The dynamic effects of clearances on planar linkage mechanisms are analyzed and a design method to reduce these effects are investigated.
In the dynamic analysis of clearances, clearance joints are modelled using Hertzian contact theory and an efficient method to choose proper initial values is proposed such that the desired limit cycle is readily obtained. To verify the effectiveness of the proposed method, a slider-crank mechanism with one clearance is studied. The results of the simulation prove that the equivalent nominal mechanism well approximates the clearance mechanism in predicting the clearance effects. In especial, the average magnitude of the contact force of the clearance model is proportional to the slope of the nominal mechanism's energy curve. The analysis of the multiple clearance mechanisms are also performed to investigate the interactions between clearances. The results of the simulation show that the increase in the magnitude of one clearance, in general, results in the increase in the contact forces at all clearance joints.
To derive a design proceduce for reducing the clearance-effects, the validity of Earles and Wu's empirical formula, which is to be used as a basic design criteria, is checked numerically for the example slider-crank mechanism. On this criteria, a concept of a perfect joint is defined as a joint which is free of clearance-effects. A general theory for conditions of a perfect joint is derived in terms of the mechanical energy and kinematic properties of the joint. This general theory is applied to a slider crank mechanism and it is shown that designing a perfect joint is theoretically possible through balancing by a nonlinear spring. Further it is shown that this technique gives a practical guide for balancing a mechanism with linear springs to reduce the possibility of contact loss in clearance joints.
