DESIGN AND ASSESSMENT OF A HIGH SPEED LOW TORQUE JOINT TRANSMISSION FOR USE IN A PARTIAL HAND, POWERED FINGER PROSTHESIS

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1 Proceedings of the ASME 25 Dynamic Systems and Control Conference DSCC25 October 28-3, 25, Columbus, Ohio, USA DSCC 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 84 Richard F. Weir Biomechatronics Development Laboratory Bioengineering Department University of Colorado, Denver Golden, Colorado 84 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 4% 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 29 [], with the similar VINCENT Finger prosthetic from Vincent Systems GmbH (Karlsruhe, Germany) following a shortly after [, 2]. 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]. Introduction Among all persons with upper limb loss in the US, over 9% have a partial hand loss, with trauma accounting for a large majority of cases [, 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. Copyright 25 by ASME

2 Standard Connection Miter a) Cable Transmission b) Transmission FIGURE : A conceptual visualization of the interphalangeal transmission. The motor is housed in the medial phalange, while the gearbox is in the proximal phalange. 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 [] 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. ). 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 FIGURE 2: A simple diagram of the two types of transmission tested - a) miter and b) cable. Both transmissions are shown at and 72 of flexion. A standard motor-gearbox connection is presented for reference at the top. 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-limb TM and the BeBionic TM 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]. 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 9 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 25 by ASME

3 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 flexion configuration was 5mm. It should be noted that since all three of the miter gears had the same diameter, in the 9 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 9 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 ( to 72 ). FIGURE 3: Finger joint transmission test bench, in a 54 relative flexion configuration. 2 Methods 2. 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 and 9, and secured at six settings in increments of 8. The motor used for all tests of both prototypes was a Faulhaber 724SR (6V,.75A) with an attached IEH2 496 CPR (counts per revolution) encoder. The motor was always powered at nominal voltage. The gearbox used was a Faulhaber 6/7 three stage planetary gearbox with a 66: reduction ratio. A pulley with a diameter of 5mm 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. 2.2 Miter Gear Transmission 2.2. Metal The metal miter gear intermediary transmission prototype was composed of three straight brass miter gears sourced from Boston Gear (.32 pitch diameter, 5 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 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, 8 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. 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 (.4 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 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 mm length. For final testing presented in this study, nylon coated stranded stainless steel fishing wire was used (Surflon R Micro Supreme, 4-lbs test, 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. 3 Copyright 25 by ASME

4 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 6 and 7 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 724SR (3V, 3.8A) motor, connected to the same 66: 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 ( 6g) 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 to 72 in 8 increments (total of five joint angle conditions). The load was then incremented by g (total of six loading conditions), and the testing started over from the 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 6 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 6 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 6g 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 = 5 mm, the gearbox reduction ratio, Rg = 66, and the motor voltage, Vin = 6.2 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 () Copyright 25 by ASME

5 where g is the acceleration due to gravity. The stall torque, T stall, 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: P out = 2 π ω T R g (2) Finally, the efficiency of the system was determined as a ratio of the power input and output: η = P out P in = P out i V in (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 39 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 (44 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 724SR, 6V) is rated at 87% of the stall torque of the benchmark motor (Faulhaber 724SR, 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 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 3 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 3 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 9, 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 5 Copyright 25 by ASME

6 5 Metal Miter Speed Torque Curve 5 Plastic Miter Speed Torque Curve Experimental Predicted 5 Cable Speed Torque Curve RPM RPM RPM Metal Miter Power Curve 2 Plastic Miter Power Curve Experimental Predicted 2 Cable Power Curve Power Output (W).5.5 Power Output (W).5.5 Power Output (W) Overall Efficiency (%) Overall Metal Miter System Efficiency Overall Efficiency (%) Overall Plastic Miter System Efficiency Experimental Predicted Overall Efficiency (%) Overall Cable System Efficiency deg 8 deg 36 deg 54 deg 72 deg 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 9 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. 4. Limitations The main limitation of the current study was the mechanical durability and sturdiness of the testing setup. The use of plastic 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. 6 Copyright 25 by ASME

7 5 Conclusion We presented design and characterization results for two types of high speed, low torque transmissions that operated under shaft misalignments ranging from to 9, intended for implementation in powered finger prostheses. The miter gear-based transmission presented consistent operation under all load conditions and joint angle positions, except 9 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., 29. State-of-the-art: Upperlimb prosthetics technology. The O&P EDGE [ [] Anon., n.d., accessed: i-limb digits. [ /i-limb-digits-partial-hand-solution]. [] Anon., n.d., accessed: VINCENTfinger. [ [2] Schulz, S., 2. 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. REFERENCES [] Ziegler-Graham, K., MacKenzie, E. J., Ephraim, P. L., Travison, T. G., and Brookmeyer, R., 28. Estimating the prevalence of limb loss in the United States: 25 to 25. Archives of Physical Medicine and Rehabilitation, 89(3), pp [2] Dillingham, T. R., Pezzin, L. E., and MacKenzie, E. J., 22. Limb amputation and limb deficiency: epidemiology and recent trends in the United States. Southern Medical Journal, 95(8), pp [3] Whelan, L., Flinn, S., and Wagner, N., 24. Individualizing goals for users of externally powered partial hand prostheses.. Journal of Rehabilitation Research & Development, 5(6), p [4] Rondinelli, R. D., Genovese, E., Brigham, C. R., Association, A. M., and others, 28. Guides to the evaluation of permanent impairment. American Medical Association. [5] Belter, J. T., Segil, J. L., Dollar, A. M., and Weir, R. F., 23. Mechanical design and performance specifications of anthropomorphic prosthetic hands: a review. J Rehabil Res Dev, 5(5), pp [6] Anon., n.d., accessed: Bebionic. [ [7] Anon., n.d., accessed: i-limb. [ [8] Cipriani, C., Controzzi, M., and Carrozza, M. C., 2. The SmartHand transradial prosthesis. Journal of neuroengineering and rehabilitation, 8(), p Copyright 25 by ASME