Analysis and Design of Basic Linkages for Harmonic Motion Generation

This paper deals with basic planar linkages driven by relatively small cranks, and as a consequence generating approximate simple harmonic motion at the output members. A unique approach is presented to yield the kinematic equations, as exemplified by planar crank-rocker and offset slider-crank linkages. The method involves the presumption of a mean linkage configuration and a small motion excursion therefrom. Its validity is demonstrated by means of several error plots, generated for varying, nondimensional linkage parameters and a constant mean transmission angle. These plots also serve to illustrate the order of approximation involved for a particular combination of parameters. Finally, the synthesis of a crank-rocker linkage for a representative set of requirements is exemplified using the equations developed herein.