Function Generation With Finitely Separated Precision Points Using Geometric Constraint Programming

Abstract

This paper extends geometric constraint programming (GCP) to function generation problems involving large numbers of finitely separated precision points and complex mechanisms. In parametric design software, GCP uses the sketching mode to graphically impose geometric constraints in kinematic diagrams and the numerical solvers to solve the relevant nonlinear equations without the user explicitly formulating them. For function generation, the same approach can be applied to any mechanism, requiring no unique algorithms. Implementation is straightforward, so the designer can quickly generate solutions for a large number of precision points and/or with complex mechanisms to accurately match the function. Examples of function generation with a four-bar linkage, a Stephenson III six-bar linkage, and a seven-bar linkage with a mobility of two are presented.