A Scale-Independent and Frame-Invariant Index of Kinematic Conditioning for Serial Manipulators
When defining an index of kinematic conditioning based on the minimum attainable value of the condition number of a manipulator Jacobian, dimensional inhomogeneities arise. As a means to eliminate the latter, an alternate definition of the twist of the end effector—containing all information necessary to determine the velocity field of the end effector—was proposed elsewhere. This is based on the velocities of three noncollinear points, thereby eliminating the angular velocity, which is the source of the aforementioned problem. As a consequence, the Jacobian becomes dimensionally homogeneous, what thus leads to a scale-invariant index of kinematic conditioning. We show in this paper that, if the points defining end-effector twist are the vertices of a Platonic solid, then a plausible conditioning index is derived.
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