Optimum design of robotic manipulators using dexterity indices

This paper presents new dexterity indices that can be applied to planar and spatial manipulators. These indices are based on the condition number of the Jacobian matrix of the manipulators which is known to be a measure of their kinematic accuracy. Dexterity indices based on that same criterion have been presented elsewhere. However, due to the formulation of the kinematic equations, the existing indices are affected by a scaling of the manipulator when both the position and the orientation of the end effector are included in the kinematic equations. A new formulation of these equations is proposed here to avoid this problem of dimensional dependence. Two dexterity indices are presented for planar manipulators: the first one is based on a redundant formulation of the velocity equations whereas the second one is based on the minimum number of parameters. The corresponding indices are also derived for spatial manipulators. Finally, an example is included to illustrate the use of these indices in the context of design and optimization of manipulators.