Approximate Kinematic Equations for Multiple-Input Small-Crank Mechanisms: Four-Bar Based Mechanisms

Approximate kinematic equations are developed for multiple-input small-crank mechanisms derived from a basic planar four-bar linkage. Application of a method in which an output link is presumed to comprise a mean and a perturbational motions, the vector loop approach, and a recursive formulation facilitates derivation of the approximate kinematic equations. For a general n-input mechanism, two sets of constraint equations are established: a set of nonlinear recursive equations relating the mean link orientations and a set of linear recursive equations for the purturbational motions. The recursive procedure is demonstrated by developing approximate kinematic equations for four-bar based two-, three- and four-input small-crank mechanisms.