Local Analysis of Singular Configurations of Open and Closed Loop Manipulators

Abstract

The paper gives a general approach to the local analysis of singularconfigurations of both serial and parallel manipulators. For all possiblecases the maximum rank deficiency of the manipulator Jacobian is given andshown never to exceed 4. This is the equivalent to the maximum number oflinear dependent constraint equations for kinematic loops. Singularconfigurations of serial/parallel manipulators are roughly classified withrespect to the active and passive joints. An algorithm is presented whichdetermines the singular motion of a mechanism. This algorithm is purelyalgebraic and involves at maximum three steps. It is based on theinstantaneous screw system of the considered mechanism. It is shown thatfourth order analysis is always sufficient to locally characterize theconfiguration space manifold in singular points. Thus the singular set canlocally be approximated by a hypersurface of maximum degree 4. The approachcan easily be implemented in existing simulation tools Finally theminimum number of joints is given that a serialmanipulator must activate in order to escape from a singular configuration.