FINAL DESIGN REPORT
ME 350
SECTION 4
TEAM 43
James Butler
Gregory Caputo
Mary Molepske
Samuel Shrago
PREPARED FOR
Dr. Jeffrey Stein
Professor of Mechanical Engineering,
University of Michigan
Dr. Michael Umbriac
Assistant Professor of Mechanical Engineering,
University of Michigan
Mr. Yang Xu
Graduate Student of Mechanical Engineering
University of Michigan
December 10, 2013
Table of Contents
1 Introduction and Specifications.....................................................................................4-5
1.1 Design Requirements.........................................................................................4
1.2 Considerations....................................................................................................4
1.21 Torque and Transmission.....................................................................4
1.3 Final Report.......................................................................................................5
2 Functional Decomposition.............................................................................................5-6
3 Motion Generation.........................................................................................................7-9
3.1 Design Process...................................................................................................7
3.2 Design Matrix....................................................................................................8
3.3 Choosing the Final Design.................................................................................8
3.4 Test Results........................................................................................................9
3.4.1 Initial Test...........................................................................................9
3.4.2 Final Test............................................................................................9
3.5 Revisions to Final Design..................................................................................9
4 Energy Conversion and Transmission.........................................................................9-15
4.1 Down Selection: Belt vs. Gears....................................................................9-10
4.2 Summary of Values .........................................................................................10
4.3 Operating Speed ..............................................................................................10
4.4 Maximum Torque............................................................................................10
4.5 Gear Ratio........................................................................................................10
4.6 Torque Verification..........................................................................................11
4.7 Speed and Time................................................................................................12
4.7.1 Motor Low Speed.............................................................................12
4.7.2 Time of Low Speed Travel...............................................................12
4.7.3 Time of High Speed Travel...............................................................12
4.7.4 Angular Displacement at High Speed...............................................12
4.7.5 Angular Velocity at High Speed.......................................................12
4.7.6 Angular Velocity of Motor Shaft at High Speed..............................12
4.8 Remarks...........................................................................................................13
4.9 Input Power, Output Power Draw..............................................................14-15
4.10 Mounts and Joints..........................................................................................15
4.10.1 Motor and Transmission Mounts....................................................15
5 Safety and Motor Controls........................................................................................16-18
5.1 Sensor Capabilities...........................................................................................16
5.2 Threshold Values.............................................................................................16
5.3 Relevant Equations.....................................................................................16-17
5.3.1 Given and Measured Parameters......................................................16
5.3.2 Lower Count Threshold....................................................................17
5.3.3 Upper Count Threshold.....................................................................17
5.4 Changes to Arduino Code...........................................................................17-18
2
5.6 Sensor Mounting..............................................................................................18
6 Design Critique..........................................................................................................18-21
6.1 The Good....................................................................................................18-19
6.2 The Bad............................................................................................................19
6.3 Linkage vs. Computer Model..........................................................................19
6.4 Load Considerations...................................................................................19-20
6.4.1 Loading of Backpack........................................................................19
6.4.2 Friction .............................................................................................20
6.5 Mechatronics....................................................................................................20
6.5.1 Control Algorithm.............................................................................20
6.5.2 Sensors..............................................................................................20
6.6 What We Could Have Done Differently..........................................................20
6.7 Mechanism Safety............................................................................................21
6.8 Final Remarks..................................................................................................21
3
1 Introduction and Specifications
Our objective is to design a mechanism that pivots a backpack from the back of a
wheelchair to the chair’s side, bringing a disabled person’s possessions within reach. Such
a mechanism requires a safe and sturdy aluminum linkage driven by a robust transmission.
The specifications of the mechanism, both technical and abstract, will be discussed in this
section.
1.1 Design Requirements
We successfully met the requirements for a linkage with an angle offset no greater
than 15º (ours was 0), a horizontal offset no lesser than 2 inches and no greater than
10 inches (ours was 3.625 in), a forward offset no lesser than 6 inches and no
greater than 17 inches (ours was 8.5 in), a travel time of 9 seconds (ours was 9.2
seconds), a deceleration speed of 10º/s (ours was 9.8º/s), an operating torque of
453.28 oz-in, a gear ratio of 6:1, an input motor power of 13.6 W and an output
motor power of 2.08 W. The mechanism volume is 1,202.91 in2. In terms of any
considerable figures obtained from mount and joint analysis, we determined that a
shear stress of 9234 ozf/in2 acts on the hole through which a dowel is press-fitted,
connecting the input gear to the input link. Upon investigation of the motor and its
mount, we found a bending moment, M of 1368.45 oz-in acting on the motor shaft
by the motor mount. The motor shaft was found to undergo a deflection of 6.44x104
inches. Furthermore, the top plate of the motor mount assembly was found to be
subject to a stress of 3899 ozf/in2, ultimately causing a vertical deflection of
2.67x10-4 inches. Although these figures are not negligible, they are not significant
enough to cause any serious deformation of our assembly.
1.2 Considerations
Considerations included in the determination of a linkage to satisfy these
requirements are transmission design (down selection, gear ratio, DC motor
characteristics), mounts and joints (visual and written explanations of both
motor/transmission mounts and torque transferring joints, discussion of gate 1
values) and transmission loading (stress analysis at torque transmitting joints,
deflection analysis).
1.2.1 Torque and Transmission
In our design, the torque provided by the motor shaft (188 oz-in) is not
enough to carry the torque required by our linkage (453.28 oz-in). The
preferred gear ratio is 6:1 (rounded up from 5.69:1, which was calculated
from our system’s operating speed of 4.635 RPM and operating torque of
453.28 oz-in). A belt drive will be used because it has proven to be the most
advantageous transmission in terms of design flexibility, maintenance, cost
and user safety.
4
1.3 Final Report
This report provides a thorough explanation of the design process from the
formulation and choosing of individual designs to the final design. The functional
decomposition breaks down the mechanism into its constituent components and
their basic functions, which provides clear reasoning for the inclusion of each part.
