Proceedings of the ASME 2015 Dynamic Systems and Control Conference
DSCC2015
October 28-30, 2015, Columbus, Ohio, USA
DSCC2015-9782
DESIGN AND ASSESSMENT OF A HIGH SPEED LOW TORQUE JOINT
TRANSMISSION FOR USE IN A PARTIAL HAND, POWERED FINGER PROSTHESIS
Anton Filatov∗, Ozkan Celik
Biomechatronics Research Laboratory
Department of Mechanical Engineering
Colorado School of Mines
Golden, Colorado 80401
Email: [afilatov,ocelik]@mines.edu
Richard F. Weir
Biomechatronics Development Laboratory
Bioengineering Department
University of Colorado, Denver
Golden, Colorado 80401
Email: Richard.Weir@ucdenver.edu
ABSTRACT
This paper presents the design and assessment results of two
types of miniature, high speed, low torque transmissions to be
used in a partial hand, powered finger prosthesis. Transmissions enabling torque transfer across varied flexion angles of
a finger joint can allow placement of a motor and a gearbox
in adjacent phalanges, significantly decreasing space requirements for partial hand prostheses. Bevel gear-based and cablebased transmission designs for a variety of flexion angles are
implemented and tested in comparison with a direct cascaded
motor and gearbox (benchmark) configuration. The miter-gear
transmission provided consistent operation at tested flexion angles, but demonstrated reduced efficiency in comparison with
the benchmark configuration. Cable transmission matched efficiency of the benchmark configuration at low flexion angles but
lacked mechanical durability at high loads and flexion angles.
The designs presented complementary strengths and weaknesses,
with the miter-gear design demonstrating better overall mechanical reliability, while the cable transmission excelled in secondary
characteristics.
among newborns the situation is reversed. Over half (58%) of all
congenital limb deficiencies occur in the upper limb, with 46%
of those being partial hand [2]. Despite the innocuous sounding
modifier, partial hand loss can have severe consequences for the
function of the affected limb and the quality of life of the person [3]. The loss of a thumb alone can lead to a 40% impairment
rating in the affected hand, cascading to a 36% impairment in the
arm, and a whole body impairment rating of 22% [4].
To date, the vast majority of functional upper limb prosthesis designs have focused on more proximal amputation sites [5],
such as trans-radial deficiencies. Recent years have seen a proliferation of both commercial powered hand devices, such as
the BeBionicTM (RSL Steeper, Leeds, United Kingdom) [6] and
the i-limbTM quantum (Touch Bionics, Livingston, United Kingdom) [7] among others, and research-focused systems such as
the SmartHand [8]. Conversely, the field of partial hand powered prostheses is far less crowded, with only two companies
offering such a product, though a recent recognition of this product gap by the industry has contributed to some advances [9].
The i-LimbTM Digits device from Touch Bionics debuted in 2009
[10], with the similar VINCENT Finger prosthetic from Vincent Systems GmbH (Karlsruhe, Germany) following a shortly
after [11, 12]. The limited selection of powered devices addressing partial hand loss has objective underlying causes, such as the
highly individual nature of the residual limb and the high incidence of comorbidities [3].
1
Introduction
Among all persons with upper limb loss in the US, over 90%
have a partial hand loss, with trauma accounting for a large majority of cases [1, 2]. In addition, while lower limb amputation
is more common than upper limb loss in the adult population,
∗ Address
In addition, from a purely technical perspective, the small
volume available to house a power source, controller, actuator
all correspondence to this author.
1
Copyright © 2015 by ASME
Standard
Connection
Motor
a)
0°
Motor
72°
Motor
Gearbox
Miter
Transmission
Gearbox
Cable
b) Transmission
0°
Motor
72°
Motor
Gearbox
rbox
Gea
rbox
Gea
FIGURE 2: A simple diagram of the two types of transmission
tested - a) miter and b) cable. Both transmissions are shown at
0 and 72 of flexion. A standard motor-gearbox connection is
presented for reference at the top.
