MATHEMATICAL MODELING OF VARIABLE LEAD HELIX AND DESIGN OF TRANSITION CURVE IN VLSM

Abstract

This paper established the general mathematical model of variable radius variable lead helix, which applies the theory method for variable lead transmission. It also studeid the geometrical characteristics of variable lead helix in cylindrical surface, and the curvature and torsion is expressed by function , which is good to the research of transition curve. The corollary is put forward and explained that the geometric curvature of the helix on the cylindrical surface is equal to the geometric curvature of plane line which is obtained by expanding the cylindrical surface along axial direction, that transition curve design can be carried out in the plane. In the design of transition curve, circular arc and polynomial curve were chosen to connect two known curves respectively, and then according to the extreme conditions the transition curve functional is built up.

DOI: http://dx.doi.org/10.5755/j01.mech.19.3.4664