Criterion for the Locality of a Manipulator Arm with Respect to an Operating Point

Abstract

Criteria for determining an optimum locality of a manipulator arm are developed. In many cases, in a manufacturing environment, the tools, fixtures and targets that a manipulator has to deal with cannot be relocated. Thus, the choice of the manipulator locality is important. The method presented in this paper uses the notion of a service sphere to determine required orientability at an operating point. The boundary surfaces to the wrist-accessible output set is determined and positioned such that the service sphere is inside the wrist-accessible output set. To determine boundary surfaces of the wrist-accessible output set, manipulator singularities (internal boundary, and higher order) are computed and substituted into the constraint equation to parameterize singular surfaces. Part of these surfaces may lie internal to the boundary while other parts are a subset of the boundary. Singular surfaces are then intersected to determine second-order singularities. Second-order singularities partition surfaces into subsurfaces. Those subsurfaces on the boundary are determined by perturbing a point on the surface and concluding whether the perturbed point satisfies the constraint equations. The boundary to the wrist-accessible output set is then located with respect to the service sphere. The locality of the manipulator is determined for maximum orientability.