Four-Bar Linkage Synthesis for a Combination of Motion and Path-Point Generation

Abstract

This paper develops techniques that address the design of planar four-bar linkages for tasks common to pick-and-place devices, used in assembly and manufacturing operations. Pick-and-place tasks often require the exact position and orientation of an object (motion generation) at the end points of the task. Within the range of movement, the motion restrictions are less rigorous with only the position of the object (path-point generation) being specified to avoid obstacles. Established synthesis theory has been developed for either motion generation or path-point generation tasks. This paper presents four-bar linkage synthesis methods for tasks that include a combination of motion and path requirements. This synthesis challenge is addressed via two approaches: Geometric Constraint Programming (GCP) and numerical solutions to synthesis equations. Using GCP, a step-by-step methodology has been established to find solutions to these synthesis challenges. Using numerical methods, techniques are presented to formulate kinematic chain constraint equations and solve for appropriate link lengths and pivot locations. Examples of various combinations of motion and path-point generation are presented.