Abstract
In this paper, an inverse kinematic model has been used for the computation of joint coordinates, given the Cartesian coordinates of five-axis manipulators of arbitary architecture. The model leads to a formally overdetermined nonlinear algebraic system of six equations in five unknowns. Their least-squares approximations produce the desired joint coordinates. Monte Carlo method is developed to find the initial guess for these nonlinear equations. This procedure is illustrated on a five axis robot. The algorithm developed is found to be more efficient when compared with that of continuation techniques. The method developed can also be used to analyze high nonlinear equations in kinematics. Then using an optimization algorithm the inverse kinematic solutions have been obtained.
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References
Angeles, J. “Iterative Kinematic Inversion of General Five-Axis Robot Manipulators” Int. J., Robotic Research, Vol. 4, No.4, pp59–70, Winter 1986.
Angeles, J., Rojas, A. A. “Manipulator Inverse Kinematics via Condition-number Minimization and Continuation” Int. J., Robotics & Automation, Nov. 1986.
Denavit, J. “Description and Displacement Analysis of Mechanisms Based on 2x2 Dual Matrics” Ph.D Thesis, Mechanical Engineering, Northwestern U., Evanston, I11., 1956.
Frobery, C. E. “Numerical Mathematics” The Benjamin/Cummings Publishing Company, Inc., 1985.
Fu, K. S., Gonzalez, R. C. and Lee, C. S. G., “Robotics: Control, sensing, vision, and intelligence” McGraw-Hill Book Company, 1987.
Kohli, D., Soni, A. H. “Kinematic Analysis of Spatial Mechanisms via Successive Screw Displacements” J. Engr. for Industry, Trans. ASME, vol.2, series B, pp.739–747,1975.
Lee, C. S. G., Ziegler, M. “A Geometric Approach in Solving the Inverse Kinematics of PUMA Robots” IEEE Ans. Aerospace and Electronic Systems, vol. AES-20, no.6, pp.695–706,1986.
Paul, R. P. “Robot Manipulator: Mathematics, Programming and Control” MIT Press, Cambridge; Mass. 1984.
Pieper, D. L. “The Kinematics of Manipulators under Computer Control” Artificial Intelligence Project Memo No.72, Computer Science Department, Stanford University, Pelo Alto, Calif. 1968.
Ronald, E. W., Raymond H. M. “Probability and Statistics for Engineers and Scientists” Macmillan Pub. Co. 1978.
Rubinstein, R. Y. “Simulation and the Monte Carlo Method” John Wiley & Sons, 1981.
Uicker, J. J., Denavit, J., Hartenberg, R. S. “An Iterative Method for the Displacement Analysis of Spatial Mechanisms” Trans. ASME, J. Appl. Mech., vol.31, series E, pp.309–314,1964.
Vanderpleats, G. N. “Numerical Optimization Techniques for Engineering Design” McGraw-Hill Book Company, 1984.
Yang, A. T., Freudensteim, R. “Application of Dual Number Quaterniam Algebra to the Analysis of Spatial Mechanisms” Trans. ASME, J. Appl. Mech., vol.31, series E, pp.152–157,1964.
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© 1988 Springer-Verlag New York Inc.
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Shen, H., Radharamanan, R. (1988). Inverse Kinematic Analysis for a Five Axis Robot Using Monte Carlo Method. In: Radharamanan, R. (eds) Robotics and Factories of the Future ’87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73890-6_38
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DOI: https://doi.org/10.1007/978-3-642-73890-6_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-73892-0
Online ISBN: 978-3-642-73890-6
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