The design process is explained, starting with the formulation of a preliminary
model in lincages as a confirmation that the link dimensions are within ratio, to a
model in Solidworks as a confirmation that the project materials can satisfy the
aforementioned design, to a model in Adams as a confirmation that the design will
not undergo significant deflection. Test results are discussed after the design
process. In the energy conversion section we discuss the down-selection process
between belts and gears, gear ratio calculation, operating speed calculation,
maximum torque calculation, input and output power calculation, speed, time,
mounts and joints. Included in these explanations are relevant equations used to
determine these vital design parameters. Afterwards we discuss the safety and
motor controls, weigh the capabilities and limitations of various mechatronic
sensors, determine the threshold values, changes to the Arduino code and the
consider the positioning of the sensors. At the end we critique the design process,
which serves to answer questions that address the project as a whole and develop
the bigger, broader picture of the project.
2 Functional Decomposition
The following diagram on the next page is a functional decomposition of the linkage
system. The functional decomposition helped us organize and simplify the function and
form of the project by determining what our design must accomplish and map out how it
would do so. This process allowed us to deeply understand the design problem and its
functional needs thus, allowing us to efficiently find our solution. This also helps simplify
the project by outlining the primary and auxiliary functions.
5
Figure 2
Functional Decomposition
Turn on/off,
backward or forward
movement
(H-Bridge)
Function Decomposition Key
Hold H-Bridge
(mount)
Current
Backpack
Torque
HEAT
Convert electric
energy to mechanical
(motor)
Voltage
Angular Velocity
Hold motor
(bearing)
FRICTION
Transfer mechanical
energy
(shaft)
Hold shaft
(bearing)
FRICTION
Transform mechanical
energy
(gears)
Hold gears
(mount)
FRICTION
FRICTION
FRICTION
Transfer mechanical
energy
(linkages)
Use mechanical
energy to move
backpack
(linkages)
Decelerate linkage
movement
(motor)
Stop linkage
movement
(motor)
Signal
Hold backpack
(mount)
Connect Links
(bearings)
Ground
input link
(mount)
Convert user input
(rocker switch)
Measure motor
rotation
(motor encoder)
Detect
obstructions
(Prox Sensors)
Process sensor
information
(Arduino)
Detect end of motion
(limit Sensors)
6
Hold Arduino
(mount)
3 Motion Generation
The final plans for our design emerged from having chosen the most preferable preliminary
design in terms of the project requirements. This section breaks down the design process,
includes a Pugh chart to illustrate the elimination process, discusses results from testing
trials with the finished linkage and mentions several revisions to the original chosen(not
sure could do either) design.
3.1 Design Process
The first step in our design process was to individually create a four bar linkage
model using Lincages software. We each imported a picture of the wheelchair for
a reference frame and used the sketch function to create a design that would be able
to move the coupler link to the right side of the wheelchair. Each linkage was
designed for a transmission angle between 30 and 150 degrees. Once we found
each link’s length by hand, we each created our own SolidWorks model and
imported it into ADAMS . In ADAMS we created joints and simulated the forces
acting on them creating a graph of the forces throughout the linkage movement.
Specific details on each individual design can be found in appendix A.
Next we analyzed each individual’s design using the Pugh chart below. We
weighted our design criteria based the criteria’s importance for the final
design. . As a group we discussed how the four designs compared, and ranked them
with a 1 or -1, better or worse, for each category. After, we multiplied the criteria’s
weight by the designs’ ranks and summed all categories for each design. These
results contributed to the creation of our final design.
7
3.2 Design Matrix
Below is a Pugh chart weighing the attributes of the project requirements and the
scores we assigned to them. In the far right column is the final design, whose values
were obtained from the final testing.
Figure 3.2
Preliminary Design Pugh Chart
Weight
(1-3)
Design 1
Design 2
Design 3
(Mary)
Score (Greg)
Score (Jimmy)
Design 4
Score (Sam)
Score
FINAL
DESIGN
Volume (in^2), A
3
169.2
0
53.94
1
143.9
1
390
1
1202.906
Angle Offset,
3
~0.0
0
0
0
0
0
5
-1
0
Horizontal Offset (in), B
3
5.85
0
5.67
0
3.14
1
5.49
0
3.625
Forward Offset (in), C
3
7.26
0
6.94
-1
1.36
-1
5.98
-1
8.5
Maximum Force (Lb)
3
-33 to 25
0
-100 to
100
-1
-169.07 to
157
-1
-13 to 13
1
2.6
Minimal (force graph from Adams)
Ease of Manufacturing
Simple part design, easy to
reproduce
1
0
1
1
1
1
Cost Effectivness
Effective use of kit, minimal
purchasing required
2
0
0
0
0
0
Safety
# of pinch points, minimizes user
injury, angular velcocity
3
0
0
-1
1
-1
Radius of Motion
maximum distance backpack is from
wheel chair (minimize)
1
0
1
1
1
1
Roubustness
ability to resist load while
minimizing deformation, lifspan
(ability to undergo maximum
number of iterations)
2
0
-1
-1
-1
-1
TOTAL:
0
-3
-3
3
-3
3.3 Choosing the Final Design
We based our final design on Sam’s preliminary design because it had the highest
score of all the mechanisms and therefore the most desirable characteristics and
least potential for failure. The dimensions of the individual links in Sam’s design
were the most preferable because the mechanism had the most compact range of
motion while also satisfying the project requirements. Other attributes of Sam’s
design were altered at a later point in time (such as the ground plate, addition of
sandwich plates, addition of transmission and mechatronics, etc.).
8
3.4 Linkage Specifications
Input: 9.8336”
Output: 11.3607”
Coupler: 12.2479”
Figure 3.4a
Position 1 (Initial):
Figure 3.4b
Position 2 (Intermediate):
Figure 3.4c
Position 3 (Intermediate):
Figure 3.4d
Position 4 (Final):
9
Figure 3.4e
Transmission Angle v. Time
An ideal transmission angle is between 30 degrees and 150 degrees. Throughout the
movement process of the linkage our transmission angle stays within those limits. This
means our linkage has an ideal transmission angle.
