Purpose This paper aims to propose a four-point measurement model for directly measuring the pose (i.e. position and orientation) of industrial robot and reducing its calculating error and measurement uncertainty. Design/methodology/approach A four-point measurement model is proposed for directly measuring poses of industrial robots. First, this model consists of a position measurement model and an orientation model gotten by the position of spherically mounted reflector (SMR). Second, an influence factor analysis, simulated by Monte Carlo simulation, is performed to investigate the influence of certain factors on the accuracy and uncertainty. Third, comparisons with the common method are carried out to verify the advantage of this model. Finally, a test is carried out for evaluating the repeatability of five poses of an industrial robot. Findings In this paper, results show that the proposed model is better than the three-SMRs model in measurement accuracy, measurement uncertainty and computational efficiency. Moreover, both measurement accuracy and measurement uncertainty can be improved by using the proposed influence laws of its key parameters on the proposed model. Originality/value The proposed model can measure poses of industrial robots directly, accurately and effectively. Additionally, influence laws of key factors on the accuracy and uncertainty of the proposed model are given to provide some guidelines for improving the performance of the proposed model.

Angle measurement is widely used in various fields of science and technology. With the development of technology, the measurement uncertainty of angle metrology becomes more and more demanding. To achieve high-precision calibration of a high-precision angle comparator with a sub-arc-second level, a method of angle position error calibration and measurement uncertainty evaluation based on no material reference was established. Firstly, the structure of the angle comparator with a vacuum preloaded air bearing driven by an ultrasonic motor drive and the construction of the whole calibration system are briefly introduced. Then, the basic principle, algorithm and error separation principle of angle calibration based on the optical angle measurement method were studied, and the test process is introduced. Finally, the measurement results and error sources were analyzed, the measurement uncertainty model was established and the measurement uncertainty was evaluated. The experimental results show that the high-precision angle comparator with a vacuum preloaded structure has an angle position error of 0.12″ and a measurement uncertainty of 0.05″ (k  =  2). Through many experiments, it is shown that the measurement system has a stable high-precision calibration capability with a sub-arc-second level for circular division artifacts.

The radial error is the key performance indicator of ultra-precision axis. In order to measure and evaluate the radial error of ultra-precision axis with nanometer accuracy, a measurement system with an accuracy of nanometer based on capacitive displacement probes and standard spheres is developed. The nonlinearity error of capacitive displacement probes, misalignment error of the probes, eccentric error of standard spheres, error caused by environment temperature change, environment vibration and error separation methods are analyzed and the effects of the above factors are obtained; Multiple measurement examples carried out with the measurement system this paaper constructed indicate the repeatability of the measurement system reaches 10.5 nm and the roundness error of artifact separated is less than 4.03 nm. In order to evaluate the measurement dispersion of the ultra-precision axis radial error, the major uncertainty components and the complete process of the comprehensive evaluation of the measurement uncertainty are proposed. The combined uncertainty of radial error motion measurement of the ultra-precision axis with Donaldson reversal is 31.64 nm (k = 2).

Purpose This paper aims to propose a reasonable method to evaluate uncertainty of measurement of industrial robots’ orientation repeatability and solve the non-linear problem existing in its evaluation procedure. Design/methodology/approach Firstly, a measurement model of orientation repeatability, based on laser tracker, is established. Secondly, some factors, influencing the measurement result of orientation repeatability, are identified, and their probability distribution functions are modelled. Thirdly, based on Monte Carlo method, an uncertainty evaluation model and algorithm of measurement of industrial robot’s orientation repeatability are built. Finally, an industrial robot is taken as the research object to validate the rationality of proposed method. Findings Results show that the measurement model of orientation repeatability of industrial robot is non-linear, and the proposed method can reasonably and objectively estimate uncertainty of measurement of industrial robots’ orientation repeatability. Originality/value This paper, based on Monte Carlo method and experimental work, proposes an uncertainty evaluation method of measurement of industrial robots’ orientation repeatability which can solve the non-linear problem and provide a reasonable and objective evaluation. And the stochastic ellipsoid approach is firstly taken to model the repeatability of laser tracker. Additionally, this research is beneficial to decide whether the orientation repeatability of the industrial robot meets its requirements.

Purpose This paper aims to solve the nonlinear problem in the uncertainty evaluation of the measurement of the positioning repeatability (RP) of industrial robots and provide guidance to restrict the uncertainty of measurement of RP (uRP). Design/methodology/approach Firstly, some uncertain sources existing in the measurement procedure of RP are identified. Secondly, the probability distribution function (PDF) of every source is established on the basis of its measurements. Some spatial combined normal distributions are adopted. Then, a method, based on Monte Carlo method (MCM) and established measurement model, is developed for the estimation of uRP. Thirdly, some tests are developed for the identification and validation of the selected PDFs of uncertain sources. Afterwards, the proposed method is applied for the evaluation and validation of the uRP. Finally, influence analyses of some key factors are proposed for the quantification of their relative contributions to uRP. Findings Results show that the proposed method can reasonably and objectively estimate the uRP of the selected industrial robot, and changes of the industrial robots’ position and the laser trackers measurement are correlated. Additionally, the uRP of the selected industrial robot can be restricted by using the results of its key factors on uRP. Originality/value This paper proposes the spatial combined normal distribution to model the uncertainty of the repeatability of the laser tracker and industrial robot. Meanwhile, the proposed method and influence analyses can be used in estimating and restricting the uRP and thus useful in determining whether the RP of a tested industrial robot meets its requirements.