The correspondence between finite screw systems and projective spaces

This paper discusses the correspondence between vector subspaces and screw systems. The goal is to differentiate finite screw systems from screw systems arising in instantaneous kinematics and statics. This paper shows that a finite screw system corresponds to the projective space associated with the vector subspace spanned by the basis screws of the screw system. As a result, if finite displacement screws of a body constitute a screw system, the number of degrees of freedom of the motion of the body is one less than the order of the screw system.