Parasitic Motions of 3-PRS Parallel Mechanisms with Two Different Branch Chain Arrangements

Abstract

The kinematics of 3-PRS parallel mechanisms (PMs), an important category of 2R1T PMs, is very important for the motion control and error compensation of PMs. In order to produce a spindle head that could meet the requirements of various machining accuracy levels, a definite kinematics analysis of the PMs par should be taken with caution firstly. Here, the mathematical models of two 3-PRS PMs with different branch chain arrangements were established using the Euler angle. The kinematic equations of two 3-PRS PMs were obtained by establishing the closed-vector loop equation according to structural conditions. Parasitic motions that would cause a great effect were obtained, and their variations with structural and kinematic parameters were also obtained through MATLAB. Since the relationship between parasitic motions, and the given structural and kinematic parameters, is inextricable, an analysis is performed for the purpose of reducing or eliminating parasitic motion to ensure the accuracy of end-effector movement. The caused effect of parasitic motion can be improved with scale optimization and precision compensation. Lastly, two improved 3-PRS PMs without the parasitic motion of different branch chain arrangements used as the spindle head were obtained. Parasitic motion was related to the mechanism configuration and could be avoided in the configuration design stage with the comprehensive optimization of the structural and kinematic parameters, which provides a reference to obtain a sufficient workspace and improve the precision of traditional five-axis CNC machine tools.