0.08/0.18
6.45
Density (g/cc)
600
Max Recovery Force (MPa)
Recommended Deformation Force (MPa) 35
1000
Breaking Strength (MPa)
1
Work Output (J/g)
Energy Conversion Efficiency (%)
5
Maximum Deformation Ratio (%)
8
Heat Capacity (cal/g*C)
Recommended Deformation Ratio (%)
3-5
Table C1 Flexinol Muscle Wire Properties (Mondotronics 1994)
The common method of heating these SMA wires through their range of transition
temperatures is through resistive heating. As a current is passed through the wire, the
temperature rises due to Ohm's Law, P = i2R.
102