FIGURE 1: A conceptual visualization of the interphalangeal
transmission. The motor is housed in the medial phalange, while
the gearbox is in the proximal phalange.
shifts the entire motor assembly out of the palm, freeing up space
and potentially growing the pool of suitable candidates to include
those with phalangeal amputations. Persons with smaller limbs,
such as petite adults and adolescents will also benefit from this
approach, as the prosthesis may be scaled to match their anatomy
without compromising performance. Additionally, this arrangement could potentially be employed in traditional powered hand
prostheses, such as the i-limbTM and the BeBionicTM hand, which
are also constrained by space limitations. Note that this project
focuses on establishing the feasibility of such a design, leaving
concerns such as mechanically linking the finger phalanges to
generate realistic motion for later. In any case, a variety of such
linkages has already been demonstrated in current prostheses [5].
and mechanical transmission components presents a significant
design challenge. The use of current technology leads to compromises. In particular, the development of sufficient torque in the
finger requires the use of a geared electrical motor. The length of
this component is restrictive, using up the already scarce available volume, and forcing it to be at least partially located in the
palm section of the prosthesis. This limits the suitable users to
those with an amputation proximal to the metacarpal phalangeal
joint [10] and relegates the fingers to housing mostly passive elements. As an added consequence, none of the powered hand devices cited above utilize fingers with three phalangeal segments
as is the case in the organic hand. Thus, a more innovative arrangement of the actuator components is required in order to address these limitations.
In summary, even though persons with partial hand loss account for an overwhelming percentage of all people with upper
limb deficiencies, lack of space available to house the necessary components for a powered finger prosthesis contributes to
a dearth of assistive devices for this population. This project
aims to address this specific technological problem by designing
and implementing a novel finger joint transmission that can efficiently utilize the volume available in a finger prosthesis. This
approach aims to grow the pool of suitable users for these devices, potentially being particularly significant for users with
smaller limbs.
An alternative system which could address the issue is one
in which the motor and gearbox are separated and housed in the
proximal and middle phalanges of the finger prosthesis, respectively (see Fig. 1). The motor transmits the torque to the gearbox through the interphalangeal joint, and the gearbox output
actuates the entire digit through mechanical linkages. This setup
Appropriately sized motors and gearboxes are readily available on the market (from Faulhaber or Maxon), and thus the design hinges on the creation of a durable interphalangeal transmission capable of passing the high speed, low torque output of the
motor across a joint capable of moving through at least 90◦ of
relative rotation.
In this study, prototypes of three such transmissions were
built and tested using a custom motor characterization setup. Of
the three prototypes, two utilized miter gears of different materials (metal and plastic) and the third used a cable. A basic diagram
comparing the transmissions with a standard motor-gearbox connection is provided in Fig. 2. This paper describes the details
of the construction of the transmissions, as well as their performance in terms of power and efficiency. Section 2 describes the
materials and design details for the transmissions and the used
for characterization. Sections 3 and 4 present the results obtained and a discussion comparing the advantages and limitations
of each type of transmission. Section 5 concludes the paper.
2
Copyright © 2015 by ASME
meshed even as the relative angle of the motor and the gearbox
was changed. All three shafts were supported by ball bearings.
Ignoring the length of the connector shafts, the length of the active components of this gearbox in the 0◦ flexion configuration
was 15mm.
It should be noted that since all three of the miter gears
had the same diameter, in the 90◦ configuration, the gears on
the output of the motor and the input of the gearbox interlocked
with each other, preventing rotation. Through manual adjustment of the relative positions of the gears, rotation at 90◦ could
be achieved, though with suboptimal meshing and efficiency. Because of this limitation, the characterization tests were limited to
the first five of the six finger joint angle conditions (0◦ to 72◦ ).
FIGURE 3: Finger joint transmission test bench, in a 54◦ relative
2.2.2 Plastic For the plastic version of the intermediary transmission, the brass miter gears discussed above were
replaced with nylon miter gears sourced from McMaster-Carr
(.375” pitch diameter, 18 teeth). Though not an exact geometrical match for the brass miters, these gears were similar enough
to provide a reliable comparison between the two materials. In all
other respects, this setup replicated the one used with the metal
gears.
flexion configuration.
