Haptic manipulation of virtual linkages with kinematic loops

This paper proposes an approach to providing realistic force feedback to users manipulating virtual linkages with kinematic loops. In the proposed approach, users feel the effect of the effect of the virtual kinematic loops: (a) on the inertia of the virtual linkage at the user-selected operational point (OP); and (b) on their freedom of motion. The approach introduces a method for computing the inertia of linkages with kinematic loops at arbitrarily selected OPs. It uses this inertia to select the directions of motion resisted by the virtual joints. Users feel the apparent inertia via impedance control, and the motion restrictions via stiffness control. Controlled experiments within a planar haptic interaction system validate that the proposed approach successfully renders the kinematic loop closure constraints to users.