On the feasibility of overconstrained linkages having screw- joints with tangent-based pitch

In works devoted to the determination of existence criteria for mobile overconstrained kinematic chains possessing screw-joints it has been assumed that the pitch of any such articulation defines a linear relationship between rotation about and translation along the screw. Recent investigations into finite-displacement screws have established the utility of a pitch which is related to the tangent of half of the angular displacement. We consider here the possibility of incorporating in mobile spatial loops screw-joints with pitches so interpreted.