The governing differential equilibrium equations of the quasi-static loading model for nonlinear helical buckling of tubing in constant-curvature wells are solved by the finite element method.

The equilibrium equations and the potential energy function of tubing buckling with weight in constant-curvature wells are derived.

By combining the conjugate theory of spatial envelope surface used in traditional design of globoidal cam with motion character of globoidal cam indexing device,globoidal cam surface is created from ruled surface and its offset surface.

Analytic properties of offset surfaces are stu died and their first and second fundamental forms are given.

In this method, curves are gi ven by the track on the parametric domains of the original surfaces rather than approximation of offset surface or inversion of t he 3D intersection to 2D parametric domains.

This paper intends to make us understand topological structures deeply,and it takes advantage of exact homology sequence and Morse inequalities to estimate the upper bound of the rank of q-dimensional singular homology group of energy level surface(q is an arbitrary nature number).

The author of the paper [1] estimates how many types of large-scale periodic orbits of a energy level surface exist in a nonlinear mechanical system.

Our algorithm applies a subdivision surface to CAD/CAM system,adapts to an arbitrary topology triangle model and produces NC cutting tool path with given precision by controlling the offset surface error.