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Determining the maximal singularity-free circle or sphere of parallel mechanisms using interval analysis

Published online by Cambridge University Press:  13 June 2014

Mohammad Hadi Farzaneh Kaloorazi ,
Mehdi Tale Masouleh  and
Stéphane Caro
Mohammad Hadi Farzaneh Kaloorazi*
Affiliation:
Human-Robot Interaction Lab (TaarLab), Faculty of New Sciences and Technologies, University of Tehran, North Kargar, Tehran, Iran
Mehdi Tale Masouleh
Affiliation:
Human-Robot Interaction Lab (TaarLab), Faculty of New Sciences and Technologies, University of Tehran, North Kargar, Tehran, Iran
Stéphane Caro
Affiliation:
IRCCyN/CNRS, UMR 6597, 1 rue de la Noë, 44321 Nantes, France
*
*Corresponding author. E-mail: mhfarzane@ut.ac.ir
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Summary

This paper proposes a systematic algorithm based on the concept of interval analysis to obtain the maximal singularity-free circle or sphere within the workspace of parallel mechanisms. As case studies the 3-RPR planar and 6-UPS parallel mechanisms are considered to illustrate the relevance of the algorithm for 2D and 3D workspaces. To this end, the main algorithm is divided into four sub-algorithms, which eases the understanding of the main approach and leads to a more effective and robust algorithm to solve the problem. The first step is introduced to obtain the constant-orientation workspace and then the singularity locus. The main purpose is to obtain the maximal singularity-free workspace for an initial guess. Eventually, the general maximal singularity-free workspace is obtained. The main contribution of the paper is the proposition of a systematic algorithm to obtain the maximal singularity-free circle/sphere in the workspace of parallel mechanisms. The combination of a maximal singularity-free circle or sphere with the workspace analysis by taking into account the stroke of actuators, as additional constraint to the latter problem, is considered. Moreover, the center point of the circle/sphere is not restrained to a prescribed point.

Keywords

Parallel manipulatorsSingularity analysisWorkspace analysisKinematicsInterval analysis
Type
Articles
Information
Robotica , Volume 34 , Issue 1 , January 2016 , pp. 135 - 149
Copyright
Copyright © Cambridge University Press 2014 

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