2 Methods
2.1 Testing Setup
The testing setup consisted of a 3D-printed housing which
allowed for controlled angular displacement of the motor output
shaft relative to the gearbox input shaft (see Fig. 3). The gearbox
was held steady, while the motor section was left free to rotate.
Its angle relative to the gearbox could be adjusted between 0◦
and 90◦ , and secured at six settings in increments of 18◦ .
The motor used for all tests of both prototypes was a Faulhaber 1724SR (6V, 1.75A) with an attached IEH2 4096 CPR
(counts per revolution) encoder. The motor was always powered at nominal voltage. The gearbox used was a Faulhaber 16/7
three stage planetary gearbox with a 66:1 reduction ratio. A pulley with a diameter of 50mm was attached to the output of the
gearbox via a set screw. To provide a known load for torque output testing, bottles of water were used, the weights of which were
verified using a digital scale with an accuracy of 2.5g. A Quanser
Q8-USB data acquisition board interfaced with Matlab/Simulink
was used to record the output of the encoder, and a Rigol DP832
power supply was used to power the motor and monitor the current draw.
2.3
Cable Transmission
The cable transmission prototype consisted of a single
length of cable running between the output of the motor and the
input of the gearbox. A close up of the design is shown in Fig.
4. Similarly to the miter gear transmission, two steel shafts were
machined to create a mechanical connection to the motor and the
gearbox. A small (0.410” diameter) hole was drilled in the free
ends of the shafts, and the cable was inserted and secured using
set screws. The total length of the cable was limited to less than
10 mm, though as with the miter gear transmission the overall
distance between the motor and the gearbox was larger due to
the connector shafts. The input shaft of the gearbox was supported by a ball bearing, however the bearing on the output shaft
of the motor was removed, since its presence markedly decreased
the efficiency of the system. This effect was most likely due to
loose tolerances in cable positioning.
Several cables were pilot tested for use in the transmission,
including those specifically designed for torque transmission.
However, these cables did not present sufficient flexibility to provide efficient transfer of torque with 10mm length. For final testing presented in this study, nylon coated stranded stainless steel
R Micro Supreme, 40-lbs test,
fishing wire was used (Surflon
American Fishing Wire). This cable had the advantages of low
cost and ease of availability, and also met the bending flexibility
requirements of the application. However, since it’s design was
not optimized for torque transmission, it suffered from durability
problems, especially under high speeds which result in significant cyclic loading at various joint angles.
2.2
Miter Gear Transmission
2.2.1 Metal The metal miter gear intermediary transmission prototype was composed of three straight brass miter
gears sourced from Boston Gear (0.312” pitch diameter, 15
teeth). A close up image of the prototype is shown in Fig. 4.
One of the gears was press fit onto a custom machined shaft secured by a set screw to the output of the motor, the other to a
custom shaft connected to the input of the gearbox. The third
gear, acting as an intermediary connection between the other two
was placed on a freely rotating shaft, which ran perpendicular
to the other shafts. This configuration enabled the gears to stay
3
Copyright © 2015 by ASME
FIGURE 4: Close up of the three transmission prototypes: metal miter (left) plastic miter (center) and cable (right). For reference the
gearhead and motor body diameters are 16 and 17 mm respectively.
2.4
Testing Procedure
experimental data. The next iteration of the test setup will feature
an increased load limit and allow for a more complete evaluation
of the plastic gearbox design.
Benchmark data was collected using a Faulhaber 1724SR
(3V, 3.81A) motor, connected to the same 66:1 gearbox using a
standard pinion and collar, hence in the direct cascaded configuration that is currently used in powered hand prostheses. The
benchmark motor, while not identical to the motor used for the
prototype transmission systems, was a very similar motor which
provided a relevant benchmark condition for comparison with the
performance of the three joint transmissions. For all configurations, overall efficiency of the combined motor, transmission and
gearbox system was calculated by comparing mechanical power
generated at the gearbox output shaft with the electrical power
provided to the motor.
