Research Papers

Efficiency of High-Sensitivity Gear Trains, Such as Cycloid Drives

[+] Author and Article Information
Jonathon W. Sensinger

Departments of Physical Medicine and
Rehabilitation/Mechanical Engineering,
Northwestern University,
Room 1309, 345 E, Superior Street,
Chicago, IL 60611
e-mail: Sensinger@ieee.org

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received July 24, 2012; final manuscript received April 5, 2013; published online xx xx, xxxx. Assoc. Editor: Avinash Singh.

J. Mech. Des 135(7), 071006 (May 24, 2013) (9 pages) Paper No: MD-12-1379; doi: 10.1115/1.4024370 History: Received July 24, 2012; Revised April 05, 2013

Compact, high torque ratio, high efficiency transmissions are required in many applications, such as robotics. However, compact size and high torque ratios often come at the expense of surprisingly low efficiency. Here we apply Del Castillo's sensitivity framework (Del Castillo, J. M., 2002, “The Analytical Expression of the Efficiency of Planetary Gear Trains,” Mech. Mach. Theory, 37(2), pp. 197–214) to explain the low efficiency of a subset of transmissions that exploit small differences in tooth number between gears to generate high torque ratios. We add adjustment factors for several transmissions within this category, such as cycloids and harmonic drives; demonstrate that the models match empirical results for the case of cycloids across a range of torque ratios, topologies, and roller conditions; and compare and optimize the topologies of the various mechanisms. We demonstrate that for this subset of transmissions, the efficiency approaches a function of the torque ratio.

