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A geometric approach for the workspace analysis of two symmetric planar parallel manipulators

Published online by Cambridge University Press:  24 July 2014

Banke Bihari ,
Dhiraj Kumar ,
Chandan Jha ,
Vijay S. Rathore  and
Anjan Kumar Dash
Banke Bihari
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur 613401, Tamil Nadu, India
Dhiraj Kumar
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur 613401, Tamil Nadu, India
Chandan Jha
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur 613401, Tamil Nadu, India
Vijay S. Rathore
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur 613401, Tamil Nadu, India
Anjan Kumar Dash*
Affiliation:
School of Mechanical Engineering, SASTRA University, Thanjavur 613401, Tamil Nadu, India
*
*Corresponding author. E-mail: anjandash@mech.sasta.edu
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Summary

The workspace is often a critical parameter for optimum design of parallel manipulators. Workspace shape and area are two important considerations under this. In this paper, 5-R and 3-RRR planar parallel manipulators having symmetric link lengths are considered for workspace analysis. Here, symmetric means that the lengths of the first and second links of the legs are the same in all branches. Workspace analysis for such manipulators is normally done in a nondimensional way. The determination of the workspace area is one of the important parameters in the optimum design of a manipulator, and the determination of the area in terms of nondimensional parameters is extremely difficult in the case of 3-DOF and higher-DOF manipulators. In this paper, a geometric method is presented to determine different workspace shapes and areas. Based on this, all possible shapes of workspace are presented for both 5-R and 3-RRR planar parallel manipulators. For each case, a geometrical relationship between the link lengths is determined. The geometric approach gives a closed-form expression for the area calculation, which is not possible when adopting a nondimensional approach. In addition, this approach provides relationships between workspace shape and area and link lengths.

Keywords

5-R and 3-RRR planar parallel manipulatorsWorkspace shapeWorkspace areaGeometrical approach
Type
Articles
Information
Robotica , Volume 34 , Issue 4 , April 2016 , pp. 738 - 763
Copyright
Copyright © Cambridge University Press 2014 

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