For all tests, a known load (0–600g) was attached to the output pulley of the Faulhaber gearbox. The motor was powered,
and torque supplied by the output gearbox caused the pulley to
rotate, lifting the load. Encoder counts were recorded throughout
the test, and processed to provide a record of the rotational velocity of the motor. This velocity, combined with the known torque
applied to the output, was used to calculate the overall power output. The current draw of the motor was manually recorded from
the readout of the power supply. In combination with the nominal voltage supplied to the motor, the current draw was used
to calculate the total electrical power used by the system in a
given condtion. From the power input and ouput values, an overall efficiency for the system was calculated. For a majority of
the tests, the current value was stable within 2mA. At a given
load level, the test was repeated for all flexion settings from 0◦
to 72◦ in 18◦ increments (total of five joint angle conditions).
The load was then incremented by 100 g (total of six loading
conditions), and the testing started over from the 0◦ flexion condition. For the both of the miter gear designs, this process was
followed throughout all tests. However, the cable transmission
tests involved numerous mechanical failures of the cable during testing, and thus the tests for the cable transmission did not
follow the same monotonously increasing order of loading conditions. The results for the cable transmission presented in the
next section are derived from data obtained during several separate testing sessions with a variety of loads. This is elaborated
on in the Discussion section below. The 600 g load limit was
imposed by the mechanical constraints of the test setup - loads
higher than this overwhelmed some of the 3D printed components of the setup, preventing data collection. This limit affected
only the plastic miter transmission, as both of the other prototypes stalled or failed below the 600 g threshold. The available
data for the plastic geared transmission still allows for a meaningful and relevant comparison of its performance. In addition,
the performance of the plastic miter design beyond the 600g load
limit was forecast based on a linear extrapolation for the obtained
2.5
Analysis
During testing, the following data were recorded - motor
speed, ω (RPS), motor current, i (A) and test load, M (kg).
Relevant constants include the cable pulley radius, L = 50 mm,
the gearbox reduction ratio, Rg = 66, and the motor voltage,
Vin = 6.02 V. The mass of the cable used to haul up the test
load was disregarded, and the pulley radius was assumed to
be constant over the course of all test runs. From these data
and known constants, three performance characteristics of the
motor-gearbox combinations were calculated - stall torque, Tstall ,
power output, Pout and overall system efficiency, η. Note that all
characterization considered the performance of the entire motortransmission-gearbox system, rather than the performance of
each individual part. However, since the motor and gearbox were
identical during all transmission tests, the data allows for a comparative evaluation of the transmission designs.
The torque, T, on the gearbox output was calculated as follows:
T = g∗L∗M
4
(1)
Copyright © 2015 by ASME
where g is the acceleration due to gravity. The stall torque, Tstall ,
was defined as the torque at which the system failed to raise the
test load. The power output of the system was calculated as follows:
Pout =
2∗π ∗ω ∗T
Rg
cable design, both of the miter transmissions had lower overall efficiency, peak power, and a slightly faster drop off in the
speed-torque curve. However, the geared transmissions were far
more reliable, completing all 30 tests without a mechanical failure. Their performance was also insensitive to the relative angle
between the motor and the output gearbox. Conversely, while the
cable transmission at times demonstrated performance comparable to the benchmark case, it failed to complete 7 of the 30 test
conditions due to mechanical failure. In addition, its efficiency
was highly sensitive to the angle of deflection between the motor
and the gearbox. However, the cable transmission was found to
be significantly superior to both miter designs in secondary characteristics, such as noise level, weight, and length. In addition, its
manufacture was far simpler and required far looser tolerances of
the various mechanical connectors than those demanded by the
miter gear transmissions.
When looking at the miter design, nylon is clearly the superior material choice for this low-torque, high-speed application.
