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Stiffness synthesis of 3-DOF planar 3RPR parallel mechanisms

Published online by Cambridge University Press:  28 May 2015

Kefei Wen ,
Chan-Bae Shin ,
Tae Won Seo  and
Jeh Won Lee
Kefei Wen
Affiliation:
School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, Republic of Korea
Chan-Bae Shin
Affiliation:
School of Mechanical Engineering, Ulsan College, Ulsan 682-715, Republic of Korea
Tae Won 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

Force control is important in robotics research for safe operation in the interaction between a manipulator and a human operator. The elasticity center is a very important characteristic for controlling the force of a manipulator, because a force acting at the elasticity center results in a pure displacement of the end-effector in the same direction as the force. Similarly, a torque acting at the elasticity center results in a pure rotation of the end-effector in the same direction as the torque. A stiffness synthesis strategy is proposed for a desired elasticity center for three-degree-of-freedom (DOF) planar parallel mechanisms (PPM) consisting of three revolute-prismatic-revolute (3RPR) links. Based on stiffness analysis, the elasticity center is derived to have a diagonal stiffness matrix in an arbitrary configuration. The stiffness synthesis is defined to determine the configuration when the elasticity center and the diagonal matrix are given. The seven nonlinear system equations are solved based on one reference input. The existence and the solvability of the nonlinear system equations were analyzed using reduced Gröbner bases. A numerical example is presented to validate the method.

Keywords

Elasticity centerStiffness synthesisParallel mechanismReduced Gröbner basesScrew theory
Type
Articles
Information
Robotica , Volume 34 , Issue 12 , December 2016 , pp. 2776 - 2787
Copyright
Copyright © Cambridge University Press 2015 

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