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Sensinger, J. W., 2010, “Selecting Motors for Robots Using Biomimetic Trajectories: Optimum Benchmarks, Windings, and Other Considerations,” IEEE Conference on Robotics and Automation, pp. 4175–4181.
Weir, R. F. ff., and Sensinger, J. W., 2009, “Design of Artificial Arms and Hands for Prosthetic Applications,” Biomedical Engineering and Design Handbook, M.Kutz, ed., McGraw-Hill, New York, pp. 537–598.
Tuplin, W. A., 1957, “Designing Compound Epicyclic Gear Trains for Maximum Efficiency at High Velocity Ratios,” Mach. Des., April 4 issue, pp. 100–104.
Yang, D. C. H., and Blanch, J. G., 1990, “Design and Application Guidelines for Cycloid Drives With Machining Tolerances,” Mech. Mach. Theory, 25(5), pp. 487–501. [CrossRef]
Onvio, 2005, “Zero Backlash Speed Reducers Catalog (online),” http://www.onviollc.com/objects/pdf/onvio_catalog_zero-backlash-speed-reducers.pdf
Shin, J.-H. H., and Kwon, S.-M. M., 2006, “On the Lobe Profile Design in a Cycloid Reducer Using Instant Velocity Center,” Mech. Mach. Theory, 41(5), pp. 596–616. [CrossRef]
Sensinger, J. W., 2010, “Unified Approach to Cycloid Drive Profile, Stress, and Efficiency Optimization,” ASME J. Mech. Des., 132(2), pp. 1–5. [CrossRef]
Malhotra, S. K., and Parameswaran, M. A., 1983, “Analysis of a Cycloid Speed Reducer,” Mech. Mach. Theory, 18(6), pp. 491–499. [CrossRef]
Gorla, C., Davoli, P., Rosa, F., Longoni, C., Chiozzi, F., and Samarani, A., 2008, “Theoretical and Experimental Analysis of a Cycloidal Speed Reducer,” ASME J. Mech. Des., 130(11), p. 112604. [CrossRef]
Blagojević, M., Marjanović, N., Đorđević, Z., Stojanović, B., and Dišić, A., 2011, “New Design of Two-Stage Cycloidal Speed Reducer,” ASME J. Mech. Des., 133(8), pp. 1–15. [CrossRef]
Morita, T., and Sugano, S., 1996, “Development of 4-D.O.F. Manipulator Using Mechanical Impedance Adjuster,” IEEE International Conference on Robotics and Automation, Minneapolis, MN, pp. 2902–2907.
Sensinger, J. W., and Weir, R. F., 2006, “Improved Torque Fidelity in Harmonic Drive Sensors Through the Union of Two Existing Strategies,” IEEE-ASME Trans. Mechatron., 11(4), pp. 457–461. [CrossRef]
Albu-Schaffer, A., Eiberger, O., Grebenstein, M., Haddadin, S., Ott, C., Wimbock, T., Wolf, S., and Hirzinger, G., 2008, “Soft Robotics–From Torque Feedback-Controlled Lightweight Robots to Intrinsically Compliant Systems,” IEEE Rob. Autom. Mag., 15(3), pp. 20–30. [CrossRef]
Sensinger, J. W., and Weir, R. E. F., 2008, “User-Modulated Impedance Control of a Prosthetic Elbow in Unconstrained, Perturbed Motion,” IEEE Trans. Biomed. Eng., 55(3), pp. 1043–1055. [CrossRef] [PubMed]
Apró, F., 2003, “The Place of the Wolfrom (3K) Planetary Gear Drive Among Connected Drives,” International Conference on Power Transmissions, G.Dobre, ed., Sinaia, Romania, pp. 1–3.
Mathis, R., and Remond, Y., 2009, “Kinematic and Dynamic Simulation of Epicyclic Gear Trains,” Mech. Mach. Theory, 44(2), pp. 412–424. [CrossRef]
Tomczyk, H., 2004, “Adjusting Device With Planetary Gears,” U.K. patent, 2004, EP 1244880 B1.
Del Castillo, J. M., 2002, “The Analytical Expression of the Efficiency of Planetary Gear Trains,” Mech. Mach. Theory, 37(2), pp. 197–214. [CrossRef]
Buchsbaum, F., and Freudenstein, F., 1970, “Synthesis of Kinematic Structure of Geared Kinematic Chains and Other Mechanisms,” J. Mech., 5, pp. 357–392. [CrossRef]
Salgado, D. R., and Del Castillo, J. M., 2005, “Selection and Design of Planetary Gear Trains Based on Power Flow Maps,” ASME J. Mech. Des., 127(1), pp. 120–134. [CrossRef]
Sensinger, J. W., and Lipsey, J. H., 2012, “Cycloid Versus. Harmonic Drives for use in High Ratio, Single Stage Robotic Transmissions,” IEEE Conference on Robotics and Automation, St. Paul, MN, pp. 4130–4135.
Shigley, J. E., Mischke, C. R., and Budynas, R. G., 2004, Mechanical Engineering Design, McGraw-Hill, New York.
Harris, T. A., and Kotzalas, M. N., 2006, Essential Concepts of Bearing Technology, Taylor & Francis, Boca Raton, FL.
Koriakov-Savoysky, B. A., Aleksahin, I. V., and Vlasov, I. P., 1996, “Gear System,” U.K. patent, WO1996004493.
Mimmi, G. C., and Pennacchi, P. E., 2000, “Non-Undercutting Conditions in Internal Gears,” Mech. Mach. Theory, 35(4), pp. 477–490. [CrossRef]
Hwang, Y.-W. W., and Hsieh, C.-F. F., 2007, “Geometric Design Using Hypotrochoid and Nonundercutting Conditions for an Internal Cycloidal Gear,” ASME J. Mech. Des., 129(4), pp. 413–420. [CrossRef]
Chen, B., Fang, T., LiC., and Wang, S., 2008, “Gear Geometry of Cycloid Drives,” Sci. China, Ser. E: Technol. Sci., 51(5), pp. 598–610. [CrossRef]
Tuttle, T. D., 1992, “Understanding and Modeling the Behavior of a Harmonic Drive Gear Transmission,” Massachusetts Institute of Technology, Master thesis.
Taghirad, H. D., and Belanger, P. R., 1998, “Modeling and Parameter Identification of Harmonic Drive Systems,” ASME J. Dyn. Syst., Meas., Control, 120(4), pp. 439–444. [CrossRef]
Kennedy, C. W., and Desai, J. P., 2003, “Estimation and Modeling of the Harmonic Drive Transmission in the Mitsubishi PA-10 Robot Arm,” IEEE International Conference on Intelligent Robotics and Systems.
Harmonic Drive Technologies, 2001, “Harmonic Drive T-cup component gear sets,” p. 4. Available at: http://www.harmonicdrive.net/media/support/catalogs/pdf/csf-csg-catalog.pdf
Seyfferth, W., Maghzal, W., and Angeles, J., 1995, “Nonlinear Modeling and Parameter Identification of Harmonic Drive Robotic Transmissions,” IEEE International Conference on Robotics and Automation, Nagoya, Japan, pp. 3027–3032.
Tuttle, T. D., and Seering, W. P., 1996, “A Nonlinear Model of a Harmonic Drive Gear Transmission,” IEEE Trans. Rob. Autom., 12(3), pp. 368–374. [CrossRef]
Kircanski, N. M., and Goldenberg, A. A., 1997, “An Experimental Study of Nonlinear Stiffness, Hysteresis, and Friction Effects in Robot Joints With Harmonic Drives and Torque Sensors,” Int. J. Robot. Res., 16(2), pp. 214–239. [CrossRef]
Ghorbel, F. H., Gandhi, P. S., and Alpeter, F., 2001, “On the Kinematic Error in Harmonic Drive Gears,” ASME J. Mech. Des., 123(1), pp. 90–97. [CrossRef]
Loewenthal, S. H., and Zaretsky, E., 1985, Design of Traction Drives, NASA.
Puchhammer, G., 2011, “Wobble Mechanism,” U.S. Patent No. 2011/0237381 A1.


