Ellipse Synthesis of a Five-Bar Linkage

This paper formulates synthesis equations for a two degree-of-freedom planar five-bar linkage to reproduce specified velocity ellipses at specified points in its workspace. The synthesis procedure finds a mechanism that exactly reproduces two ellipses, and affords the designer the free choice of one ground pivot. This paper shows how four solutions to these synthesis equations can be obtained in closed form. Each solution describes a five-bar linkage. The solution procedure reveals shared structure between these five-bars. The new synthesis procedure is applied to a few examples.