Integral Invariants of Mannheim Offsets of Ruled Surfaces

Abstract

In this study, we identify the instantaneous Pfaffian vector of the closed motion defined along the striction curve of the ruled surface phi* which is a Mannheim offset of closed ruled surface phi in E-3. Using this vector, we get the Steiner rotation vector and the Steiner translation vector of this motion and give new characteristic results about the pitch and the angle of the pitch which are the integral invariants of Mannheim offsets of ruled surface.