Dexterity indices for planar and spatial robotic manipulators

Novel dexterity indices that can be applied to planar and spatial manipulators are presented. 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. The formulation of the kinematic equations used leads to dexterity indices that are frame invariant, whereas previous indices are affected by a scaling of the manipulator when both the position and the orientation of the end effector are included in these equations. Two indices are proposed for planar manipulations: the first one is based on a redundant formulation of the velocity equations and the second one on the minimum number of parameters. The corresponding indices are also derived for spatial manipulators. An example is included to demonstrate the invariance of the indices