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