Abstract: Based on the principle of action, movement method of geometric track internal principle is discussed, in order to solve the geometry precision of numerical control and dynamic accuracy control problem of CNC processing track. According to the principle of action, the action of traditional path control method is calculated. It shows that interpolation method is a serious violation of the laws of nature. Functional analysis method is used to analyze the path and the mapping relationship of movement and to establish the motion vector space, measuring orbit geometry function and its derivative, controlling state vector error, monitoring curvature or high prices of derivative changes at the same time. The speed and small displacement are all along the given way. Analyzing of time and space of relativity, the use of a reference time is proposed to control technology process. It presents a new method for trajectory control, which uses motion law taking the place of position parameters to control, And uses self defined time to substitute real time to control proceeding. It is proved that it is a good way to control geometry and motion comprehensively, to reduce computation times and to increase the ability of environmental adaptation for path planning.

Key words: Principle of action, Self defined time, Standard time, Trajectory function