PROBABILISTIC BEHAVIOR OF JOINT FORCES IN MECHANISMS

Abstract

This paper discusses the influence of the clearance in joints on the joint reaction forces in mechanisms. By using mathematical programing, the optimal parameters of kinematic chains can be efficiently obtained by using the deterministic approach. However, the situation becomes more sophisticated if random effects of tolerances of the arm lengths and the random pin positions have to be considered. In this work the influence of clearances on joint forces is calculated by using the Taylor approximation and the Monte Carlo method. Using the two methods was necessary, because the Taylor approximation usually yields satisfying results only for small values of clearances and for this reason it makes sense to compute the required quantities also by another independent method. The implementation of the model is illustrated with two examples. The first example considers a closed loop chain, representing a four-bar mechanism being an actual part of a hydraulic support, employed in mining industry. The hydraulic support must fulfill some requirements so it’s very important to have influence of clearances on joint forces in control. The second example considers joint reaction forces of car wiper mechanism. It will be shown, that the clearance in joints have some influence on the joint reaction forces.