Line-Point Constraints and Robot Surgery

The space of rigid-body displacements that move a line so that its remains in contact with a fixed point is studied. This constraint variety is related to robot surgery where a straight, rigid cannula is inserted into the patient through a trocar. A surgical robot manipulates the cannula so the insertion point is fixed. The space of displacements determined by a pair of these constraints is also studied briefly. This correspond to a pair cannulas with their ends rigidly connected