On the exact motion synthesis of planar four-bar-linkages with prismatic and revolute joints

Abstract

This paper introduces a novel and simple approach that can be used in the exact motion synthesis of planar four-bar linkages with prismatic (P) and revolute (R) joints to up four given poses. Only basic knowledge of vectors is required and does not depend on either, advanced concepts of kinematic mapping or cumbersome graphic skills. As a result, the design equations are very simple, and they can provide up to a maximum of twenty solutions, which can be real or imaginary. Each pair of different real solutions allows the design of a mechanism that can accurately achieve the given poses. The details of the methodology are illustrated by considering several challenging examples found in the literature.