Kinematics of Articulated Planar Linkages

Abstract

This paper proposes a kinematics algorithm in screw coordinates for articulated linkages. As the screw consists of velocity and position variables of a joint, the solutions of the forward and inverse velocities are the functions of position coordinates and their time derivatives. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. Both the forward and the inverse kinematics have the similar calculation process in this method. Through examples of planar open-chain linkage, single closed-chain linkage and multiple closed-chain linkage, the kinematics algorithm is validated. It is particularly fit for developing numerical programmers for forward and inverse kinematics in the same procedures, including the velocity, displacement and acceleration which provide the fundamental information for dynamics of the linkage.