A study of the optimal allocation of tolerances and clearances in planar linkage mechanisms

Abstract

The work falls into two separate parts, involving respectively kinematic and dynamic aspects of planar linkage mechanisms. The first and major part reported in Part I concerns the development of a procedure for optimal allocation of tolerances and clearances in plane linkage mechanisms. The theory developed takes into account the sensitivity of the mechanism output to small deviations in the parameter dimensions and the cost-tolerance relationships for the parameters. A procedure is then derived from the theory and incorporated into a computer program to allocate tollerances to linear dimensions and angles, and clearances to the joints in the mechanism. To demonstrate the applicability of the method to a wide range of planar linkage mechanisms, a number of examples are given which include 4-, 6-, 8- and 10-bar linkages. Part II describes the investigation of possible methods for maintaining contact in the joints of a plane four-bar mechanism by means of mass redistribution, the aim being to reduce or eliminate vibration due to impact in joints with clearance. An optimization routine is used with constraints upon the magnitude of the joint forces and the rate at which those forces change direction based on a 'no-clearance' analysis. The method was applied to several examples with little success due to inherent limitations of the analysis method used.