Articulated Arm Coordinate Measuring Machines Research Articles

Metrological assessment of the carbon tubes behavior under thermal variation for the compensation of 3D devices

Abstract Composite materials are increasingly used in 3D metrology, especially for portable measuring devices such as articulated arm coordinate measuring machines (AACMM), 3D scanners, and ball bars. Their use is justified by their interesting mechanical properties including their low density, good rigidity, and especially their light weight, which makes them ideal for portable devices, that are meant to be often transported by the user. However, due to their complex composition, the characterization of the thermal behavior of composite materials remains complicated compared to standard materials and is nowadays an active research subject. In fact, the coefficient of thermal expansion of composite materials is dependent of the very specific composition of the composite material considered. Hence, it is function of several parameters such as the orientation of the fibers, the fiber volume fraction, the ply sequence, the cooling rate, etc.
In the other hand, in 3D metrology, and especially in portable 3D metrology, determining the expansion coefficient of the different part of the measurement devices used is necessary. In fact, the portable measurement machines are often integrated and used directly on the shop floor, where the thermal variations can be important and then heavily impact the measurements results. in some cases, the lack of knowledge of the coefficient of thermal expansion of the composite materials that compose the portable measuring machine can significantly increase the measurement uncertainty.

Dynamic error modeling and analysis of articulated arm coordinate measuring machine with integrated joint module

The self-driven articulated arm coordinate measuring machine (AACMM) is a new non-orthogonal flexible coordinate measuring equipment providing automatic positioning and measurement with integrated joint modules introduced to its rotary joints. The dynamic measuring accuracy is the crucial indicator of the self-driven AACMM performance. However, the part manufacturing assembly error and structural dynamic deformation error will seriously reduce the dynamic measuring accuracy. Therefore, a modeling compensation approach based on error propagation and accumulation mechanism analysis of the above two aspects is necessarily required to preserve the automatic measuring accuracy of the self-driven AACMM. In this paper, the authors propose an innovative modeling method for evaluating and compensating for the dynamic measuring errors of the self-driven AACMM. The ideal measuring model is constructed assisted with on the classical Denavit–Hartenberg parameter methodology and the complex structure of the self-driven AACMM. The source and its propagation mechanism of the dynamic error from the self-driven AACMM were analyzed systematically to decouple the superposed error impact on measuring precision. The dynamic measurement error compensation mechanism model is presented considering the influence of instantaneous spatial attitude on the dynamic structural parameters of self-driven AACMM. Experimental results indicate that the single-point repeatability measurement error fluctuation of the self-driven AACMM is 0.046 mm. The radius measuring error of the gauge ball reduces from −0.26 mm to −0.19 mm after the error model compensation. Additionally, the measuring accuracy is demonstrated to be effectively improved by the dynamic error compensation mechanism model.

A Comparison of CMM and CMA Capabilities in Product Feature Verification Metrology

To control variations and guarantee that a part will function as intended in an assembly, measurement verification must be conducted with specialized metrology equipment. The Coordinate Measuring Machine (CMM) and the Articulated Arm CMM (AA-CMM) are analyzed in this comparative study, to identify their respective advantages and disadvantages when measuring flatness. The goal of this pilot study is to detect the measuring limitations of each machine and propose a methodology to identify appropriate use of each device based on its capabilities. For measuring flatness, contact and contactless measurement experiments were designed. As expected, it is observed that the CMM performs better than the CMA in flatness measurement because it has a higher resolution [1]. By looking at the measured flatness obtained during the experiment, it was determined that the CMM had a smaller minimum measurable tolerance in all permutations of the test when compared to its counterpart. Resulting in the proposal of different functional working envelopes for these machines. Establishing working envelopes permits the use of both machines for overlapping working purposes as the versatility of CMAs in Geometry verification in settings where CMMs cannot be deployed, could have a great impact as long as they operate on the corresponding working envelopes defined in this research, which were defined as follows: CMM has a minimum measurable tolerance of 0.0006in, CMA contact, has a minimum measurable tolerance of 0.0024in and CMA contactless, has a minimum measurable tolerance of 0.0045in.

