The motion accuracy of a linear axis is represented by the geometric errors defined in the current standards. However, the geometric errors are the local properties for the error-included motion of the moving component and their values are related to the position of the measured function point or line. This will cause uncertainties for the results of an accuracy test. Thus, a new invariant approach is presented for the motion accuracy test and motion error identification of a linear axis. The translational and angular error motions of the moving component are identified definitively according to the global kinematic properties of the error-included motion. The invariant errors, including the range of translational error motion, the range of tilting error motion and the range of rolling error motion, are defined to evaluate the motion accuracy. The relationships between the geometric errors of the trajectory traced by an arbitrary point or line and the motion errors of the moving component are established to replace the Abbe principle and the Bryan principle for accuracy test in a rigorous mathematical way. The motion of a linear axis in a machine tool is tested as the experiments to illustrate the advantages of the invariant approach. The results show that the invariant errors are independent of the measured function point or line. The geometric errors of the trajectory traced by an arbitrary point or line can be calculated, and the deviations caused by the translational and angular error motions are distinguished using the invariant approach.

线性轴的运动精度由当前标准中定义的几何误差表示。但是，几何误差是运动组件中包含误差的运动的局部属性，其值与测量的功能点或测量线的位置有关。这将导致准确性测试结果的不确定性。因此，提出了一种新的不变方法用于线性轴的运动精度测试和运动误差识别。根据包含错误的运动的整体运动学特性，确定运动组件的平移和角度错误运动。定义包括平移误差运动范围，倾斜误差运动范围和滚动误差运动范围在内的不变误差，以评估运动精度。建立由任意点或线跟踪的轨迹的几何误差与运动部件的运动误差之间的关系，以严格的数学方式代替阿贝原理和布莱恩原理进行精度测试。机床上的线性轴运动作为实验进行了测试，以说明不变方法的优点。结果表明，不变误差与测得的功能点或线无关。可以计算出任意点或线所跟踪的轨迹的几何误差，并使用不变方法来区分由平移和角度误差运动引起的偏差。