Singularity Analysis of Mechanisms and Robots via a Velocity-Equation Model of the Instantaneous Kinematics

This paper presents a new generalized approach to the singularity analysis of a general mechanism (arbitrary kinematic chain), considered as a non-redundant inputoutput device with equal number of inputs and outputs. The instantaneous kinematics of a mechanism is described by means of a velocity equation, explicitly including not only the input and output velocities but also the passive-joint velocities. A precise definition of singularity of a general mechanism is provided. On the basis of the six types of singular configurations introduced in lhe paper singularity classifications are proposed.