Error Analysis of a Coordinate Measuring Machine with a 6-DOF Industrial Robot Holding the Probe

A complex surface measurement is important for quality control and manufacturing processes. Articulated arm coordinate measuring machines (AACMMs) are widely used in measuring the complex surface. However, the AACMMs that are currently used always require manual operation, which reduces efficiency and introduces operator errors. This study presents a measuring device with a 6−DOF industrial robot holding a contact probe, which realizes the automation measurement of a complex surface and eliminates operator errors compared with the traditional measurement process of an AACMM. In order to explore the source of the measuring errors of the device, the influence of three measurement parameters (approaching velocity, contact angle, and measurement position) on the measurement error of the device is analyzed in this paper. A calibration ball measurement experiment is conducted for each parameter. The results show that the optimal approaching velocity of the measuring device is around 2 mm/s, the probe should be as perpendicular as possible to the surface being measured during the measurement, and the maximum measurement error at different positions is 0.1979 mm, with a maximum repeatability error of 0.0219 mm. This study will help improve the automation measuring errors of the AACMM by utilizing an industrial robot to hold the probe, pushing for a wider application of the AACMM.

Calibration method for structural parameters of the articulated arm coordinate measuring machine utilizing a modified hybrid algorithm

In order to increase the precision and decrease the movement uncertainty of the articulated arm coordinate measuring machine (AACMM), a calibration method is proposed in this paper, where the accuracy of single-point repeatability and volumetric accuracy (indicated by distance precision) are simultaneously considered. Considering the good ability of global exploitation and local exploration granted by chicken swarm optimization (CSO) and tabu search (TS), respectively, the CSO and TS are hybridized to construct the tabu searching-based CSO (TSCSO). To help the TSCSO jump out of the local optimal area when it is trapped in it, a transformational criterion of convergence precision is designed to integrate TSCSO with simulated annealing (SA) to formulate the hybrid algorithm called TSCSO with TSCSO-SA, which simultaneously possesses the good ability to globally exploit, locally explore, and jump out of the local optimal area when the population is trapped in it. Moreover, calibration experiments are conducted based on the accuracy of single-point repeatability and volumetric accuracy to verify the effectiveness, efficiency and suitability of the method and algorithm used in this paper. The results of the experiments and verifications show that the precision and movement uncertainty of the AACMM are immensely increased and decreased, respectively, further revealing that the method and algorithm proposed in this paper are able to effectively, efficiently and suitably calibrate the structural parameters of the AACMM.

Novel kinematic model of articulated arm coordinate measuring machine with angular position measurement errors of rotary axes

The measurement accuracy of an articulated arm coordinate measuring machine (AACMM) is determined by its kinematic model to estimate the end effector position from angular positions of rotary axes. In conventional studies, the Denavit–Hartenberg (DH) model, containing position and orientation errors of the rotary axis average lines as error sources, has been widely employed. This study first proposes a novel kinematic model including angular position measurement errors of rotary axes. To identify the proposed model, a new Single Point Articulation Test (SPAT) setup is presented with the R-Test to measure the stylus sphere's three-dimensional displacement. The prediction accuracy of the proposed model is experimentally evaluated.

A variable-measurement-space-based method for improving the measurement accuracy of AACMMs

Articulated arm coordinate measuring machines (AACMMs) are usually used to measure mechanical parts of different sizes in practical applications. When the size of parts is smaller than that of the AACMM, a redundant measurement space of the measuring machine is generated, resulting in reduced measurement accuracy of the AACMM. Moreover, due to the series structure of the AACMM, the joint errors would be propagated with the increasing length of the bar, which could amplify the measurement error. Therefore, on the premise of ensuring the measurement space required by the measured parts, this work proposes a new method based on variable measurement space, i.e. locking some movable joints of the AACMM, to improve the measurement accuracy of the AACMM for small mechanical parts. The measurement accuracy of the AACMM is examined under various measurement spaces. Firstly, the Monte Carlo method is used to simulate the measurement space of the AACMM with one or more joints locked. Then, the spatial error of the AACMM and the multipoint calibration with joint locked are simulated and discussed in detail. Finally, the feasibility and effectiveness of the proposed variable-measurement-space method are verified by the standard single-point cone experiments. The results show that the measurement accuracy of the AACMM is substantially improved under three kinds of strategies, i.e. locking joint 1, joint 2, and joint 3, respectively.

