Establishment of Relatively Unified Mathematical Model for Spiral Surface Based on Movement Characteristics of Particle

Abstract

From the viewpoint of the forming principle of spiral curve and classification from the kinematics, established relatively unified mathematical model of spiral curve based on the movement characteristics of particle and the forming principle of space surface shape, and in turn relying on relatively unified mathematical model of spiral curve, combined the similarity of forming movement between spiral curve and spiral surface, derived the relatively unified mathematical model of spiral surface with the concept of sequence of operator presented for the first time. The relatively unified mathematical model has been validated that it not only expressed the relationship of movement synthesis for commonly spiral surface’s forming movement, but also depicted new spiral surface to be required or named through changing parameters.