IJERT-EMS
IJERT-EMS

Jacobian Analysis of Limited DOF Parallel Manipulator using Wrench and Reciprocal Screw Principle


Jacobian Analysis of Limited DOF Parallel Manipulator using Wrench and Reciprocal Screw Principle
Authors : Hassen Nigatu, Ajit Pal Singh, P. Prabhu
Publication Date: 10-04-2014

Authors

Author(s):  Hassen Nigatu, Ajit Pal Singh, P. Prabhu

Published in:   International Journal of Engineering Research & Technology

License:  This work is licensed under a Creative Commons Attribution 4.0 International License.

Website: www.ijert.org

Volume/Issue:   Vol. 3 - Issue 4 (April- 2014)

e-ISSN:   2278-0181

Abstract

This paper presents a new methodology of formulating Jacobian matrix for limited degree of freedom (DOF) parallel kinematic machine (PKM), which is a very important tool to relate the end-effector velocity with the joint rate velocity. Even if it is believed by many researchers that Jacobian matrix is critical to generating the trajectories of the prescribed geometry in the end-effector space, it was cumbersome to formulate in simple and descriptive form by partial differentiation. In this work screw mathematics is used to formulate the Jacobian matrix in simple and integrated form under a unified framework and it is proved that the resulted Jacobian matrix is 6 6 which provides clear information about the architecture and singularity condition of the manipulator. Obtaining Jacobian matrix in unambiguous way is very crucial step to formulate and solve velocity, acceleration and motor torque equations with less computational burden. The 3PRS parallel kinematic machine is selected as an example to demonstrate the methodology. The numerical solution is obtained using MATLAB.

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