3.5 Final Design Description
Transmission
Sandwich
Figure 3.5a
Isometric View of Wheelchair + Mechanism
10
This 3-D isometric view shows our linkage design including ground link, input link,
coupler link, follower link, and the backpack holder. The input link is on top of the
ground and is supported between the ground and the transmission triangular plate
which will be used later to hold the transmission. The ground link has a large area
in this model because we have not yet designed our transmission and mechatronic
systems for the wheelchair design.
Input Link
Backpack
Holder
Bottom
Ground
Link
Coupler Link
Output Link
Figure 3.5b
Top View of Wheelchair + Mechanism at Initial State
This 3-D isometric view shows our linkage design including ground link, input link,
coupler link, follower link, and the backpack holder. The input link is on top of the
ground and is supported between the ground and the transmission triangular plate
which will be used later to hold the transmission. The ground link has a large area
in this model because we have not yet designed our transmission and mechatronic
systems for the wheelchair design.
Figure 3.5c
11
Top View of Wheelchair + Mechanism at Final State
In the ending position the Backpack is parallel to the side of the wheelchair which
gives the user easy access to their backpack. The forward offset, angle offset, and
horizontal offset are all within the required values in the end position.
3.6 Loading Analysis
Figure 3.6a
Forces on Joints
Max Forces at Pin-Joints:
Input-Coupler: FIC = -14 lb
Follower-Coupler: FFC = 16.5 lb
Follower-Ground: FFG = 17.5 lb
Coupler-Holder: FCH = 12 lb
In our loading analysis we calculated our total deflection by summing the deflection
from each individual link. We assumed that one end of the link was fixed, starting
at the ground-input link. This allowed us to use the equation for a cantilevered
beam with a force at the end. We had to modify the equation for the coupler link
because it has a force in the center and on the end due to the coupler supporting
both the backpack holder and the follower link. (See Appendix A for detailed
calculations and Free Body Diagrams)
12
Our total deflection is .04134 inches. This is a realistic number because the square
aluminum stock we used is very strong and aluminum has a high Young’s Modulus.
In addition, our downward force is very small in comparison to the material
strength, causing only a small deflection. This deflection is totaled from three
different links and will not be noticeable to the naked eye.
This deflection will affect the joints because it will cause slight misalignment in
them. This causes out of plane loading (off-axis loading) creating friction at each of
the joints. To counteract this large friction force, caused by the deformation in each
link, we made sure to use bushings in pairs. We also used the shortest links
possible (that still achieve our desired forward offset) in order to reduce the moment
that the force at each joint creates, thus reducing defection and reducing friction.
We compared our max forces and the pin-joints, taken from our ADAMS loading
analysis graph and we compare with the Bearing/Bushing rates below; we found
that all our forces were smaller than our Bearing/Bushing ratings which means that
we are not at risk of causing damage to any of our bearings or bushings. The force
capacity for our shoulder screws is not listed. However, after talking with a GSI he
told us that, “The shoulder bolt can withstand a much larger load than you would
apply in this project.” Using this knowledge we can assume the shoulder bolts will
not be damaged by deflection. This makes sense because the material in the screws
is Alloy Steel, which has a large Young’s Modulus and the bolts have a thick radius
which provides large support against outside loads.
Bearing/Bushing load ratings:
Steel Thrust Ball Bearing
Steel Washers, for 3/8" Shaft Diameter, 13/16" OD
Dynamic Load Capacity: 31 lb (From McMaster-Carr
SAE 841 Solid Bronze Thrust Bearing
for 3/8" Shaft Diameter, 3/4" OD, 1/16" Thick
Pressure max: 2,000 lb/in2 (From McMaster-Carr)
Area: 1.32536 in2
Load Capacity: 2650.71 lb (See Appendix A)
SAE 841 Bronze Sleeve Bearing
for 3/8" Shaft Diameter, 1/2" OD, 1" Length
Pressure max: 2,000 lb/in2 (From McMaster-Carr)
Area: .323611 in2
Load Capacity: 687.22 lb (See Appendix A)
The Dynamic Load Capacity of the Steel Thrust Ball Bearings are given directly on
the McMaster-Carr website and can be immediately compared to the forces at the
pin-joints.
The Load Capacity of the Bronze Thrust Bearing was calculated by using the Max
Pressure from McMaster-Carr of 2,000 lb/in2 and the Area of 1.32536(See
Appendix A). Applying the formula P=F x A to solve for force we obtained a Load
Capacity of 2650.71 lb which was the compared to the forces at the pin-joints
13
The Load Capacity of the Bronze Sleeve Bearing was calculated by using the Max
Pressure from McMaster-Carr of 2,000 lb/in2 and the Area of .323611 in2 (See
Appendix A). Applying the same P = F x A formula we obtained a Load Capacity
of 687.22 lb and then compared it to the forces at the pin-joints.
Below you can find
Coupler Link
Shoulder Bolt
Input Link
Thrust Washer
Bushing (2)
Thrust Bearing
Figure 3.6b
Cross Section
Coupler-Input, Coupler-Output
Thrust Washer
Shoulder Bolt
Coupler Link
Follower Link
14
Transmission
Sandwich
Figure 3.6c
Cross Section
Ground-Input
Ground Link
Thrust Washer
Bushing (3)
Thrust Bearing (2)
Follower Link
Transmission Sandwich
Thrust Washer
15
Figure 3.6d
Cross Section
Ground-Follower
3.7 Test Results
Several tests were performed on the final linkage in order to determine the force on
the linkage and therefore the required transmission ratio for a given DC motor.
Several weeks after these trials came the final testing results, which provided vital
information about the mechanism’s motion.
