Full parameter calibration of parallel mechanism

Calibration of a parallel mechanism using a specified artifact, artifact calibration, is an effective method. However, there are strong correlations between each parameter in an artifact calibration of a parallel mechanism. Therefore, it is difficult to identify all kinematic parameters included in a kinematic model of the parallel mechanism from measuring data. In this research, we propose two improved methods for the calibration of parallel mechanisms. One is using adjustable links for calibration. The adjustable links enlarge the workspace of parallel mechanisms and enables one to make a choice of more advantageous measuring arrangements for parameter identification. The other is using a priori knowledge to constrain the identified values of kinematic parameters. This method is available for any mechanisms when approximate values and tolerances of its kinematic parameters are known from their design specification or some other measurements. Both methods enable the full parameter identification of parallel mechanisms without divergence in the least squares method and improve the positioning accuracy after calibration. Introduction In the application of parallel mechanisms, it is necessary to calibrate the kinematic parameters (1) and improve the positioning accuracy for accurate task performance. Calibration of a parallel mechanism using a specified artifact, artifact calibration, is an effective method. However, there are strong correlations between all of the parameters in the kinematic calibration of a parallel mechanism. Therefore, it is difficult to identify all kinematic parameters included in a kinematic model of the parallel mechanism from measuring data. To calibrate a parallel mechanism, we must eliminate these correlations. In this study, we propose two methods that eliminate the correlations and make the calibration calculation robust. One is using nonsymmetrical links for calibration. Using several nonsymmetric links, the correlations are eliminated and each parameter is identified with a small standard deviation. This method is available for parallel mechanisms with adjustable links. The other is using a priori knowledge in a non-linear squares method. This method is available for any mechanisms when the values and tolerances of its kinematic parameters are pre-approximated. Using each method, we identify all kinematic parameters of the parallel mechanism and improve the positioning accuracy after calibration. Artifact Calibration of a Parallel Mechanism Artifact calibration is a calibration method that estimates the values of kinematic parameters from the residual error of specified artifacts measurement. Artifacts are calibrated pieces or devices, for example gauge block, ball plate, double ball bar system (DBB), coordinate measuring machine (CMM), etc. In artifact calibration, each parameter’s value is calculated with the least squares method using the observation equation vector, the Jacobian matrix and the error matrix associated with the measurement of artifacts. Usually, a parallel mechanism is designed symmetric. The positioning accuracy of the symmetric formed parallel mechanism is insensitive to the tolerances of kinematic parameters because the error propagation from a parameter’s error to the endeffector cancels out one another. However, although this is advantageous for accurate positioning, it makes it difficult to calibrate the mechanism. This cancellation causes the strong correlations between parameters. Therefore, it becomes difficult to identify each parameter independently of the others with the non-linear least squares method. For accurate calibration, these correlations must be eliminated. Artifact Calibration with Adjustable Links It is hard to calibrate a symmetric formed parallel mechanism. In contrast, calibration of a nonsymmetric formed one is easy because the error cancellation effect of a nonsymmetric mechanism is less than that for a symmetric one. Therefore the correlation between parameters becomes weaker and each parameter can be identified precisely. When the form of a parallel mechanism is adjustable, we can use a nonsymmetric formed mechanism, which is easy to calibrate, at the calibration stage and adjust it to the symmetric form which is insensitive to the parameters’ tolerances, at the operation stage. Figure 1 shows a coordinate measuring machine using a parallel mechanism (Parallel CMM) . Parallel CMM is based on a 3 DOF linear actuated parallel mechanism that is designed as symmetric for accurate measurement operation. The spherical joint of the Parallel CMM consists of a magnet and a triangle hole, and holds the steel ball at three points on its spherical surface. The advantage of the joint is high repeatability because of no gap between the housing and the ball. The found value of repeatability of Parallel CMM is 2 micron at the maximum. Using this joint gives the high repeatability of the position of the end-effector when we separate all connecting rods and the end-effector from the base and reset up them. The found value of set/reset repeatability is 3 micron at the maximum. This means that we can adjust the Parallel CMM from symmetric form to Fig. 1. Parallel CMM (symmetric form for measurement operation). Fig. 2. Parallel CMM (nonsymmetric form for measurement operation) Long Links Long Links Short Links