Abstract
Based on Groebner base method, numeric-symbolic solutions to forward position analysis for a 3-RPS parallel mechanism and computer symbolic manipulating technique are proposed. A set of nonlinear polynomial equations are transformed into a set of equivalent triangularization equations by using the following operations: ordering of variables, forming all pairs of polynomials, finding S-polynomial, reduction etc. The analytical solutions in the closed form are obtained. The jacobian matrix and the equation in numeric-symbolic form for determining singularity configuration are derived. The maneuverability of the parallel mechanism and singularity configuration are investigated. The numerical examples are given for the illustration.
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References
Hang, L.-b.: Research on kinematics of the robots’ mechanism Southeast university, Doctor Degree dissertation, pp. 21–46 (2001)
Lee, K.-M., Shah, D.K.: Kinematic Analysis of a Three Degrees of Freedom In-Parallel Actuated Manipulator. IEEE Journal of Robotics and Automation 4, 3 (1988)
Huang, Z., Kong, J.-f., Fang, Y.-f.: Mechanism theory and controlling system of parallel robot. China machine press (1997)
Yu, J.-j., Wang, J., Huang, Z.: Workspace analysis of deficient-rank 3-RPS parallel platform mechanism. Machine Design and Research (1998)
Rao, Q., Bai, S.-x.: Manipulability analysis and definition of 6-6 Steward Robot. ROBOT 11, 345–349 (1994)
Fan, S.-w., Xu, L.-j.: Forward solution of position and analysis of working space for a new typed hybrid virtual axle machine tool. J. Machine Design 8, 27–29 (2002)
Fan, S.-w., Xu, L.-j.: Close Form Solution to Singularity Configuration of a New Type Parallel Machine Tool. Journal of University of Electronic Science and Technology of China 4, 369–373 (2002)
Xu, L.-j., Fan, S.-w.: A Numeric-Symbolic Approach for Analysis of Singular Position Surfaces and Workspace Boundary Surfaces of Robotic Manipulators. Mechanical Science and Technology 19, 6 (2000)
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© 2008 Springer-Verlag Berlin Heidelberg
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Wang, J., Wang, Q., Yu, Q. (2008). Numeric-Symbolic Solutions to Analyses of Forward Position and Singularity Configuration for 3-RPS Parallel Mechanism. In: Xiong, C., Liu, H., Huang, Y., Xiong, Y. (eds) Intelligent Robotics and Applications. ICIRA 2008. Lecture Notes in Computer Science(), vol 5315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88518-4_106
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DOI: https://doi.org/10.1007/978-3-540-88518-4_106
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88516-0
Online ISBN: 978-3-540-88518-4
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