Flexible Scanning Method by Integrating Laser Line Sensors with Articulated Arm Coordinate Measuring Machines

Measuring and reconstructing the shape of workpieces have been considered as a fundamental step in both reverse engineering and product quality control. Owing to increasing structural complexity of recent products, measurements from multiple directions are typically required in current scanning techniques. Specifically, the plane structured light can be applied to measure one area of a part at a time, with an additional algorithm required to merge the collected data of each area. Alternatively, the line structured light sensor integrated on CNC machines or CMMs could also realize multi-view measurement. However, the system needs to be repeatedly calibrated at each new direction. This paper presents a flexible scanning method by integrating laser line sensors with articulated arm coordinate measuring machines (AACMM). Since the output of the laser line sensor is 2D raw data in the laser plane, our system model introduces an explicit transformation from the 2D sensor coordinate frame to the 3D base coordinate frame of the AACMM (i.e., the translation and rotation the of the 2D sensor coordinate in the sixth coordinate system of AACMM). To solve the model, the “conjugate pairs” are proposed and identified by measuring a fixed point (e.g., a sphere center). Moreover, a search algorithm is adopted to find the optimal solution, which noticeably boosts the model accuracy. The experimental results show that the error of the system is about 0.2 mm, which is caused by the error of the AACMM, the sensor error and the calibration error. By measuring a complicated part, the proposed system is proved to be flexible and facilitate, with the ability to measure a part expediently from any necessary direction. Furthermore, the proposed calibration method can also be used for robot hand-eye relationship calibration.

On-site calibration method of the AACMM based on a high-precision CNC machine tool

An articulated arm coordinate measuring machine (AACMM) is a kind of instrument used to test workpieces in the industrial field, and its measurement uncertainty depends on the on-site environmental factors to a certain extent. If there is a problem with the AACMM during on-site testing, it needs to be re-calibrated to ensure the measurement uncertainty. In this work, a fast on-site calibration method for the AACMM is proposed using a high-precision computer numerical control (CNC) machine tool. The AACMM is fixed on the machine tool table. The calibration artifact is clamped on the machine tool spindle. This calibration artifact can move to any point in the global space of the AACMM along with the operation of the spindle. Then, a virtual calibration artifact with calibration points is achieved using the CNC machine tool. The positions of these points are calculated using the improved Hammersley sequence. The calibration method using a high-precision CNC machine tool is experimentally verified through the single-point articulation performance test of ASME B89.4.22-2004 and the length measurement test of ISO 10360-12. The calibration method proposed in this work only uses an on-site high-precision CNC machine tool, one of the most common machines in many industrial fields, as the calibration instrument for the AACMM calibration. No extra equipment is required, which is convenient and beneficial to calibrate the AACMM. In addition, the CNC machine tool can construct different kinds of virtual structures for the AACMM calibration, such as virtual rods, virtual circles, virtual balls and even non-uniform 3D artifacts with complex curved surfaces. This may give rise to many novel calibration methods and further improve the calibration accuracy.

