Vector Modeling of Turning Polyhedron Movement

Some polygon prisms with small planes are usually fixed in vehicles and machines. A method is brought out in this paper, which adds a rotatory movement with the same direction of to tools, which machines all kinds of polyhedrons by composing of turning and milling and can get better effect. The coordinates systems of turning polygon prisms movement are selected, and the vector models of tools and workpieces are found. Through the analysis of the vector models, the vector model´s expression of describing turning polyhedron movement is deduced, on the basis of which, the vector formula of the relative movement between tools and workpieces are built. And the vector formulas of the trajectory of tools to workpieces are deduced by using the method of transforming coordinates systems. The influence on the section shape of the scale parameter can also be deduced. The formula of straightness error of the machined surface is found through geometrical analysis. A lathe is refitted to testify the formula for machining polygon prisms. At last, the above formulas are testified through an experiment.