Incorporating Fixed-Point and -Line Constraints and Tolerance Based Synthesis in 4MDS

Abstract

This paper presents implementation of fixed-pivots, ground-link line, and tolerance based motion synthesis in the 4MDS (Four-Bar Motion Design System). This is a continuation of the first work reported on 4MDS, which provides an interactive, graphical, and geometric constraint based mechanism design system for the exact- and approximate-motion synthesis problems. Theoretical foundation of the 4MDS is laid over a kinematic mapping based unified formulation of the geometric constraints (circle, fixed-line, line-tangent-to-a-circle) associated with the mechanical dyads (RR, PR, and RP) of a planar four-bar mechanism. An efficient algorithm extracts the geometric constraints of a given motion task and determines the best dyad types as well as their dimensions that best fit to the motion. Often, Mechanism designers need to impose additional geometric constraints, such as specification of location of fixed pivots or ground-link line. If synthesized mechanism suffers from branch, circuit, or order defect, they may also desire rectified solutions by allowing a tolerance to certain or all task positions. Such functions are crucial to a practitioner and much needed during the conceptual design stage of machine design process.