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采用弧长参数进行开边曲面构件上的铺丝路径规划,基于此初始路径和等距点可用同一个数学方程表示、并用简单的算法计算。借助经典微分几何铺丝路径的计算归结为在曲面参数域(参数表示的芯模面)或 3D 空间(隐式表示的芯模面)解初值问题的常微分方程。相比较而言除了计算简单外,新方法有较好的误差控制机制。给出了数值实例证明本文方法对复合材料成型的有效性,此外在数控加工,曲面裁剪,以及其他工业与研究领域也有潜在的应用价值。
The arc length parameter is used to plan the path of the laying wire on the curved surface member. Based on this, the initial path and the equidistant point can be expressed by the same mathematical equation and calculated by a simple algorithm. The calculation with the classical differential geometry laying path is attributed to the differential equation of the initial value problem in the parameter domain of the curved surface (the core surface of the parameter representation) or in the 3D space (the core surface of the implicit representation). In contrast to the simple calculation, the new method has a better error control mechanism. The numerical examples are given to demonstrate the effectiveness of the proposed method in the fabrication of composite materials. In addition, numerical methods have potential applications in numerical control machining, surface cropping, and other fields of industry and research.