-shape acceleration and deceleration are the most widely used flexible acceleration and deceleration method in the current CNC system, but its velocity solution equation contains irrational terms, which create a more complicated solution process. When analyzing the solution process of the -shape acceleration and deceleration directly, using a traditional numerical solution method, the phenomenon of “solving the interval jump” arises, which is the main reason for low efficiency and poor stability of the solution. According to the -curve profile and solution, the concept of separating the curve profile recognition from the velocity solution was proposed, and a method of quickly identifying the interval of the solution location was introduced. Through the method mentioned above, the complete acceleration and deceleration curve parameters can be obtained through a one-time plan and a one-time solution, and the solution efficiency and stability are guaranteed; solving the Newton problem depends too much on the initial value of Newton velocity, which not only retains the speed advantage of the Newton method but also uses the downhill factor to ensure its convergence. Through the simulation comparison and analysis, the efficiency, stability, and universality of the method are verified.

中文翻译：

---

形状加减速的有效规划与求解算法

-形状加减速是当前CNC系统中使用最广泛的灵活加减速方法，但是其速度求解方程包含无理项，从而创建了更为复杂的求解过程。在直接分析-型加减速的求解过程时，采用传统的数值求解方法时，会出现“求解区间跳变”的现象，这是求解效率低，稳定性差的主要原因。根据-提出了将曲线轮廓识别与速度解分开的概念，并提出了一种快速识别解位置间隔的方法。通过上述方法，可以通过一次计划和一次求解获得完整的加减速曲线参数，并保证了求解效率和稳定性。解决牛顿问题的方法在很大程度上取决于牛顿速度的初值，这不仅保留了牛顿方法的速度优势，而且还利用下坡因子来确保其收敛性。通过仿真比较和分析，验证了该方法的有效性，稳定性和通用性。