Kinematische geometrie der axoiden und die bahnfläche einer geraden

Abstract

It is known that any motion is characterized instantaneously by the instantaneous screw axis. This present work is concerned with the properties that follow from a study of the screw axis and the shapes of the axodes. Known results are derived together with some new results. During the general motion of two bodies the instantaneous screw axis changes its position and properties and generates two different but related ruled surfaces in the respective members, called the fixed axode in the fixed member, and the moving axode in the moving member. During the motion the axodes roll and slide on each other in a special way such that tangential contact between the axodes is always maintained along the entire length of the mating generators which together determine the instantaneous screw axis at any instant. The two successive moving screws share with the two fixed ones the same common perpendicular and they also share the same angle of inclination with respect to one another. A line of moving axoides in general generates a ruled surface. In the second part of this work is given a systematic of such ruled surfaces (axodes) on the basis of four invariants. In a previous work[1] similar problems about axodes and the path of the axodes were treated analytically.