Consistent Kinetostatic Indices for Planar 3-DOF Parallel Manipulators, Application to the Optimal Kinematic Inversion

This paper investigates the problem of defining a consistent kinetostatic performance index for symmetric planar 3-DOF parallel manipulators. The condition number of the Jacobian matrix is known to be an interesting index. But since the Jacobian matrix is dimensionally inhomogeneous, a normalizing length must be used. This paper proposes two distinct kinetostatic indices. The first one is defined as the reciprocal of the condition number of the Jacobian matrix normalized with a convenient characteristic length. The second index is defined by a geometric interpretation of the “distance” to singularity. The two indices are compared and applied to the kinematic inversion in the presence of redundancy.