3.7.1 Initial Test
During the link force analysis, which was performed with an electronic
force meter, we registered a maximum force of 2.6 lbs (41.6 oz), which after
being multiplied by the length of the input link, Linput (9.08 in) and the safety
factor, SF (1.2), yielded a maximum torque, Tmax of 453.28 oz-in.
3.7.2 Final Test
In the final testing, our mechanism registered an angle offset of 0º, a
horizontal offset of 3.625 inches, forward offset of 8.5 inches, travel time of
9.2 seconds, deceleration speed of 9.8º/s and total volume of 1,202.91
square inches.
3.8 Revisions to Final Design
Alterations to the final design included the insertion of a dowel through the output
gear and input link, lengthening of the transmission sandwich spacers, and the
motor mount. We added a dowel, connecting the output gear and input link, offset
from the input joint so the gear and the input link rotated together throughout the
linkage motion. Our original input joint design did not leave enough room for the
height of the gear. We thus had to increase the length of the transmission sandwich
spacers to account this. We also had to decrease the radius of a transmission
sandwich spacer to make a path for the timing belt. Lastly we decided to design our
own motor mount, because we believed that the mount provided would not
adequately support the motor and forces acting on it. This also gave us flexibility on
choosing the location and direction of the motor.
16
4 Energy Conversion and Transmission
This section discusses the advantages of a belt-driven transmission and how it satisfies the
requirements of our design. The purpose of our transmission is to transfer the torque
output from the motor to the input link. Additionally, the transmission transforms the
torque through a gear ratio to allow the motor to operate under controlled conditions while
driving the linkage. Included in this discussion are calculations relating torque and speed
to determine the appropriate gear ratio for our design.
4.1 Down Selection: Belt vs. Gears
We prefer a belt-driven transmission because of its added flexibility to the designer
(center distance), lower cost compared to gears, shock absorption, and in the event
of a disruption in the loading (such as the mechanism striking the hard stop at a
high speed), the slipping of the belt ensures a safety overload mechanism, whereas a
gear-driven transmission may undergo internal damage. Lastly, in the event of a
design flaw that requires an unexpected modification to our linkage, the gear-driven
transmission may restrict our options for such a modification, whereas a belt
transmission provides the designer with flexibility.
4.2 Summary of Values
Combining the DC motor specifications provided by Pololu (Tstall (187.5 oz-in),
ωno-load @ 9V (60 RPM)) and the maximum torque required to move our linkage
(Tmax = 453.28 oz-in) derived from the link force test, we were able to calculate a
gear ratio of 5.59:1, which for the sake of safety we rounded to 6:1. Using free-run
current of 225 mA and stall current of 3750 mA of the DC motor at 9V, we
calculated the input power of the motor to be 13.60 W and using the previously
mentioned mechanical data, we measured the output power to be 2.08 W.
4.3 Operating Speed
The execution angle of our design is 176º, the first 146º (θ1) of which is operated at
a speed ωop and the last 30º (θ2) at a speed of 8 º/s (ω2). Also specified in the
project statement was the required runtime, trun of 9 seconds. Combining these
parameters into the following equation yields an operating speed ωop of 4.635 RPM:
t run =
θ1
ωop
+
θ2
ω2
Equation 4.3
4.4 Maximum Torque
During the link force analysis, which was performed with an electronic force
meter, we registered a maximum force of 2.6 lbs (41.6 oz), which after being
multiplied by the length of the input link, Linput (9.08 in) and the safety factor, SF
(1.2), yielded a maximum torque, Tmax of 453.28 oz-in.
17
4.5 Gear Ratio
Knowing Tstall, ωno-load @ 9V, ωop and Tmax allows us to use the following relationship
in point-slope form ([y-y1] = m[x-x1]) to solve for the desired gear ratio, N:
[N] ∗ [Tstall ] − [Tmax ] =
[N]∗[Tstall]
[N]−1 ∗[ωno−load @ 9V ]
∗ ([N]−1 ∗ [ωno−load @ 9V ] − [ωop ])
Equation 4.5
N was calculated to be 5.59:1, which for the sake of safety was rounded to 6:1.
This gear ratio was graphed and superimposed onto the motor torque speed curve
on the following page.
18
4.6 Torque Verification
Figure 4.6A
Below is verification that the motor satisfies the torque/speed requirements for the
high, medium and low torques (1050 oz-in, 560 oz-in, 290 oz-in, respectively)
given to us in the Gate 2 Review.
Figure 4.6 B
19
4.7 Speed and Time
Our low speed was first calculated by multiplying the desired motor velocity by the
transmission ratio. We then found the estimated time of low speed travel assuming
30 degrees of low speed travel. Next we subtracted this time from our total travel
time (nine seconds) to give us the time of high speed travel. We found the degrees
traveled during high speed travel by subtracting thirty degrees from the total
degrees traveled (176.2 deg, from report 2). Next, we divided the degrees traveled
during high speed travel by the time of high speed travel to get the high link speed.
Finally we multiplied this by our transmission ratio (N=6) to get the high motor
speed.
Given:
ωlink,low = 8º/sec
N=6
4.7.1 Motor Low Speed
ωmotor,low = ωlink,low * N
ωmotor,low = (8º/s)*(6) = 48º/s
Equation 4.7.1
4.7.2 Time of Low Speed Travel
Timelow = Distancelow / ωlink,low
Timelow = (30º) / (8º/s) = 3.75 s
Equation 4.7.2
4.7.3 Time of High Speed Travel
Timehigh = Timetotal – Timelow
Timehigh = 9 s - 3.75 s = 5.25 s
Equation 4.7.3
4.7.4 Angular Displacement at High Speed
Distancehigh = Distancetotal - Distancelow
Distancehigh = 176.2º-30º = 146.2º
Equation 4.7.4
4.7.5 Angular Velocity at High Speed
ωhigh = Distancehigh / Timehigh
ωhigh = 146.2º / 5.25 s = 27.85 º/s
Equation 4.7.5
4.7.6 Angular Velocity of Motor Shaft at High Speed
ωmotor,high = ωlink,high * N
ωmotor,high = 27.85 º/s * 6 = 167.09º/s
20
Equation 4.7.6
4.8 Remarks
After obtaining these values for Motor High and Low Speed we converted the
Distance Traveled at High and Low Speed (deg) to counts in order for the code to
read the encoder of the motor. These counts were thresholds for when the code
switched from low to high or high to low speeds. These count thresholds
corresponded to distances measured in degrees, not time.
