Screw axis measurement methods obtain a precise identification of the physical reality of the industrial robots’ geometry. However, these methods are in a clear disadvantage compared to mathematical optimisation processes for kinematical parameters. That’s because mathematical processes obtain kinematical parameters which best reduce the robot errors, despite not necessarily representing the real geometry of the robot. This paper takes the next step at the identification of a robot’s movement from the identification of its real kinematical parameters for the later study of every articulation’s rotation. We then obtain a combination of real kinematic and dynamic parameters which describe the robot’s movement, improving its precision with a physical understanding of the errors.

The sequential multilateration principle is often adopted in geometric error measurement of CNC machine tools. To identify the geometric errors, a single laser tracker is placed at different positions to measure the length between the target point and the laser tracker. However, the measurement of each laser tracker position is not simultaneous and measurement accuracy is mainly subject to positioning repeatability of the machine tool. This paper attempts to evaluate the measurement uncertainty of geometric errors caused by the positioning repeatability of the machine tool and the laser tracker spatial length measurement error based on the Monte Carlo method. Firstly, a direct identification method for geometric errors of CNC machine tools based on geometric error evaluation constraints is introduced, combined with the geometric error model of a three-axis machine tool. Moreover, uncertainty contributors caused by the repeatability of positioning of numerically controlled axes of the machine tool and the laser length measurement error are analyzed. The measurement uncertainty of the geometric error and the volumetric positioning error is evaluated with the Monte Carlo method. Finally, geometric error measurement and verification experiments are conducted. The results show that the maximum volumetric positioning error of the machine tool is 84.1 μm and the expanded uncertainty is 5.8 μm (�� = 2). The correctness of the geometric error measurement and uncertainty evaluation method proposed in this paper is verified compared with the direct geometric error measurement methods.