The overall performance of the miter transmission could be improved through tighter tolerances in custom connection shafts, as
well as reduction in the unwanted vibration in the system through
additional bearings. Increased precision in the positioning of the
gears could produce better meshing, leading to increased efficiency and reduced noise levels. An intermediary miter gear
that is slightly larger in diameter than the input and output gears
would remove the restriction on operation at a flexion angle of
90◦ , but would increase the space needed.
The cable transmissions mechanical failures are unsurprising given that the cable itself was not designed for torque transmission. However, the problems leading to failure must be systematically addressed for further development of this type of
transmission, despite the promise held out by its peak performance. The main mode of failure was a coiling of the cable in
on itself, which drew the motor and the gearbox closer together,
quickly locking up the entire system, and rendering the cable
unusable. This mode of failure was exacerbated by minute axial misalignments of the cable, and became especially prominent
under heavier loads and higher flexion angles. When the axial
displacements of the motor and gearbox were restricted, the resulting tension in the cable transmission made rotation extremely
inefficient or completely blocked motion. Tighter tolerances in
the manufacturing of the custom shaft connectors can reduce the
impact of this problem. However, the use of cables specifically
optimized for bi-directional torque transmission (such as double
wound cables), while still capable of the flexibility requirements,
might be the only way to significantly improve transmission performance at high torques and flexion angles.
While all of the constructed prototypes had their shortcomings, we believe that the observed problems do not prohibit development of a finger joint transmission which can satisfy majority of the design requirements. Even though the overall efficiency of the two miter gear transmission was lower than the
(2)
Finally, the efficiency of the system was determined as a ratio of
the power input and output:
η=
Pout
Pout
=
Pin
i ∗Vin
(3)
The results of these calculations were used to generate the motor
characterization curves presented in the Results section.
3
Results
Figure 5 reports the speed-torque, power and overall mechanical efficiency results for both transmission prototypes,
across the five joint angles. The missing data points in the cable transmission curves correspond to conditions under which
the cable experienced consistent failure, which are described in
detail the Discussion section.
4
Discussion
The performance of the three transmission designs reveals a
pattern of strengths and weaknesses. The plastic miter transmission outperforms its metal counterpart across the board, demonstrating better efficiency under all load and flexion angle conditions. Compared with the benchmark condition, the average relative efficiency of the plastic gearbox across all loads and rotation
angles was 75% compared to only 57% for the metal miter transmission. In addition, the predicted stall torque of the plastic miter
transmission is 390 N-mm, compared to 293 N-mm for the metal
miter setup. Both of these stall torques are below the predicted
performance of the benchmark setup (440 N-mm), with the plastic gearbox projected to reach 88% of the benchmark stall torque,
while the metal miter stalled at 66% of the projected benchmark
performance. However, as mentioned above, the motor used in
the benchmark transmission was similar, but not identical to the
one used for the flex transmission testing. In particular, the test
motor (Faulhaber 1724SR, 6V) is rated at 87% of the stall torque
of the benchmark motor (Faulhaber 1724SR, 3V). Thus, the projected stall performance of the plastic miter transmission matches
that of the benchmark setup, when adjusted for the difference in
motor performance.
