CALCULUS OF PARTIAL DERIVATIVBES OF LINK VECTORS WITH RESPECT TO DESIGN PARAMETERS IN THE OPEN- AND CLOSED-LOOP LINKAGES

Abstract

An analytical method of differentiating the link vectors in the single-loop kinematic linkage with respect to its design parameters is presented. In that the first derivative of a unit vector is perpendicular to the original one, this method is analogous to one of determining the velocity vector and the acceleration vector of link in the closed-loop kinematic chain. General expressions of the first and second derivative vectors are derived for the link vectors both in the open-loop kinematic model of the articulated robot arm and in the closed-loop 4-bar linkages.