The planning and simulating of CNC trajectory motion based on reference time

In order to solve the comprehensive control problem of trajectory and motion, this paper proposes a planning method based on relativity principle, which settles the separate control problem of position and motion. The comprehensive control of separate motion and position is realized, which simplifies the control and increased the accuracy. Multidimensional space theory is used to study the trajectory motion. Norm and operator space are established to describe the overall characteristics of trajectory. Furthermore, the CNC machining trajectory motion geometry and the relativity of motion and time are analyzed, and the relation between trajectory function and motion parameter are established to form the differential equations of trajectory motion. By using the actual moving process as reference time, and the actual geometric position as reference point, the connection between the planning and the real situation are set up. At idle state, a simple equation of coordinates and reference time is produced by solving the trajectory motion differential equations. At motional state, dynamic updated parameters can be deduced according to the updated value of reference time and the simplified expressions. It is proved by experiment and simulation that this method can handle uncertain situations during machining process, it can meet update requirements, and it´s a good method for trajectory motion planning.