Determination of Mobility in a Kinematic Chain by Properly Using the Jacobian Matrix

Abstract

This contribution presents a new and simple method for the determination of the mobility of kinematic chains whose mobility can not be determined by analyzing intersections of subalgebras of the Lie algebra, se(3), of the Euclidean group, SE(3). Previous approaches have to analyze the kinematic chain constraints or wrench space to obtain these results. In this contribution, it is shown that properly analyzing the kinematic chain Jacobian matrix, the mobility of the kinematic chain can be obtained within the realm of screw twists without resorting to wrenches or constraints.