Grahic Jump Location
Fig. 2

Diagram of a wolfrom, topologically segmented into two stages, in series, with circuit structures for each stage

Grahic Jump Location
Fig. 1

Diagram of a wolfrom planetary gear train (left) and the circuit structure (right)

Grahic Jump Location
Fig. 3

Wolfrom efficiency, as a function of torque ratio and the maximum number of teeth per gear, ranging from 1–10 in (a) to 1–20 in (b) to 1–30 in (c). Wolfrom designs are plotted in black; two-stage planetary stacks are plotted in gray. The two circled points in (c) refer to the examples noted in the text.

Grahic Jump Location
Fig. 4

Cycloid assembly includes several parts centered around an input–output axis (including the input shaft, rollers, and output disk), and several parts centered around an eccentric cam (including the offset cam cycloid disk).

Grahic Jump Location
Fig. 5

Cycloid planetary gear trains: (a) a simple cycloid and (b) a compound cycloid. Circuit structures are shown to the left. The simple cycloid only uses circuit 1; the compound cycloid uses circuits 1 and 2.

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Fig. 6

Examples of cycloids tested. Two designs used N3 = 10: simple 10:1 cycloids and compound (100:1) cycloids. One design used N3 = 100 simple 100:1 cycloid. Rollers were either fused to the annulus or free to spin

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Fig. 7

Cycloid efficiency: comparison of data from our model and from empirical measurement. Empirical measurements are indicated by asterisk; model estimations are provided by the dashed horizontal line, with a boxed ±0.3% range in friction coefficient. This ±0.3% range without incorporation of the circumference effect (i.e., using η0 instead of ηc) is indicated by the vertical gray lines for those models that used fused rollers. Ys indicate the presence of fused rollers or the inefficient output bushing.

Grahic Jump Location
Fig. 8

Comparison of planetary, wolfrom, and cycloid drive efficiency. Theoretical cycloid efficiencies are overlaid on Fig. 3(c). These include the case when the cycloid uses rollers housed in ball bearings (η = 0.9992), when the cycloid uses free rollers (η = 0.993), and when the cycloid rollers are fused to the grounded annulus (in this case η is a function of the circumference, governed by the geometry, but a representative value of η = 0.985 was chosen based off the designs reported in this paper). Planetary and wolfrom efficiencies are shown for gear-teeth permutations within a 1–30 tooth range.

Grahic Jump Location
Fig. 9

Tuttle's model of harmonic drive gear meshing, modified from Ref. [33]




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