In order to calculate the time we used a stopwatch to measure the time it took to
move from start to finish. It turned out that our time was too short (the linkage
moved too fast) so we adjusted the speed, in small increments, until the 9 second
goal was reached.
21
4.9 Input Power, Output Power Draw
Figure 4.8 A
Pololu DC Motor #1447:
Torque-Speed and Current-Speed Curves for 6:1 Gear Ratio
Figure 4.8 B
Relevant Speed/Current Equations
Ifree run @ 12V
300
12
=
=
Ifree run @ 9V
Ifree run @ 9V
9
I = mω + b
0.9 =
𝐈𝐟𝐫𝐞𝐞 𝐫𝐮𝐧 @ 𝟗𝐕 = 𝟐𝟐𝟓 𝐦𝐀
0.9 − 0.225
ω+b
10
I = 0.0675ω + 0.225
I stall @ 12V
5000
12
=
=
Istall @ 9V
Istall @ 9V
9
Operating current:
𝐈 𝐬𝐭𝐚𝐥𝐥 = 𝟑𝟕𝟓𝟎 𝐦𝐀
𝐈𝐰𝐨𝐩 = 𝐈 𝟓 𝐑𝐏𝐌 = 𝟓𝟔𝟐. 𝟓 𝐦𝐀
22
Figure 4.8 C
Functional Motor Block with Power Flow
Pout = Tω
Pin=VI=V*(Tmax/KI)=9*(453.28/6*50)
𝑷𝒊𝒏 = 𝟏𝟑. 𝟔𝟎 𝑾
Pin
Pout
𝑃𝑜𝑢𝑡 = (𝑇𝑜𝑝 ) ∗ (𝜔𝑜𝑝 )
Motor
Pout =
Ploss
Pout =
Tmax
ωno−load
∗
2
2
1128 oz − in
10
2π rad
∗
RPM ∗ (
)
2
2
60 sec
𝐏𝐨𝐮𝐭 = 𝟐. 𝟎𝟖 𝐖
𝑃𝑙𝑜𝑠𝑠 = 𝑃𝑖𝑛 − 𝑃𝑜𝑢𝑡
𝑷𝒍𝒐𝒔𝒔 = 𝟏𝟏. 𝟓𝟐 𝑾
4.9 Input Power, Output Power
The motor’s input power is 13.60 W and the output power is 2.08 W, yielding a
power loss of 11.52 W. The power quantity we can control is the mechanical
output power. We manipulate this output power with the 6:1 gear ratio. We are
designing the links and joints so that the power provided from the motor is directly
delivered to the input link by designing against friction and slip. The radial ball
bearings, thrust bearings, and thrust washers reduce the power loss, thereby
minimizing the power needed at the operating point. Although the consideration of
power minimization may be marginal in this case, it is a crucial theme because
minimal power consumption is a characteristic of intelligent design.
4.10 Mounts and Joints
This section discusses various mounts and joints used in our system. Torque
transfer and joint stress are considered, and included in the discussion are how they
relate to both deflection analysis and gate 1 parameters (volume,
horizontal/vertical/angle offset, safety, etc.).
4.10.1 Motor and Transmission Mounts
Whether for a motor or transmission, a mount is an important design theme
because it creates reaction forces, torques and bending moments that are not
negligible when considering other aspects of the design. As a precursor to
the next section on transmission loading, this section is comprised of both
explanations and images of mounts and torque-transferring joints. The
volume was somewhat affected by the addition of these mounts, since they
are located at the top of the linkage. We estimate that these mounts
contribute to 15% of the linkage’s total volume. We are unable to find any
effects of the mounting assemblies on the motion generation.
23
4.10.2 Torque Transferring Joints
Figure 4.10.2A
Transmission
(Isometric)
This 3-D isometric view shows our linkage design and focuses on our
transmission. The input to ground joint is supported by the transmission
sandwich plate, transmission sandwich spacers, and ground plate assembly,
which minimizes moments occurring at the input to ground joint.
The motor is mounted by a custom made motor mount assembly. We
believe that the bracket included with the motor is not strong enough to
counter any deflection caused by the transmission, and we decided to mount
the motor vertically so we would not need to transfer the direction of torque.
Our motor mount is made up of a plate and two rectangular spacers. It is
mounted to slots in the ground to allow adjustment of the mount and thus
the tension put on the belt.
24
4.10.2 Torque Transferring Joints (continued)
Figure 4.10.2B
Transmission
(Top)
This top view shows our linkage design focusing on our transmission
design. The ground link has a large area in this model because we have not
yet designed our mechatronic system for the wheelchair design.
25
4.10.2 Torque Transferring Joints (continued)
Figure 4.10.2C
Transmission
(Isometric #2)
(for more detail on part callouts see Assembly Plan in Appendix C)
This cut-away image shows the components of our input to ground joint.
The input link and 3.8”OD gear are attached by a press fitted pin offset from
the joint, as shown in the image above. The input link and 3.8”OD gear
rotate with respect to the shoulder bolt.
26
4.10.2 Torque Transferring Joints (continued)
Figure 4.10.2D
Transmission
(Isometric #2)
This cut-away image shows the input gear to motor connection. The input
gear has a snug fit to the motor’s shaft. The gear’s set screw is tightened
against the flat keyway on the motor shaft to keep the input gear in place
with respect to the motor shaft.
27
4.10.3 Transmission Loading
When designing a mount, important considerations have to do with the
reactionary physics of such a mount and the effects on the transmission and
surrounding componentry (in this case, joints). Included in this section are
discussions and calculations relating to such considerations.
