关键词：离散点云；边界点提取；最优测地线路径；径向线；螺旋刀位轨迹 中图分类号：V462；TH164 DOI：10.3969/j.issn.1004-132X.2025.04.006 开放科学（资源服务）标识码（OSID）：

Spiral Machining Trajectory Planning Method Based on Discrete Point Cloud Construction of Radial Lines

WU Jiangsheng CHAI Xingliang*BO Qile LIU Haibo WANG Yongqing School of Mechanical Engineering，Dalian University of Technology，Dalian，Liaoning，116000

Abstract：Aiming at the problems that it was difficult to directly generate efcient and accurate continuous smooth tool path trajectories based on discrete point clouds，a method to directly construct radial lines on point cloud and generate spiral machining trajectories through radial line interpolation was proposed herein. For the construction of radial lines，a boundary recognition method was proposed based on feature descriptors to extract boundary points as two end points of the radial lines. Taking the optimal discrete geodesics between two end points on the point cloud as the radial point set，the curvature minimization problems of discrete geodesics were proposed and solved by Newton iteration method. The B-spline curves were used to fit and resampling according to the residual height based on the radial point sets. The radial line interpolation algorithm was proposed to generate the spiral machining trajectory with equal residual height. Finally，an example was given to demonstrate the spiral machining trajectories directly generated by the point cloud data，which fully verified the effectiveness of the proposed method.

Key words： discrete point cloud; boundary point extraction; optimal geodesic path; radial line; spiral machining trajectory

0 引言

复杂曲面类零件被广泛应用于航空、航天、船舶和汽车等领域，如火箭贮箱箱底、飞机壁板、舰船螺旋桨、汽车引擎盖等。对于结构复杂、配合精度要求极高的曲面，通常采用测量设备获得型面点云数据，再通过点云处理，生成刀位轨迹，从而进行加工。

传统从散乱点云生成加工轨迹的方法通常需要对散乱点云进行曲面重构，进而进行曲面加工轨迹规划。然而，曲面重构是一个复杂的、耗时的过程，对于结构复杂的点云数据，例如存在孔洞、锐角等，很难得到满意的重构曲面[1]。此外，曲面重构的效果依赖于具体的算法和参数的选择以及技术人员熟练度，不具有通用性和鲁棒性。从分散的点构建网格会导致精度损失和拓扑问题[2-3]，为此，有学者提出了基于散乱点云直接生成加工轨迹的方法[4]。目前，基于散乱点云直接生成加工轨迹的方法主要分为直接规划法和间接规划法两种[5]。

1）直接规划法。该方法通常对点云数据直接进行处理，利用曲线或曲面与点云相交或通过约束条件进行迭代计算以获取目标点数据，并进一步推导出刀具路径，如截平面法、轮廓偏置法、等参数法等。PARK等[6直接从实测数据中计算了等平面精加工刀具路径，但该方法仅适用于规律点云。ZHANG等解决了偏置点云面自相交问题，采用截平面法生成刀位轨迹；……