This superior performance may be attributed to the more
forgiving nature of nylon, which allows for slightly looser tolerances in the meshing of the gears. When compared with the
5
Copyright © 2015 by ASME
Metal Miter Speed−Torque Curve
150
50
100
150
Torque (mNm)
200
250
Metal Miter Power Curve
Power Output (W)
0.5
100
150
Torque (mNm)
200
250
Overall Efficiency (%)
20
10
150
Torque (mNm)
250
300
350
400
0
0
450
200
Plastic Miter Power Curve
250
Experimental
50
100
50
100
150
200
250
Torque (mNm)
300
350
400
40
30
20
10
0
0
300
0 deg
50
18 deg
100
150
200
250
Torque (mNm)
36 deg
54 deg
300
350
72 deg
400
450
300
250
300
250
300
0.5
50
100
150
Torque (mNm)
200
Overall Cable System Efficiency
50
Predicted
250
1
Overall Plastic Miter System Efficiency
Experimental
200
1.5
0
0
450
150
Torque (mNm)
Cable Power Curve
2
Predicted
0.5
50
30
100
200
1
0
0
Overall Metal Miter System Efficiency
50
150
1.5
300
40
0
0
100
2
1
50
50
Torque (mNm)
1.5
50
0
0
300
50
Power Output (W)
50
2
0
0
RPM
100
Overall Efficiency (%)
0
0
Cable Speed−Torque Curve
150
Predicted
RPM
50
Power Output (W)
Experimental
100
RPM
100
Overall Efficiency (%)
Plastic Miter Speed−Torque Curve
150
40
30
20
10
0
0
50
100
150
Torque (mNm)
200
Benchmark
FIGURE 5: Mechanical performance of the two transmission prototypes. Note that efficiency values were calculated for the entire
system, including the motor and the output gearbox. The performance characteristics of the metal miter transmission is presented on the
left, those of the plastic miter transmission are shown in the center, and the cable transmission results are presented on the right. Note
the inclusion of theoretical, extrapolated data in the plastic miter graphs.
benchmark system, they demonstrated consistent operation and
efficiency across varied joint angles. Nylon gears are clearly the
superior choice and offer improvements in all performance criteria. Future work will include a more extensive evaluation of the
performance of the plastic gears at higher loads. Achieving 90◦
flexion torque transmission is possible by using a larger diameter
intermediary gear. The performance of the cable transmission
was promising, but in order to be considered a truly viable solution, a cable with the correct torque transmission capabilities
needs to be used. Such a cable would need extremely high bending flexibility (to reduce resistance or loss of efficiency due to
high frequency bending it goes through during non-zero joint angles) while presenting sufficient torsional stiffness to carry the
torque without twisting or curling.
components restricted the maximum torque that could be applied
to the system, and in particular prevented a thorough testing of
the plastic miter gear transmission. As mentioned above, work
is underway on the next version of the test setup, which will be
manufactured out of aluminum. In addition to allowing the application of higher loads to the motor-gearbox system, the use of
metal components should also increase the overall precision of
the entire assembly, resulting in more accurate estimations of the
system performance.
Though system torque, power, and efficiency were characterized, other characteristics such as stiffness and backlash were
not considered to date.
The authors acknowledge that the current technology
demonstration is yet far removed from a functional prosthetic finger. Challenges such as component miniaturization and selection
of appropriate phlangeal linkages remain. However, the results
of the current study can be viewed as providing an impetus to
solving these additional issues on the way to future partial hand,
powered finger prostheses.
4.1
Limitations
The main limitation of the current study was the mechanical
durability and sturdiness of the testing setup. The use of plastic
6
Copyright © 2015 by ASME
5
Conclusion
We presented design and characterization results for two
types of high speed, low torque transmissions that operated under shaft misalignments ranging from 0◦ to 90◦ , intended for implementation in powered finger prostheses. The miter gear-based
transmission presented consistent operation under all load conditions and joint angle positions, except 90◦ degree flexion, but its
efficiency was less than the nominal direct cascaded connection.
Cable-based transmission presented highly successful results in
low flexion angles and loads, with efficiencies matching that of
the benchmark scenario, however they were prone to mechanical
failure at high loads and flexion angles. The results obtained will
inform future transmission designs for powered finger prostheses.
[9] Fairley, M., 2009.
“State-of-the-art:
Upperlimb prosthetics technology”.
The O&P EDGE
[http://www.oandp.com/articles/2009-10-01.asp].
[10] Anon., n.d., accessed: 7-26-2015.
“i-limb digits”.
[http://www.touchbionics.com/products/active-prostheses
/i-limb-digits-partial-hand-solution].
[11] Anon., n.d., accessed: 7-31-2015. “VINCENTfinger”.
[http://handprothese.de/vincent-finger/].
[12] Schulz, S., 2011. “First experiences with the vincent hand”.
Myoelectric Symposium.
6
Acknowledgments
This project was supported in part by a Colorado School
of Mines and Children’s Hospital Colorado Collaboration Pilot
Award.
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