4.10.31 Stress Analysis
A shear stress of 9234 ozf/in2 was found to be acting on the hole,
through which the dowel is press-fitted, connecting the input link to
the input gear. Although not negligible, this shear stress is not
significant enough to cause any deformation to the assembly,
especially because the use of thrust bearings reduces any reactionary
forces and friction.
Figure 4.10.31A
Side View of Assembly Under Stress
Figure 4.10.31B
Shear Stress Equation
T=F∗r
453.28 oz − in = F ∗ (1 in)
F = 453.28 ozf
F
τ=
A
τ = 453.28 ozf⁄(π ∗ (0.252 )in2 )
𝛕 = 𝟗𝟐𝟑𝟒 𝐨𝐳𝐟/𝐢𝐧𝟐
Sandwich Plate
Gear
Input Link
Sandwich Plate
Input Gear
Figure 4.10.31C
Ariel View of Assembly Under Stress
r
Input Link
τ
Gear Center
Dowel Hole
28
4.10.4 Deflection Analysis
A net horizontal force of 1954.94 oz was found to act on the motor shaft,
while a 1368.45 oz-in bending moment was found to be acting on the motor
itself by the top plate of the motor mount. The reaction forces of the
mounting plate were +/- 570.19 oz. A shear stress of 9234.14 ozf/in2 was
found to act on the joint through which a dowel was press-fitted to
accommodate the input gear and input link. Due to a normal stress of
3898.65 ozf/in2, the top plate of the mounting plate was found to deflect by
0.000267 vertically downwards. Although not negligible, these figures are
not significant enough to deform the assembly or cause any internal motor
or transmission damage.
4.10.41 Gear-Shaft Assembly
Figure 4.10.4B
Force Analysis:
Relevant Equations
Figure 4.10.4A
Ariel View of Motor Gear – Shaft Assembly
Shaft
ϕ
Motor Gear
F1 = dFa
F1 = 0.637 ∗ 185
F1 = 117.845 lbf
𝐅𝟏 = 𝟏𝟖𝟖𝟓. 𝟓𝟐 𝐨𝐳
F1
ϕ = ϕd = 2π arcsin D−d
2C
𝛟 = 𝟑𝟑. 𝟔𝟑 º
Fnet = F1 cos ϕ + F2 cos ϕ
𝐅𝐧𝐞𝐭 = 𝟏𝟗𝟓𝟒. 𝟗𝟒 𝐨𝐳
Fnet
ϕ
Where
F2
F1 − F2 = 2T⁄d
F2 = 2 ∗ 453.271⁄0.637
𝐅𝟐 = 𝟒𝟔𝟐. 𝟑𝟖 𝐨𝐳
29
d = diameter f gear above motor
D = diameter of gear over input link
ϕ = angle between forces acting on
gear and horizontal
4.10.42 Motor Shaft
Figure 4.10.42B
Force and Moment:
Relevant Equations
Figure 4.10.42A
Side View of Motor / Motor Mount Assembly
Shaft
Fnet
Fa
Fnet = 1954.94 oz = Fmount
Fb
M = 1954.94 oz ∗ 0.7 in
𝐌 = 𝟏𝟑𝟔𝟖. 𝟒𝟓 𝐨𝐳 − 𝐢𝐧
*(Fmount is an internal force
resulting from Fnet. Together they
produce a couple moment, M)
B
M
Fmount
Taking moments about point A and
assuming mass of the motor is
negligible…
A
LAB
MA = 0:
LAB FB − M = 0
2.4FB = 1368.45
FB = 570.19 oz
∴ 𝐅𝐀 = −𝟓𝟕𝟎. 𝟏𝟗 𝐨𝐳
Motor
Figure 4.10.42C
Deflection Analysis:
Relevant Equations
ρsteel = 7.8
g
oz
= 4.51 3
cm3
in
(. 21262 )
∗ 0.7 = 0.0248 in3
4
oz
= 0.0248 in3 ∗ 4.51 3 = 0.112 oz
in
Vmotor shaft = π ∗
∴ maxle
1 2 1
0.2126 2
mr = (0.112 oz)
= 0.000633 oz − in2
2
2
2
lbf
oz
Esteel = 29,000,000 2 = 464,000,000 2
in
in
(1954.94) ∗ (0.73 )
Fl3
δ=
=
= 𝟎. 𝟎𝟎𝟎𝟔𝟒𝟒 𝐢𝐧
3EI 3 ∗ (464,000,000) ∗ (0.000633)
I=
30
4.10.43 Motor Mount (Top Plate)
Figure 4.10.43A
Bending Diagram of Top Plate of Motor Mount
Fmount
M
Fmount
State 1
Fmount
M
State 2
M
Because the square piece that the motor is mounted to is screwed
into two side supports, treat the piece as a beam clamped at both
ends. Make a cut where the moment is applied and treat the plate as
two separate beam deflections.
Figure 4.10.43B
Bending Analysis:
Relevant Equations
𝜎𝑥,1 =
𝜎𝑥,1 =
𝜎𝑥,2
𝑀𝑦 𝐹𝑚𝑜𝑢𝑛𝑡
−
𝐼
𝐴
0.25 𝑖𝑛
1954.95 𝑜𝑧
𝑜𝑧
2
−
= −3898.65 2
2
1
𝑜𝑧
(.
25
∗
2)
𝑖𝑛
𝑖𝑛
(2.4 𝑖𝑛)(2 𝑖𝑛)(0.25 𝑖𝑛) 15.607 3 ∗ 2 ∗ (𝑏2 + 𝑙2 )
12
𝑖𝑛
(1368.45 𝑜𝑧 − 𝑖𝑛)
0.25 𝑖𝑛
1954.95 𝑜𝑧
𝑜𝑧
2
=
+
= 3898.65 2
2
1
𝑜𝑧
(.
