Synthesis of a Stephenson II Function Generator for Eight Precision Positions

Abstract

This paper presents a synthesis methodology for a Stephenson II six-bar function generator that provides eight accuracy points, that is it ensures the input and output angles of the linkage match at eight pairs of specified values. A complex number formulation of the two loop equations of the linkage and a normalization condition are used to form the synthesis equations, resulting in 22 equations in 22 unknowns. These equations are solved using the numerical homotopy continuation solver, Bertini. The approach is illustrated with an example.