Dynamic performance of over-constrained planar mechanisms with multiple revolute clearance joints

Abstract

The clearances of joints in a rigid multibody system may deteriorate the motion accuracy and even cause vibrations, noise and fatigue failure of structures. In over-constrained mechanisms, the number of degree-of-freedoms is more than that of independent coordinates which leads to numerical challenges in solving the underdetermined force equilibrium equations. A comprehensive study on the dynamic model and the performance of an over-constrained planar parallelogram mechanism with multiple clearance joints is presented in this paper. Since a common angular coordinate exists in the clearance joint associated with the redundant constraint, the degree-of-freedoms are revised by eliminating the number of redundant constraints. In planar analysis, the location of mass center and the orientation of the body reference with respect to the inertial frame are selected as the generalized coordinates of the components. Clearance joints are equivalent as the spring-damper elements and the contact forces are introduced into the dynamic equations by force constraints. The developed computational algorithm is implemented by MATLAB and may analyze the dynamic performance of this mechanism due to the elimination of kinematic constraints and the nonlinear contact-impact behavior in the clearance joints. Meanwhile, an orthogonal experimental design based on a quantitative analysis method demonstrates that the clearance size and the location of clearance joints affect the kinematic accuracy and counterbalance moment of the mechanism.