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TECHNICAL BRIEF

Interpolation Error Prediction of a Three-Degree Parallel Kinematic Machine

[+] Author and Article Information
Yang Wang

Dept. of Mechanical Engineering, Laval University, Quebec, Quebec, Canada, G1K 7P4 e-mail: ywang@gmc.ulaval.ca

Tian Huang

School of Mechanical Engineering, Tianjin University, Tianjin 300072, P.R. China e-mail: htiantju@public.tpt.tj.cn

Clement M. Gosselin

Dept. of Mechanical Engineering, Laval University, Quebec, Quebec, Canada, G1K 7P4 e-mail: gosselin@gmc.ulaval.ca

J. Mech. Des 126(5), 932-937 (Oct 28, 2004) (6 pages) doi:10.1115/1.1767184 History: Received January 01, 2004; Online October 28, 2004
Copyright © 2004 by ASME
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References

Iurascu,  C. C., and Park,  F. C., 2003, “Geometric Algorithms for Kinematic Calibration of Robots Containing Closed Loops,” ASME J. Mech. Des., 125, pp. 23–32.
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Merlet,  J. P., 2001, “A Generic Trajectory Verifier for the Motion Planning of Parallel Robots,” ASME J. Mech. Des., 123, pp. 510–515.
Nenchev, D. N., and Uchiyama, M., 1996, “Singularity-Consistent Path Planning and Control of Parallel Robot Motion Through Instantaneous-Self-Motion Type,” IEEE Int. Conf. On Robotics and Automation, pp. 1864–1870.
Huang,  T., Ni,  Y. B., and Wang,  Y., 2000, “Kinematic Design of 3-HSS Parallel Machine Tool,” China Manufacturing Tech. and Mach. Tool,3, pp. 10–12.
Wang, Y., 2002, “Development of Open Architecture Numerical Control System for Parallel Machine Tool,” Ph.D. dissertation, Tianjin University.
Koren,  Y., 1995, “Five-Axis Surface Interpolators,” CIRP Ann., 44(1), pp. 379–382.
Zhang, Q. G., and Greenway, R. B., 1997, “Real-Time NURBS Trajectory Generation for a Robot Using an Open-Architecture Controller,” MIM’97, pp. 862–866.

Figures

Grahic Jump Location
Diagram of Interpolation philosophy; (a) Straight line; (b) Circle
Grahic Jump Location
Diagram of theoretical error
Grahic Jump Location
The maximum singular value distribution
Grahic Jump Location
The figure of interpolation error (a) The distribution of sup(ε) on the plane z=0; (b) The variation of sup(ε) with the change of polar angle and the radius; (c) The variation of sup(ε) with the change of programming velocity; (d) The variation of sup(ε) with the change of interpolation period

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