Analysis and synthesis of mechanical error in path-generating linkages using a stochastic approach

Abstract

A stochastic model of the four-bar, path-generating linkage has been made. Tolerances and clearances have been assumed to be random variables. The mechanical error in the path of a coupler point is analyzed for the three-sigma band of confidence level. For a specified path, the mechanical error depends on the selection of either the original or its cognate mechanism. A synthesis procedure to allocate tolerances and clearances on different members and joints of a linkage so as to restrict the output error in the path of the coupler point within specified limits is developed. The synthesis procedure helps the designer in finding out how much the tolerance or clerance on particular variable is critical in terms of affecting the output error in the path of a coupler point. Results of an illustrative example are given in the paper.