Special configurations of robot-arms via screw theory

SUMMARY The Jacobian of serial robot-arms is examined, and the matrix of cofactors of a singular Jacobian is presented as a means of explaining the physical nature of special configurations. Because the columns of both these matrices are screw coordinates, screw theory is central to proper understanding. ‘Realistic’ robot-arms are seen to behave in ways that can be explained not by particularizing from a general formulation but rather by carefully interpreting the relevant special screw systems from the outset. Higher singularities (with more than one freedom-loss) are then touched upon.