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Globally accurate manipulation and localization of the terminal of a mobile robot arm within a large workspace has always been a bottleneck problem. In this article, a planar-laser-guided solution is proposed for this issue. The core of this solution is using three movable planar lasers to designate a unique reference point with orientation information within the workspace, and designing a sensor module mounted on the terminal of the robot arm with photoelectric position sensitive devices (PSDs) to measure the relative pose between the terminal and the reference point. Thus, the terminal of the robot can be guided by this relative pose to the target in a given orientation. According to this concept, a parameterized model of the moveable planar lasers and the poses of the PSDs, as well as an expression of their geometric relationship, were derived. The manipulation strategy of the robot arm was further investigated through the model, and an error compensation method to improve the manipulation accuracy was proposed. Finally, a reduced-scale prototype system, based on this solution, was built, on which tracking and positioning experiments of the robot arm were carried out to verify the feasibility of the solution. It has been shown that this laser-guided solution is not sensitive to the blockage (occlusion) of several laser transmitters, which could be an advantage for its application in future autonomous settings.

The frames of heavy machine tools generate considerable dynamic and position-dependent thermal errors due to their large scale and irregular temperature distribution caused by ambient temperature fluctuations. They are difficult to predict by conventional experimental data-based thermal error modeling methods. In this paper, a typical gantry frame of a heavy gantry type machine tool is taken as a vehicle to present a thermal error modeling methodology. The frame was firstly divided into several parts (elements). Then, an element simplification method was put forward to approximate it by simplified square tube shapes that retain most of the information from the original element. Based on this simplification, the temperature distribution and the equivalent load of the element were explicitly derived at selected key points on the frame. The static thermal error of the frame was obtained by the matrix displacement method, where a C1 continuity stiffness matrix, including the shear deformation, was used to improve calculation accuracy. According to the formulated calculation method of the static thermal error and of the temperature impact convolution, the dynamic thermal error was derived utilizing the historical temperature sequence at the key points. Finally, the proposed thermal error model was verified by comparing it with FEM results in the static-state and by experimental results in the dynamic-state. The proposed method allows the formulation of an explicit dynamic thermal error model with a simple expression, which can be easily embedded in the PLC of a machine tool for compensation purposes. The method has the potential to be used for structural thermal error compensation in a wide range of heavy machine tools.

Calibration is considered to be the most effective way to improve the accuracy of parallel kinematic machine tools (PKMTs). However, ordinary calibrations only considered the time-invariant errors (manufacturing error), neglecting some time-variant errors, a significant one of which is thermal error. Therefore, in this paper, the influence of thermal error was considered in the calibration of a 3-P(Pa)S parallel-type spindle head. First, a new kinematic model of the spindle head was proposed, which is closer to the real physical model, so the thermal error of the spindle head can be considered in the model. Second, the structural parameters of the spindle head were expressed as the sum of the ideal parameters, the manufacturing errors, and the thermal errors. Third, the pose (position and orientation) of the end effector and the temperature of the spindle head were measured. The positions of the temperature sensors were selected using the global temperature sensitivity index (GTSI), which is derived from the global sensitivity index (GSI). Thus, by setting a standard temperature, the thermal error of the structural parameter can be obtained. Fourth, the influence of the thermal error was inputted into the identification equation for calibration, so the results are the structural parameters at the standard temperature (20 °C). To solve the ill-conditioning problem, a Regularization method was used in the identification. Finally, the calibration was verified on a 3-P(Pa)S-XY machine tool. The RTCP test, performed immediately after the measurement, shows that the maximum position error after the calibration is 0.019 mm at the tilt angle of 30° and 0.037 mm at 20°. In addition, the RTCP test after a temperature change shows that the calibration considering the thermal error can improve the average position accuracy from 0.025 mm to 0.015 mm. The calibration method in this paper is expected to be applicable for other machine tools.

