Higher Order Path Synthesis of Four-Bar Mechanisms Using Polynomial Continuation

Abstract

The path synthesis of a four-bar linkage is commonly framed so as to size links such that a coupler curve passes through specified planar precision points. It may instead be framed with consideration of higher order derivative information at each precision point. In this paper, we enumerate all 30 combinations of higher order path synthesis that lead to square polynomial systems for the four-bar. We present in detail the synthesis equations for (1) the case when one precision point is specified along with derivative information up to its eighth derivative, and (2) when three precision points are specified along with derivative information up to the second derivative at each point. For each case, 224 and 227 possible Roberts’ cognate triplets were computed, respectively.