Five-axis contour following is one of the main tasks for five-axis CNC machine tools. The contour following accuracy directly determines the final machining precision. Therefore, control of the five-axis contour error is significant. Currently, most existing definitions of five-axis contour error are in the Cartesian task space, and this inevitably requires direct and inverse Jacobian transformations between the task-space contour-error computation and the joint-space contour-error control. Different from them, this paper defines the five-axis contour error in the ℝ⁵ joint space through adjusting uniform units of five joints, and accordingly proposes a third-order estimation algorithm for the defined joint-space contour error, with the help of the concept of generalized curve. Based on the joint-space contour-error definition and estimation, a joint-space five-axis cross-coupling control scheme is finally provided. Simulation and experimental results demonstrate that the presented third-order joint-space contour-error estimation algorithm has a satisfactory estimation accuracy, and the presented joint-space five-axis contour control method can decrease both of the joint-space and the task-space five-axis contour errors by more than 49%. It is also analyzed and verified that comparing with routine task-space five-axis contour control method, the presented joint-space method not only needs not the direct and inverse Jacobian transformations during error estimation, which saves the computational burden, but also generates minimum axial contour-control commands, which enhances the control stability, thus resulting in better contour-following performances.

五轴轮廓跟随是五轴数控机床的主要任务之一。轮廓跟随精度直接决定了最终加工精度。因此，五轴轮廓误差的控制很重要。当前，大多数现有的五轴轮廓误差定义都在笛卡尔任务空间中，这不可避免地需要在任务空间轮廓误差计算和关节空间轮廓误差控制之间进行直接和逆雅可比变换。与它们不同，本文定义了ℝ五轴轮廓误差⁵通过调整五个关节的均匀单位来调整关节空间，并借助于广义曲线的概念，针对定义的关节空间轮廓误差提出了一种三阶估计算法。基于关节空间轮廓误差的定义和估计，最终提出了一种关节空间五轴交叉耦合控制方案。仿真和实验结果表明，所提出的三阶关节空间轮廓误差估计算法具有令人满意的估计精度，并且所提出的关节空间五轴轮廓控制方法可以减少关节空间和任务空间。五轴轮廓误差超过49％。分析并验证了与常规任务空间五轴轮廓控制方法相比，