In order to derive a thermal error model that can better reflect the physical model of the machine tool to improve the model’s robustness and also has an explicit and simpler expression for real-time thermal error compensation, a new thermal error model of a heavy gantry-type machine tool was established. Firstly, multi-body system (MBS) was used to transform the thermal error modeling of the machine tool into the thermal error modeling of the discrete parts of the machine tool. Then, as for the thermal error modeling of the slider-ram structure, by analyzing the characteristic of the thermal expansion of a one-dimensional rod, power function was considered to better reflect that relationship in which the index number can represent the distance between heat source and the temperature measurement location. Then, its thermal error model was expressed as the superposition of two power functions according to the thermal superposition principle and the distribution of the heat sources. As for the thermal error modeling of gantry structure, it was simplified to a frame with −3 DOF. And its thermal error model was derived by virtual work principle (VWP). Then, the whole thermal error model of the machine tool was embedded into the Simens840d NC system and S7-300 programmable logic controller to establish a thermal error compensation system. Finally, the error model and compensation was verified by machining a rhombus-shaped workpiece of which different zones reflect the thermal error in different directions. And the workpiece was measured by a CMM. The results show that the average thermal error can be reduced from around 101 to 13.5 μm after the compensation, indicating the effectiveness of the thermal error modeling and compensation for the practical application.

Thermal error is one of the major contributors to dimensional errors of machine tools. In this paper, a hybrid thermal error modeling method is proposed to forecast the thermal expansion of a heavy boring and milling machine tool in z-axis. In this model, the thermal error in z-axis is calculated as the expansion of a one-dimensional rod. The inputs of the model are temperatures of spindle motor, hydrostatic bearing and environment, selected through fuzzy c-means (FCM) clustering method. The temperatures of the nodes in the rod are solved by Thomas algorithm and the coefficients of the model are optimized by genetic algorithm (GA). The accuracy of the proposed model is compared with that of the output error model and stepwise regression model, and the performance of the proposed model is better in accuracy. In addition, a compensation system is developed based on the proposed model to reduce the thermal error in z-axis.

Ball screw drives are widely used in machine tools to provide accurate linear motion. Elastic deformation is one of the major error sources for ball screw drives in achieving high accuracy motion, and changes greatly when velocity varies. The influence of velocity on the elastic deformation can be estimated and it can be compensated by means of dynamic modeling and servo control method. This paper presents a dynamic model considering torque transmission between the ball screw and the nut. And stiffness is identified by a method of combining theoretical calculation and experimental tests on a constructed test bench, which has two novel symmetrical loading mechanisms. In order to analyze the influence of moving velocity on the elastic deformation, simulation and experiments are conducted when two trajectories which have velocity jumps are input. And the simulated elastic deformations are compared with experimental results to evaluate the accuracy of the model. The results show that the simulated results fit the experimental results with high accuracy. The relationship between the elastic deformation of ball screw drives and the velocity is linear based on the experimental results. Then the simulation results are used to compensate the elastic deformation based on the feed-forward compensation method. The results show that the differences between the actual compensation values and actual elastic deformation are small and most of the elastic deformation of the ball screw drives can be compensated. Therefore, the proposed dynamic model and compensation method can be used to improve the tracking accuracy of ball screw drives.

The 3-P(Pa)S mechanism, based on the 3-Prismatic-Rotational-Spherical (PRS) mechanism, but with three of its revolution joints and passive links replaced by parallelogram structures, provides improved stiffness and better constraint of undesired Degree of Freedom (DOFs). The general method to establish the error model of a 3-P(Pa)S mechanism is simplifying it to a 3-PRS mechanism, which fails to account for the influence of the errors in the parallelogram structure. In this article, the error model of a spindle head based on 3-P(Pa)S mechanism was established. By projecting the structural errors of the parallelogram structure to the structural errors of a 3-PRS mechanism which is simplified from the 3-P(Pa)S mechanism, the errors of the parallelogram can be included into the model. Then, the projecting method was verified by an experiment on the spindle head to prove its correctness. Based on the error model, sensitivity analysis of the structural errors was carried out. According to the characteristic of the mechanism, two new sensitivity indexes, standardized signed local sensitivity index and standardized signed global sensitivity index, were proposed which can better reflect the influence of the structural errors on the end effector error and can also indicate whether some structural errors have similar or opposite influence on the end effector. Then, the most sensitive errors were derived and the sensitivity distribution within the workspace of the spindle head was analyzed. Additionally, two possible applications based on the sensitivity analysis were proposed to reduce the error of the spindle head.