Triad Synthesis for up to Five Design Positions With Application to the Design of Arbitrary Planar Mechanisms

Abstract

A new synthesis tool, the triad, is introduced to enable simplified synthesis of very complex planar mechanisms. The triad is a connected string of three vectors representing jointed rigid links of an actual mechanism. The triad is used as a tool to model an original mechanism topology with a set of simpler components. Each triad is then used to generate a set of “relative precision positions” which, in turn, enables the dimensional synthesis of each triad with well-established motion and path generation techniques for simple four-bar linkages. Two independent derivations of the relative precision positions are provided. All common triad geometries amenable to simple dyad synthesis techniques are presented. The triad geometries summarized here may be applied to two, three, four, and five precision position problems using graphical, algebraic, or complex number formulations of Burmester theory. Examples are provided.