Reformulation of Theories of Kinematic Synthesis for Planar Dyads and Triads

Methods for solving planar dyads and triads in kinematic synthesis are scattered throughout the literature. A review of and a new compilation of the complex number synthesis method for planar dyads and triads is presented. The motivation of this paper is to formulate uniform solution procedures, pointing out the commonalities of various approaches and emphasizing a consistent method for synthesizing mechanisms defined by specified precision positions. Particular emphasis is given to the solution method using compatibility linkages. The textbook Advanced Mechanism Design Vol II by Erdman and Sandor (1984) only includes a small portion of the available information on this method, and several researchers have added to the basic knowledge in the years since. In some cases, the approach and nomenclature were not consistent, yielding a need to describe and chart a generic formulation and solution procedure for dyads/triads using compatibility linkages and solution structures. The present method offers benefits for solving for exact dyad/triad solutions for complex multiloop mechanisms and could be a promising tool for reducing the computational load of finding complex mechanisms, and for visualizing properties of the solution space.