The relative relationship analysis of trajectory movement time theory holds that there is no absolute static space at all, there is no absolute same time, all time and space are relative, and they are all related to moving objects. For any reference frame and coordinate system, there is only space and time belonging to this frame of reference and coordinate system.
According to the relative nature of time: different time movements are produced with reference to different objects. An isolated operating system can define its own time; a time base can be chosen at will; a thing with operational connections can only select one time as the standard time.
If you think of a CNC machining system as an isolated system, you can define the time as needed. The development process of the process is selected as the reference time. The reference time is measured by the rate of change and length of the relative standard time. For example, the wire cutting machine uses the voltage change process between the electrodes, and the grinding force change process of the CNC grinding machine, Yaltintas, proposes to control the machining process according to the geometric curvature of the machining track. The main factor affecting the process progress is selected as the isolated time of the CNC system, so that the machining plan meets the process requirements.
The differential equation of motion can be expressed as the product of a static norm and a dynamic norm. The static norm is the product of the geometric mapping operator and the rate of change of the geometric parameter t to the reference time. The dynamic functional is the rate of change of the reference time to the standard time. Therefore, in dynamic control, static functionals can be planned in advance, and dynamic parameters can be introduced in due course.
The motion process can be described as follows: the geometric factor changes with respect to the parameter t, and the parameter t varies with respect to the reference time: the standard time variation of the NC machining motion planning method based on the custom time. In order to simplify the trajectory control, the geometric parameter t can be selected as the control parameter. Geometric parameters are irrelevant to time, and the relationship between them is artificially given, such as trapezoidal velocity law, finite acceleration law, and the above rules must be completed in the entire process of the orbit. This is based on the planning of the spatial location.
The application of motion planning Traditional position control has problems that are difficult to solve: with a small enough step size, the approximation of the position and its derivative cannot be solved, and the calculation amount is large, even if it is a linear trajectory, the control is very cumbersome. The motion parameters are derived from the displacement parameters and are simpler and even more constant than the positional parameters. In trajectory motion, the positional parameters are infinitely variable, and the motion parameters may be constant or lower order variables. In short, motion parameter control is simpler and more comprehensive than position control.
Conclusion Through the analysis of geometrical relativity and time relativity of trajectory motion, the equation of trajectory motion is derived. A new concept of using process key factors as reference time is proposed, and a simple method of motion planning based on ideal model and actual model is found. In the ideal state, based on the shortcomings of position or standard time motion planning, a motion planning method based on custom time is proposed. The result of the planning is a simplified calculation of the motion parameters, including geometric parameter expressions and information on timely changes in reference time. The method can analyze and calculate complex geometric functions when offline, and use the reference time dynamic data to perform simple calculations online, to meet the timeliness requirements of numerical control processing, and improve the ability to handle uncertain events.
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