Continuous linear commands are widely executed in computer numerical control (CNC) machining. The tangential discontinuity at the junction of consecutive segments restricts the machining efficiency and deteriorates the surface quality. Corners of linear segments have been successfully blended by inserting parametric splines. There still exists challenges when the common methods are employed in the line-segment commands due to part of the following restrictions: (1) the stringent computation for iteratively calculating the arc-length; (2) the unwanted feedrate fluctuation; (3) the oversize contour deviation for separately completing curve fitting and velocity planning.

A novel smoothing method based on a clothoid pair to synchronously accomplish planning of geometry blending and speed scheduling is proposed, the spline parameter of which is arc-length-parameterized. The arc-length, curvature extreme, and geometric shape of the transition curve are analytically expressed by the transition length. On these bases, the transition curve and the velocity profile are concurrently constructed based on the predefined approximation error, the reachable velocity, and normal kinematic constraints in the look-ahead stage. Then, a real-time interpolation scheduling is developed to overcome the crossing difficulties between the linear and parametric segments. Compared with existing methods, the proposed method can analytically calculate the length of transition curves for the arc-length-parameterized expression form. Furthermore, the feedrate fluctuation is eliminated in the fine interpolation. Moreover, the overlarge contour derivation produced by corner smoothing is significantly avoided. It is friendlier to the CNC system for the on-line executing smooth motion since more computing resources can be released to handle other tasks, smoother motion can be achieved and higher contour accuracy can be obtained. The experimental results also demonstrate its practicability and reliability.

连续线性命令在计算机数控（CNC）加工中得到广泛执行。连续节段的交点处的切线不连续会限制加工效率并降低表面质量。线性段的角已通过插入参数样条线成功融合。由于以下限制的一部分，当在线段命令中采用通用方法时仍然存在挑战：（1）严格计算以迭代方式计算弧长；（2）不必要的进给率波动；（3）超大轮廓偏差，分别完成曲线拟合和速度规划。

提出了一种基于回旋曲线对的平滑方法，用于同步完成几何混合规划和速度调度，样条参数为弧长参数化。过渡曲线的弧长，极限曲率和几何形状由过渡长度解析表示。在这些基础上，基于预定义的逼近误差，可达到的速度以及在超前阶段的正常运动学约束，可以同时构造过渡曲线和速度曲线。然后，开发了实时插值调度以克服线性段和参数段之间的交叉困难。与现有方法相比，该方法可以解析地计算出弧长参数化表达式的过渡曲线的长度。此外，在精插补中消除了进给速度波动。此外，显着避免了由拐角平滑产生的过大轮廓求导。在线执行平滑运动比CNC系统更友好，因为可以释放更多的计算资源来处理其他任务，可以实现平滑的运动并可以获得更高的轮廓精度。实验结果也证明了其实用性和可靠性。可以实现更平滑的运动，并且可以获得更高的轮廓精度。实验结果也证明了其实用性和可靠性。可以实现更平滑的运动，并且可以获得更高的轮廓精度。实验结果也证明了其实用性和可靠性。