Nano scale dynamic track control in multidimensional space

According to the experimental and theoretical derivation, we present the first study of the CNC machine tool control theory based on the relation between geometry and motion. By studying the trajectory characteristics in both multidimensional space and time space, the displacement and its derivatives are designed as a motion vector space. With this vector space, the relationship among geometric parameters, dynamic parameters, function and its derivatives, can be studied all together. They can also be studied respectively according to its geometric and physical meanings. The time-derivative can increase the middle variables as a reference time for the control technology process. If the variation ratio of real time to reference time is known or measurable, the trajectory differential equation can be completely solved. We put forward a new method: to control the track realization process is the way to control the trajectory movement parameter. Through experiment and simulation, it has been proven that this method can realize geometry and integrated control, reduce motion trajectory calculation, and while improving precision, it increases path planning adaptability to the environment. It is therefore a good method to control tracks for machine tools.