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A closed-form solution for the position analysis of a novel fully spherical parallel manipulator

Published online by Cambridge University Press:  17 September 2015

Javad Enferadi  and
Amir Shahi
Javad Enferadi*
Affiliation:
Department of mechanical engineering, Mashad Branch, Islamic Azad University, Mashad, Iran
Amir Shahi*
Affiliation:
Department of mechanical engineering, Mashad Branch, Islamic Azad University, Mashad, Iran
*
*Corresponding authors. E-mail: [email protected], [email protected]
*Corresponding authors. E-mail: [email protected], [email protected]
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Summary

In this paper, a novel 3(RPSP)-S fully spherical parallel manipulator (SPM) is introduced. Also, an innovative method based on the geometry of the manipulator is presented for solving the forward position problem of the manipulator. The presented method provides a framework for the future research to solve the forward position problem of the other fully spherical PMs (for examples 3(UPS)-S and 3(RSS)-S). In the proposed method, two coupled trigonometric equations are obtained by utilizing the geometry of the manipulator and Rodrigues' rotation formula. Using Bezout's elimination technique, the two coupled equations lead to a polynomial of degree eight. We show that the polynomial is minimal and optimal. Furthermore, the other method is proposed for selecting an admissible solution of the forward position problem. This algorithm is required to control modeling and dynamic simulations.

Keywords

Spherical parallel manipulatorPosition analysisBezout's elimination techniqueAdmissible solution
Type
Articles
Information
Robotica , Volume 33 , Issue 10 , December 2015 , pp. 2114 - 2136
Copyright
Copyright © Cambridge University Press 2015 

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