Dimensional Synthesis, Dexterity Analysis and Experimental Validation of a Six Degree of Freedom Parallel Manipulator

Abstract

This paper presents a design approach based on the dimensionless Jacobian matrix to determine the maximum dextrous workspace for a Six Degree of Freedom (DoF) 3-PPSS (P-Prismatic, S-Spherical) parallel manipulator. As the end-effector of the 3-PPSS manipulator can exhibit both translational and rotational motions, the Jacobian matrix mapping the end-effector velocities and the joint velocities will be dimensionally inhomogeneous. These dimensional inconsistencies within its elements make calculating the associated condition number impossible. Hence, a unit vector approach is introduced in this paper to derive a Jacobian matrix with dimensionless terms to study the dexterity characteristics of the 3-PPSS manipulator. The design procedure follows a systematic approach of choosing the manipulator dimensions corresponding to the maximum dextrous workspace. The manipulator dexterity is characterized by the Global Conditioning Index (GCI). This paper also illustrates the Local Conditioning Index (LCI) distribution within the workspace corresponding to the optimal manipulator dimensions. Finally, the performance of the 3-PPSS manipulator is evaluated experimentally by implementing an intelligent control based on the Inter-Integrated Circuit (I2C) protocol.