Distribution Characteristics of Screw Axes Belonging to General Three-System of Screws

Abstract

The cylindroid describes the exact distribution of the ∞1 screw axes of the general two−system of screws. For the general three−system, this article introduces the surface on which lies the position vector endpoints of its ∞2 screw axes, and then develops the finite distribution zone in which they most densely distribute. In particular, this paper explores the inner structure of the zone by partitioning the general three−system into ∞1 two−subsystems, and then reveals the principle of constructing the distribution space of the general three−system by that of the general two−system in Euclidean three−space. In pursuit of a generalized decomposition method, we propose the varying−pitch ruled surface carrying the screws whose pitch value continuously varies according to any desired function rule, based on the pitch−hyperboloid carrying all the equal−pitch screws. This investigation provides some useful guides for the axode planning and then the motion planning of three degree−of−freedom parallel mechanisms.