Conditions for transverse-regularity of serial manipulators

Transverse-regularity is a point-wise manipulator property, ensuring that the singular set Sigma is locally a smooth manifold. A generic manipulator is one which is transverse-regular in any configuration. This paper gives a necessary and sufficient condition for transverse-regularity. The condition requires the manipulator´s joint screws and their screw products. An expression for the tangent space to Sigma at transverse-regular singularities is derived. It is 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. A necessary and sufficient criterion for degree-one singularities is given in terms of the mechanism´ joint screws. In particular, any non-redundant manipulator is transverse-regular in a degree-one singularity.