Curve Cognate Constructions Made Easy

Abstract

Cognate linkages are mechanisms that share the same motion, a property that can be useful in mechanical design. This paper treats planar curve cognates, that is, planar mechanisms whose tracing point draws the same curve. While Roberts cognates for planar four-bars are relatively simple to understand from a geometric drawing, the same cannot be said for planar six-bar cognates, especially the intricate diagrams Dijksman presented in cataloging all the known six-bar curve cognates. The purpose of this article is to show how the six-bar cognates can be easily understood using kinematic equations written using complex vectors, giving a simple method for generating these cognates as alternatives in a mechanical design. The simplicity of the approach enables the derivation of cognates for eight-bars and possibly beyond.