On the curvature theory of non-null cylindrical surfaces in Minkowski 3-space

Abstract

This paper presents the curvature theory of non-null cylindrical surfaces in Minkowski 3-space. The definition of the line of striction and generator trihedron for cylindrical surfaces in Minkowski 3-space are given. The derivation formulae and Darboux instantaneous rotation vectors of generator trihedrons which play important role in robot kinematics are found. Moreover, curvature theory of a Lorentzian circular cylinder is given as an example.