Harmonic drive gears are widely used in space applications, robotics, and precision positioning systems because of their attractive attributes including near-zero backlash, high speed reduction ratio, compact size, and small weight. On the other hand, they possess an inherent periodic positioning error known as kinematic error responsible for transmission performance degradation. No definite understanding of the mechanism of kinematic error as well as its characterization is available in the literature. In this paper, we report analytical and experimental results on kinematic error using a dedicated research Harmonic Drive Test Apparatus. We first show that the error referred to in the literature as kinematic error actually consists of a basic component, representing “pure” kinematic error, colored with a second component resulting from inherent torsional flexibility in the harmonic drive gear. The latter component explains the source of variability in published kinematic error profiles. The decomposition of the kinematic error into a basic component and a flexibility related component is demonstrated experimentally as well as analytically by matching a mathematical model to experimental data. We also characterize the dependence of the kinematic error on inertial load, gear assembly, and rotational speed. The results of this paper offer a new perspective in the understanding of the mechanism of kinematic error and will be valuable in the mechanical design of harmonic drive gears as well as in the dynamic modeling and precision control of harmonic drive systems.

Issue Section:
Technical Papers
Keywords:
robot kinematics, position control, errors, flexible structures, manipulator kinematics
Topics:
Errors, Kinematics, Gears, Stress
1.
Harmonic Drive Technologies, Peabody, MA, 1995, HDC Cup Component Gear Set Selection Guide.
2.
Musser, C., 1955, “Strain Wave Gearing,” United States Patent Number 2,906,143.
3.
Musser, C., 1960, “Breakthrough in Mechanical Drive Design: The Harmonic Drive,” Mach. Des. pp. 160–172 (Research Adviser for the United Shoe Machinery Corp., Boston, MA).
4.
Emel’yanov
,
A.
, et al.,
1983
, “
Calculation of the Kinematic Error of a Harmonic Gear Transmission Taking into Account the Compliance of Elements
,”
Sov. Eng. Res.
,
3
, No.
7
, pp.
7
–
10
.
5.
Klypin
,
A.
, et al.,
1985
, “
Calculation of the Kinematic Error of a Harmonic Drive on a Computer
,”
Sov. Eng. Res.
,
5
, No.
11
, pp.
9
–
12
.
6.
Shuvalov
,
S.
,
1974
, “
Calculation of Harmonic Drives with Allowance for Pliancy of Links
,”
Russ. Eng. J.
54
, No.
6
, pp.
47
–
52
.
7.
Seyfferth, W., and Angeles, J., 1995, “A Mechanical Model for Robotic Joints with Harmonic Drives,” Technical Report, McGill University Department of Mechanical Engineering & Centre for Intelligent Machines, Montreal, Quebec, Canada. TR-CIM-94-13.
8.
Seyfferth, W., Maghzal, A., and Angeles, J., 1995, “Nonlinear Modeling and Parameter Identification of Harmonic Drive Gear Transmissions,” Proc. of the 32nd IEEE Conference on Robotics and Automation, pp. 3027–3032.
9.
Kircanski, N., Goldenberg, A., and Jia, S., 1993, “An Experimental Study of Nonlinear Stiffness, Hysteresis, and Friction Effects in Robot Joints with Harmonic Drives and Torque Sensors,” Proc. of the 3rd International Symposium on Experimental Robotics, pp. 327–340.
10.
Hidaka, T., Ishida, T., Zhang, Y., Sassahara, M., and Tanioka, Y., 1990, “Vibration of a Strain Wave Gearing in an Industrial Robot,” Proc. of the 1990 International Power Transmission and Gearing Conference—New Technology Power Transmission, pp. 789–794.
11.
Sakuta
,
H.
,
Yoshitani
,
Y.
, and
Yonezawa
,
T.
,
1988
, “
Vibration Absorption Control of Robot Arm by Software Servomechanism-2nd report
,”
Nihai Kikkai Gakk. Ronbun.
,
54
, No.
197
, pp.
217
–
220
. (In Japanese).
12.
Hashimoto, M., 1989, “Robot Motion Control Based on Joint Torque Sensing,” Proc. of the IEEE International Conference on Robotics and Automation, pp. 256–261.
13.
Tuttle
,
T.
,
1992
, “Understanding and Modeling the Behavior of a Harmonic Drive Gear Transmission,” Master’s Thesis, MIT. MIT Artificial Intelligence Laboratory Technical Report No. 1365.
14.
Tuttle, T., and Seering, W., 1993, “Kinematic Error, Compliance, and Friction in a Harmonic Drive Gear Transmission,” The 1993 ASME Design Technical Conferences—19th Design Automation Conference, pp. 319–324.
15.
Nye, T., and Kraml, R., 1991, “Harmonic Drive Gear Error: Characterization and Compensation for Precision Pointing and Tracking,” Proc. of the 25th Aerospace Mechanics Symposium, pp. 237–252.
16.
Hsia, L., 1988, “The Analysis and Design of Harmonic Gear Drives,” Proc. of the 1988 IEEE International Conference on Systems, Man, and Cybernetics, pp. 616–619.
17.
Ramson, R., 1988, “Positional Error Analysis of Harmonic Drive Gearing,” Master’s Thesis, Clemson University.
18.
Were
,
M.
, and
Ghorbel
,
F.
,
1997
, “Analysis and Control of Kinematic Error in Harmonic Gear Drive Mechanisms.” Internal Report ATP96-1, Dynamic Systems and Control Laboratory, Rice University Department of Mechanical Engineering.
19.
Hejny, S., and Ghorbel, F., 1997, “Harmonic Drive Test Apparatus for Data Acquisition and Control,” Internal Report ATP96-2, Dynamic Systems and Control Laboratory, Rice University Department of Mechanical Engineering.
20.
Gandhi, P., and Ghorbel, F., 1999, “Closed Loop Compensation of Kinematic Error in Harmonic Drives for Precision Control Applications,” Proc. of the IEEE 37th Conference on Decision and Control, Arizona, pp. 5268–5270.
21.
dSPACE Digital Signal Processing and Control Engineering GmbH, 1993, DSP-CITeco LD31/LD31NET User’s Guide.
Copyright © 2001
 by ASME
You do not currently have access to this content.