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

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 t...

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Bibliographic Details
Published in:Journal of mechanics 2016-10, Vol.32 (5), p.555-563
Main Author: Enferadi, J.
Format: Article
Language:English
Subjects:
Assembly
Control theory
Industrial equipment
Manipulation
Manipulators
Mathematical analysis
Mathematical models
Mechanics
Modelling
Optimization
Polynomials
Robot arms
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Summary: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).
ISSN:1727-7191
1811-8216
DOI:10.1017/jmech.2016.23