Local dexterity analysis for open kinematic chains

Two methods for determining the dexterity of manipulator arms are presented. A numerical method is illustrated for determining all possible orientations of the end-effector of an open kinematic chain based upon a row-rank deficiency of the sub-Jacobian of the kinematic constraint equations. This numerical method has been adapted from a theory for determining the accessible output set for planar and spatial manipulators. Boundaries of regions representing orientation solutions are mapped using continuation algorithms. One-dimensional curves in three-dimensional space are traced. Orientations of the manipulator end-effector at a point are studied (local dexterity). Only local dexterity solutions can be found. A second analytical method is also presented which determines the global dexterity of the system. This method relies upon determining all singularities of the system and identifying singular surfaces and singular curves. Regions of singular surfaces that are boundaries are identified and intersected with a service sphere. This method, however, although analytical and accurate, has many limitations. The two methods are compared via implementation into a six degree of freedom manipulator.