Generalized Cardan Motion

Abstract

Cardan motion has been treated in the literature principally in terms of infinitesimally separated positions. Here Cardan motion is synthesized for all combinations of up to five infinitesimally and finitely separated positions of the moving plane. For each of the five distinct combinations which exist for four positions, the circle point curve is shown to degenerate into a circle and a line and the center point curve into a line at infinity and a hyperbola. Elementary analytical and graphical design procedures are provided and supported by examples. The five position problem is shown to be constrained only by the well-known Scott-Russell mechanism or a double-slider mechanism.