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A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann–Cayley algebra

Published online by Cambridge University Press:  17 August 2015

Kefei Wen ,
TaeWon Seo  and
Jeh Won Lee
Kefei Wen
Affiliation:
School of Mechanical Engineering, Yeungnam University, Gyeongsan 712–749, Republic of Korea
TaeWon Seo*
Affiliation:
School of Mechanical Engineering, Yeungnam University, Gyeongsan 712–749, Republic of Korea
Jeh Won Lee*
Affiliation:
School of Mechanical Engineering, Yeungnam University, Gyeongsan 712–749, Republic of Korea
*
*Corresponding author. E-mail: taewon_seo@yu.ac.kr, jwlee@yu.ac.kr
*Corresponding author. E-mail: taewon_seo@yu.ac.kr, jwlee@yu.ac.kr
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Summary

Singular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

Keywords

SingularityPlanar parallel manipulatorsGrassmann–Cayley AlgebraScrew theoryPlücker coordinates
Type
Articles
Information
Robotica , Volume 35 , Issue 3 , March 2017 , pp. 511 - 520
Copyright
Copyright © Cambridge University Press 2015 

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