Dexterity Analysis of a 4-UPS-RPS Parallel Mechanism

Abstract

A novel 4-UPS-RPS spatial 5 degrees of freedom parallel mechanism is introduced and its dexterity measures are analysed. The stationary platform of the parallel mechanism is connected with the moving platform by the same four UPS (universal joints-prismatic pairs-spherical joints) driving links and a RPS (revolute joints-prismatic pairs-spherical joints) link. The velocity Jacobian matrix and the force Jacobian matrix of the parallel mechanism are derived, and the dimensionless velocity Jacobian matrix is established. On this basis, the three dexterity measures, including average conditional number, the smallest singular value and operation, are obtained. According to these, the square mean dexterity coefficient, which is used to comprehensively evaluate the dexterity of various configurations, is proposed. In addition, the distribution of different dexterity measures above in the workspace is analysed respectively. This research can provide an important theoretical base for the dimensional synthesis and trajectory planning for a parallel mechanism.