中文摘要：

这篇文章使用弧长度参数路径计划在开轮廓的结构上执行机器的纤维放置(RFP ) 。这允许由更简单的算术用一个相同数学方程和计算代表起始的路径和偏移量点。在古典微分几何学的帮助下，放纤维的路径的计算可以在参量的域(参量地定义的模子表面) 或在 3D 空格(含蓄地定义的模子表面) 被归结为一阶的平常的微分方程的起始值的问题的答案，显著地从而在存在方法上改善。与常规方法相比，除它的计算简洁以外，建议方法在计算起始的路径和偏移量点有更好的错误控制机制。数字实验也被执行在合成形成的进程并且也表明新方法的可行性它在计算机的潜在的应用程序用机器制造的数字控制(计算机数值控制) ，表面修剪，和另外的工业惯例。

英文摘要：

This article uses arc-length parameters for path planning to carry out robotic fibre placement （RFP） over open-contoured structures This allows representing the initial path and offset points using an identical mathematical equation and computation by more simple arithmetic. With the help of classical differential geometry, the calculation of fiber-placing paths may be reduced to solution of initial-value problems of first-order ordinary differential equations in the parametric domain （parametrically defined mould surface） or in 3D space （an implicitly defined mould surface）, thereby significantly improving on the existing methods. Compared with the conventional methods, the proposed method, besides its computational simplicity, has a better error control mechanism in computing the initial path and offset points. Numerical experiments are also carried out to demonstrate the feasibility of the new method in composite forming processes and also its potential application in computer numerical control （CNC） machining, surface trim, and other industrial practices.