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Gröbner basis and resultant method for the forward displacement of 3-DoF planar parallel manipulators in seven-dimensional kinematic space

Published online by Cambridge University Press:  28 April 2015

Davood Naderi ,
Mehdi Tale-Masouleh  and
Payam Varshovi-Jaghargh
Davood Naderi*
Affiliation:
Department of Mechanical Engineering, Bu-Ali Sina University, Hamedan, Iran
Mehdi Tale-Masouleh
Affiliation:
Human and Robot Interaction Laboratory, Department of Mechatronics, Faculty of New Science and Technology, University of Tehran, Tehran, Iran
Payam Varshovi-Jaghargh
Affiliation:
Department of Mechanical Engineering, Bu-Ali Sina University, Hamedan, Iran
*
*Corresponding author. E-mail: d_naderi@basu.ac.ir
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Summary

In this paper, the forward kinematic analysis of 3-degree-of-freedom planar parallel robots with identical limb structures is presented. The proposed algorithm is based on Study's kinematic mapping (E. Study, “von den Bewegungen und Umlegungen,” Math. Ann.39, 441–565 (1891)), resultant method, and the Gröbner basis in seven-dimensional kinematic space. The obtained solution in seven-dimensional kinematic space of the forward kinematic problem is mapped into three-dimensional Euclidean space. An alternative solution of the forward kinematic problem is obtained using resultant method in three-dimensional Euclidean space, and the result is compared with the obtained mapping result from seven-dimensional kinematic space. Both approaches lead to the same maximum number of solutions: 2, 6, 6, 6, 2, 2, 2, 6, 2, and 2 for the forward kinematic problem of planar parallel robots; 3-RPR, 3-RPR, 3-RRR, 3-RRR, 3-RRP, 3-RPP, 3-RPP, 3-PRR, 3-PRR, and 3-PRP, respectively.

Keywords

Forward kinematic problem3-DoF planar parallel robotSeven-dimensional kinematic spaceGröbner basisStudy's parametersResultant method
Type
Articles
Information
Robotica , Volume 34 , Issue 11 , November 2016 , pp. 2610 - 2628
Copyright
Copyright © Cambridge University Press 2015 

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