Generalized Ridges and Ravines on an Equiform Motion

Abstract

In this paper we investigate a new type of ridges and ravines of the configuration space corresponding to an equiform motion in the Euclidean space R3. Necessary and sufficient conditions for the existence of generalized ridges and ravines are expressed as a partial differential inequalities involving the principal curvatures. For special case we obtain the solution of the differential equations which characterize some type of singularities. The singularities are displayed through figures [1, 2, 3].

Key words Equiform motion; Configuration space; Generalized ridges and ravines