An inverse position analysis of five-bar planar parallel manipulators

Abstract

In this paper, we present a simple method to obtain joint inputs needed to attain any point in the reachable workspace of a class of five-bar planar parallel manipulators which are based on five rigid links and five single degree of freedom joints – revolute and prismatic joints. Depending on the topology of the manipulators, two mathematical expressions describing the path traced by the tip of two links connected to each other are obtained and solved simultaneously in order to determine the intersection points of the two paths which are the Cartesian coordinates of the connection points for the links. For the class of manipulators considered in this study, one of the links is the link activated by an actuator fixed to the ground. So, rotational and/or translational joint inputs can be determined from the Cartesian coordinates of the tip of the activated links. Sylvester's dialytic elimination method is employed to solve the equations. Such a methodology is easy to implement, computationally efficient and sound to compute all possible solutions. A numerical example is provided for each manipulator and the inverse position solutions are verified by substituting them into forward position equations. It is concluded that the proposed method is useful in trajectory planning and control of five-bar planar parallel manipulators in joint space.