Mathematical Modeling and Kinematic analysis of 3-RRR Planar Parallel Manipulator

Abstract

Parallel mechanisms are found as positioning platforms in several robot manipulator applications tool manufacturing applications. Today, various types of these mechanisms are classified based on the structure, type of joints, and degree of freedom. An important and basic planar mechanism providing three degrees of freedom at the end-effector (movable platform) is a 3-RRR linkage. The forward kinematics in parallel mechanisms is a multi-solution problem and involves cumbersome calculations compared to inverse kinematics. With forward kinematics, the input kinematic parameters for any manipulator are known, and the end effector coordinate must be determined. The kinematic equations are generated with mechanics principles, and Jacobian matrices are formulated, With the Jacobian matrix, the regular workspace and dexterous workspace analysis calculated. The main objective is to fabricate a model of this planar manipulation mechanism with calculated dimensions and observe the practical workspace and dexterous workspace available at the end effector. The practical workspace and calculated workspace is presented in this paper. This final output data is useful for manipulator designers to design manipulators for different applications. In addition to this, the stress analysis is performed with Ansys software's help to estimate the moving platform's failure zone.

Kinematic study of feasibility of geared planar parallel manipulator

“…The study of Chablat et al 10 showed a recursive modeling for the kinematics of a 3-PRP planar parallel manipulator with vertical legs, focusing on the computing of the kinematic parameters and singularities. Shahed et al 11 computed the dimensions and established the practical and dexterous workspace available at the end-effector of a planar parallel manipulator 3- R RR. Wang 12 optimized the overall transmission performance of a 3- R RR planar parallel manipulator with optimal shapes and sizes of platform.…”