An algorithm for planar four-bar motion generation with optimization

A set of fixed and moving pivot loci can represent an infinite number of planar four-bar motion generator solutions for a given series of prescribed rigid-body poses. Unfortunately, given the vast number of possible mechanical solutions in a set of fixed and moving pivot loci, it is difficult for designers to arbitrarily select a fixed and moving pivot loci solution that ensures full link rotatability, produces feasible transmission angles and is a compact design. This work presents an algorithm for selecting planar four-bar motion generators with respect to Grashof conditions, transmission angle conditions and having the minimum perimeter value. This algorithm has been codified into MathCAD for enhanced analysis capabilities and ease of use. The example in this work demonstrates the synthesis of a compact planar, four-bar crank-rocker motion generator with feasible transmission angles.