Dynamic analysis of a parallel robot with spherical joints with consideration for joint clearance

Abstract

This paper proposes a dynamic analysis method for evaluating the vibrational behavior of a parallel robot having spherical joints with clearance. By using variables that represent the relative displacement between the elements of clearance joints as generalized coordinates, it is enabled to implement a general algorithm regardless of the combination of spherical joints with clearance. The constraint equations are eliminated from the set of differential algebraic equations to be solved, and therefore the method does not need to use Baumgarte constraint stabilization method. The method was applied to a DELTA robot and were examined by measurement with a real machine. The acceleration of output link when using the special trajectories, which are likely to cause the impact only at a single spherical joint at the beginning of motion, was investigated. From the results of simulation, several motion modes of joint elements due to the clearance are confirmed; free flight, impact, and continuous contact modes. The acceleration of the output link fluctuates significantly at the time when the joint elements are in the impact mode, which shows the fact that the impact of joint elements at the spherical joints with clearance causes vibrational behavior of the robot. The appearance of the acceleration fluctuations are coincided with that of experimental results, which shows the effectiveness of the proposed method as a method for analyzing the vibrational behavior of parallel robots caused by joint clearance.

Keywords

• parallel robot
• multi-body dynamics
• constraint stabilization
• joint clearance
• contact model
• vibrational behavior