25
∗
2)
𝑖𝑛
𝑖𝑛
(2.4 𝑖𝑛)(2 𝑖𝑛)(0.25 𝑖𝑛) 15.607 3 ∗ 2 ∗ (𝑏 2 + 𝑙 2 )
12
𝑖𝑛
(−1)(1368.45 𝑜𝑧 − 𝑖𝑛)
𝜎𝑦 = 0 = 𝜎𝑧
𝜀𝑦𝑦 = −
𝑣𝜎𝑥𝑥 −.33(−3898.65)
=
= 0.000223
𝐸
5780366.72
𝜀𝑦𝑦 =
𝑙 − 𝛥𝑙
𝑙
𝜟𝒍 = 𝟎. 𝟎𝟎𝟎𝟐𝟔𝟕 𝒊𝒏
The plate sinks by 0.000267 in
31
5 Safety and Motor Controls
The purpose of this section is to introduce the capabilities and limitations of the proximity
sensors, how threshold values were chosen for the IR sensors and the encoder, changes
made to Arduino code, and the mounting of the proximity sensors. This section covers the
mechatronic decisions made by our team in order to successfully meet goals for mechanism
movement and improve safety for the user.
5.1 Sensor Capabilities
The proximity sensors have the capability to sense an obstruction in the view range.
The output can then be interpreted by code to stop or start the desired motion. One
of the limitations of the sensors is that the range of view is a cylinder facing out
from the sensor which does not allow the proximity sensors to “see” objects that
approach from the side until they break the plane of the cylinder. Another
limitation is that the sensors do not take perfect readings and output ranges of
numbers at certain distances. These sensors also have a maximum range and can
have a “false positive” if readings are taken further out.
5.2 Threshold Values
The threshold values of the proximity sensors were chosen based on a guess and
check method. We did tests using a binder (large flat surface, gives consisting
blocking of sensor) to find the distance where the sensors needed to be triggered.
After each test we adjusted the code so the value of each sensor’s range would be
closer to the desired range. The final values of the proximity sensor’s values were:
500 and 140.
The threshold values of the encoder count were chosen using calculations based on
a total travel distance of 176.2 degrees (from report 2) and 30 degrees of low speed
travel. However, we ended up using 40 degrees for low speed travel because we
wanted to give a safety period of ten degrees for the mechanism to change speeds
and slow down to the lower speed. The total counts were measured by running the
mechanism in the forward direction and recording the max value of the encoder
count.
The calculations are shown in the next section and can be found in Appendix D.
5.3 Relevant Equations
The calculations required include the lower and upper count threshold.
5.3.1 Given and Measured Parameters
Givens and Measured:
Total Counts = 12963 counts
6 rev. gearbox
131 rev. encoder
32 counts/rev
32
5.3.2 Lower Count Threshold
40 deg of encoder rev. = 40deg(1 rev. input/360deg)(6 rev. gearbox/1 rev. input)
(131 rev. encoder/1 rev. gearbox)= 87.333 revolutions of encoder
LowerCountThreshold = (87.3 rev. encoder)(32 counts/1 rev.) = 2794.667 counts
5.3.3 Upper Count Threshold
UpperCountThreshold = TotalCount - LowerCountThreshold
UpperCountThreshold =12,963 counts - 2794.667 counts = 10,169 counts
5.4 Changes to Arduino Code
We made four changes to the Arduino code. The first change we made was in the
“void doEncoder”. The change was made because the program was adding a
negative number, one for each count, to the encoderCount value when going in the
forward direction. This gave us a large negative value when we needed to switch to
low speed, however the code was written expecting a positive value. Therefore, in
the “if( digitalRead(encoderPinA) == digitalRead(encoderPinB) )” we switched
“encoderCount++” to “encoderCount--”. The code was counting the numbers in an
opposite fashion when the mechanism was moving backwards so, in the “else” we
changed the “encoderCount--” to “encoderCount++”. These changes allowed the
high and low speeds to enable at the right time and the were determined based on an
understanding of how the encoder counts and talking with the GSI’s.
The second change we made to the code was adjusting the values for the High and
Low speed. This was done using a guess and check method. We changed the high
and low speed because our calculated values were not reaching the desired time of
nine seconds. We used a stopwatch to record the time it took the mechanism to
move in the forward direction. Our time was under nine seconds so we lowered the
high speed and the low speed until we reached the desired time. The high speed
was lowered more, from our calculated values, in order to decrease the amount of
power needed to move the backpack. The final value for high speed was: 60
deg/sec and the low speed was: 14 deg/sec.
The third change we made to the code was adjusting the proximity switch values.
These are the values that determine if an object is in a pinch point of the
mechanism. It is important that these values are precise because they are integral to
the safety of the mechanism. Again, we utilized a guess and check method. A
binder was used to trigger the sensors and then the values were adjusted in the code
based upon whether the sensor needed to reach further or closer. We repeated this
process until the sensors were triggered at the proper distances in order to protect
outside objects from getting pinched in the moving mechanism.
The fourth change we made to the code was changing the upper and lower threshold
count values. These needed to be changed in order for the high and low speed to be
used at the right angles in the mechanism’s motion. These values were determined
using calculations similar to those provided in the mechatronics lab tutorial.
33
The final change we made to the code was to the “float Ki” integration control
constant. We lowered this value to zero in order to eliminate the steady state error
and it was determined to lower it based on the suggestion from a GSI.
5.5 Sensor Mounting
Our Proximity Sensors are attached to the ground plate and are calibrated to sense
an obstruction near a pinch point. We chose to attach them to the ground plate so
the wires connecting the proximity sensors to the Arduino board would not get
tangled and would not have to move with every rotation of the mechanism. This
takes away a large possibility of failure from the wires breaking or failing under
heavy use.
We attached the proximity sensors by using the double sided tape. This held the
proximity sensor in place securely because the proximity sensor is light and does
not create that large of a torque on the tape.
A hand or object moving from above will be caught in the pinch point when the
mechanism is moving in the reverse direction; therefore, the first sensor is
positioned to sense any obstructions in the position above the linkage. This sensor
was calibrated at a value of 140.
