The Synthesis of Planar 4R Linkages With Three Task Positions and Two Specified Velocities

Abstract

In this paper, we consider the complete synthesis of planar 2R chains, in which the five design parameters of the chain are determined using kinematic specifications on the movement of the floating link. We use three positions and two velocities to define algebraic design equations which are solved to obtain multiple solutions. Our primary concern is how to ensure that a 4R chain constructed from two of these solutions moves smoothly through the given task. This is achieved by mapping the design data to an image space of planar displacements and comparing it to the curve traced by the movement of the coupler of the resulting design. Examples show that a designer can work in this image space to adjust the task specification to obtain an effective linkage design.