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A Novel Approach for Obtaining Assembly Modes of a 3UPS-S Fully Spherical Parallel Manipulator

Published online by Cambridge University Press:  14 April 2016

J. Enferadi
J. Enferadi*
Affiliation:
Department of Mechanical Engineering Mashhad Branch Islamic Azad University Mashhad, Iran
*
*Corresponding author ([email protected])
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Abstract

The 3(UPS)-S fully spherical parallel manipulator is the most famous fully spherical parallel manipulator (FSPM). In this paper, we propose a novel approach to model the forward displacement analysis of the manipulator to obtain its assembly modes. Rodrigues’ formula is used as a mathematical tool to perform the proposed modeling. Utilizing geometry of the manipulator, two coupled trigonometric equations are obtained. Using Bezout's elimination method, the two coupled equations are transformed to one polynomial of degree eight. Finally, an example is given with eight real solutions. Therefore, the degree of the polynomial is minimal and the introduced modeling method is optimal. This is very important to control modelling and dynamics simulation. Also, the proposed method can be extended to the other FSPMs (e.g., 3(RPSP)-S, 3(RPSP)-S and 3(RSS)-S).

Keywords

Fully spherical parallel manipulator (FSPM)Rodrigues’ FormulaForward displacement problemBezout's elimination method
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 5 , October 2016 , pp. 555 - 563
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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