A hand or object moving from below can also fit into a pinch point when the
mechanism is moving backwards, Therefore, the second proximity sensor is
positioned to sense any obstruction in the position below the linkage.
The sensors’ placement did not affect the previous volume or offset because they
were placed on the ground plate and did not extend out of the previous height,
length, or width.
34
6 Design Critique
As with every design, ours had its features and flaws. This section will clarify these
positive and negative attributes of the design process and derive meaning from the
experience as a whole.
6.1 The Good
The most positive aspects of the design process were the benefits of having a meticulously
planned model. For example, we cut no corners in the determination of each joint assembly
and the necessary bolts and bearings, which left us with no unpleasant surprises during the
manufacturing process. This sort of meticulousness ultimately played to our benefit.
Another benefit was the division of labor between the group. Mary and James were very
experienced with the lathe, whereas Greg and Sam were experienced with the mill. Given
that we had a variety of parts that required both machines, the group was able to divide the
labor based on the different skills of its members. Added to this division of labor was
Mary’s expertise with SolidWorks – a skill she honed during an internship. Mary’s
expertise allowed the group to quickly update changes to the CAD model in the case of a
design alteration.
In addition to being meticulous and varied in skillsets, the group was always diligent,
punctual and mindful of deadlines. The group always opted to contact Mr. Xu or Professor
Umbriac to avoid confusion that would have otherwise led to mistakes. We met often and
had the habit of planning our next meeting ahead of time. This ensured that we stayed on
schedule and met each requirement in a timely manner.
6.2 The Bad
The group is pleased to report that the occurrence of error was minimal. Despite very minor
errors made during manufacturing, we encountered no situations that required us to
remanufacture any vital components. These small, almost negligible errors included a
misinterpretation of a dimension on a motor mount drawing and consequently led to an
error in the hole locations. The error was resolved.
The most significant error was our failure to predict the effects of the belt tension on our
mechanism. Our transmission was designed in such a way that the belt would fit perfectly –
in other words, the belt tension was extremely high and caused stripping in the threaded
holes of the motor, consequently destroying the mechanism that kept the motor in place and
thus rendering our transmission useless. This failure inconveniently occurred during the
final testing and could have been avoided if we separated the belt from the transmission
during the overnight storage.
Prediction of these situations is a subtle, yet crucial theme of engineering and we became
more mindful and careful with these situations.
35
6.3 Linkage vs. Computer Model
Our mechanism behaved exactly like the computer models. The computer models were
designed in such a way to limit the forces on the joints to the maximum possible degree.
Because our linkage minimized friction at joints and its deflection analysis yielded
favorable values, we are pleased to report that our linkage behaves like the computer
model.
6.4 Load Considerations
Conditions for load are crucial considerations in the design, even if the mechanism operates
well with no load. The two major areas for load consideration are the loading of the
backpack and friction.
6.4.1 Loading of Backpack
The device moved slower when loaded with the backpack than under no load. The
added vertical force increases friction between joints therefore increasing the torque
required for motion. The added weight also increases the linkage’s moment of
inertia and greatly affects its start up speed and ability to decelerate.
6.4.2 Friction
We realize that friction greatly affected the required torque for motion. We
compensated for this by using thrust bearings at interfaces between moving links.
There were also instances where we used friction to our advantage. For instance, in
addition to a set screw, we relied on a press fit to attach the gear to the motor. We
also relied on a tight fit for an off axis pin to fit into the input link.
6.5 Mechatronics
When implementing a mechatronic system, one must consider the many tradeoffs and
effects involved in his options. The two major areas of consideration for mechatronics are
the control algorithm and the choice and placement of sensors.
6.5.1 Control Algorithm
One goal of the control algorithm is to maintain certain operating speeds. The
torque is not constant throughout operation, and when the linkage is loaded with the
backpack, these changes in torque are amplified. Therefore the control algorithm
can be adjusted to expect these changes in torque and therefore vary motor speed to
maintain a constant speed of the input link. Also, the control algorithm can be
improved by varying sensitivity of the proximity sensors throughout motion. This
would allow the proximity sensors to be mounted on moving links and more
accurately patrol pinch points while not being triggered by the linkage itself.
6.5.2 Sensors
The proximity sensors could have been used as limit switches. The presence of the
linkage would trigger sensor to stop the mechanism.
36
6.6 What We Could Have Done Differently
Although we had access to different aluminum stock, we decided on using the square
tubing for our links immediately without even considering the other materials. Using the
flat aluminum plate instead of the tubing would have allowed for a more compact design
and would have reduced the final volume of our linkage.
The supplies we were provided with such as screws for the motor were not optimized
for our device. Therefore, we should have spent more time on coming up with
alternative ways of mounting the motor apart from using screws.
In addition to paying more attention to our supplied materials we could have also
made changes within our team. Although we worked effectively together, we would
have liked to spend more time on the ideation phase. For instance we could have
created a physical sketch model of our final prototype prior to manufacturing to
iterate further on our design. This would have improved the overall quality of our
final product.
6.7 Mechanism Safety
On a scale from 1-5 (1 = very unsafe, 5 = very safe), our mechanism scores a 3.
The proximity sensors do a great job of protecting pinch points, however there are other
safety concerns that should be addressed. For instance, the motor and belt transmission are
exposed and it is possible for the users hair to get caught while sitting in the chair during
operation. Also, there is no sensor that prevents the linkage from hitting a casual onlooker.
A possible suggestion is a sensor that detects added stress to the motor that will turn off the
motor instead of allowing it to stall upon hitting an object.
6.8 Final Remarks
We would not recommend that our device go to market at this point. In addition to
the above stated safety issues, we feel that aluminum may not be the most
appropriate or appealing material to use. Also, we feel that there has not been enough
market research, and as a first prototype, there has not been enough design iteration.
Having a choice of more than one motor would have allowed more design freedom.
Also, smaller square tubing would have made it easier to make a more compact
design.
37