A genericity condition for general serial manipulators

Generic manipulators possess the desireable properties that their set of singulartities is a smooth manifold, and that the drop of rank of the manipulator Jacobian is bounded. A sufficient condition for genericity is the transverse-regularity of its Jacobian mapping in any configuration. In this paper a necessary and sufficient condition for transverse-regularity is presented. The condition is based on the manipulator's joint screws and their screw products. It is also shown that a manipulator is non-generic if it can attain a pose where the rank of the manipulator's screw system together with the screw products is not the maximal rank of the Jacobian.