Structural design and performance analysis of a self-driven articulated arm coordinate measuring machine

In order to solve the problem that a traditional articulated arm coordinate measuring machine (AACMM) cannot measure automatically, a self-driven AACMM is proposed. Based on the self-driven AACMM design indicators, the length of the connecting rods of the self-driven AACMM was allocated. The self-driven AACMM virtual prototype was designed and assembled based on joint module selection and joint component design, and its measurement space range was also verified. The key components of the structural optimized design and dynamic performance analysis of motion parameters are adopted, respectively, to correct the positioning error of the self-driven AACMM’s probe caused by static and dynamic deformations. The static deformation of the structure caused by the self-driven AACMM’s weight was analyzed. The influence of the dynamic flexible deformation on the positioning error of the probe of the self-driven AACMM during the variable-speed approach and the constant-speed touch measurement stage was studied. The results show that the measurement space range of the self-driven AACMM designed in this paper can meet the design index of the measuring radius. The probe position error caused by static deformation of the measuring machine after structural optimization is reduced by an order of magnitude, and the equivalent stress of the mechanical structure of the self-driven AACMM is within the allowable stress of the material. The positioning error of the probe caused by the dynamic deformation of the self-driven AACMM structure meets the positioning accuracy index. During the stage of self-driven AACMM constant-speed touch measurement, the instantaneous position error of the probe changes linearly with the touch time and the optimal touch speed (6.6 mm s−1, 6.4 mm s−1) exists to minimize the probe positioning error. During the variable-speed approach stage, the influence of the angular acceleration and the angular velocity of each joint on the positioning error of the probe is negligible when the self-driven AACMM is in the typical posture. In the extreme posture, with the optimal joint angular acceleration () and angular velocity (), the inertial force of the measuring machine structure and the instantaneous position error of the probe are the smallest, and the movement stability is the best. The structural optimization design and motion parameter performance analyses of the self-driven AACMM can provide a theoretical research foundation for subsequent motion parameter optimization and dynamic error compensation modeling.

Multi-point calibration method for articulated arm coordinate measuring machine based on an observability index

Kinematic calibration is an effective way to improve the accuracy of articulated arm coordinate measuring machine (AACMM). In this paper, a multi-point calibration method for AACMM based on observation index is proposed. First, the kinematic model is established according to the D–H method, and the measurement error model is established on the basis of the D–H model. Then, the feasibility of using the observation index to evaluate the posture of AACMM is analyzed, and simulations are carried out to verify the correlation between the level of the observation index and the quality of the calibration results. In the simulation, the influence of the number of measurement positions and the number of measurement points on the calibration results are studied in combination with the observability index, and on this basis, a multi-point calibration method is proposed. Finally, experiments are carried out to verify the superiority of the multi-point calibration method. The results show that, compared with the single point calibration method, the multi-point calibration method can improve the measurement accuracy by 31.58%, and the average measurement error of the AACMM after the multi-point calibration method is 0.0091 mm.

Research on improving the measurement accuracy of the AACMM based on indexing joint

In order to improve the measurement accuracy of articulated arm coordinate-measuring machines (AACMMs), a new kind of AACMM based on an indexing joint structure is proposed in this paper. The working principle of the indexing joint is introduced, and a kinematic model of the measuring machine is established based on this principle. The influence weight of the angle error for each joint on the measurement accuracy is analyzed by simulations, and the changes in the accuracy, measurement space and flexibility of the measuring machine before and after adopting the indexing joint are compared. The results show that the use of the indexing joint can effectively improve the measurement accuracy of the AACMM, and the replacement of the first two joints with the indexing joints has the most obvious improvement effect on the measurement accuracy, and has little influence on the measurement space and flexibility. The indexing joint-based AACMM can provide a new idea for the research of improving the measuring accuracy of the AACMM.

Improving the measuring length accuracy of articulated arm coordinate measuring machine using artificial neural network.

A new method for further improving the measuring length accuracy of the articulated arm coordinate measuring machine (AACMM) is proposed. The detailed procedure of the proposed method involves kinematic error calibration with the Levenberg-Marquardt algorithm and then non-kinematic error (such as link deflection, thermal errors, and error motions of the rotation shaft) compensation with a back-propagation neural network optimized by the mind evolutionary algorithm. In order to verify the effectiveness and correctness of the proposed method, the simulation and experiment were carried out on an AACMM. The simulated and experimental results demonstrate that the measuring length accuracy of the AACMM is improved significantly after kinematic error calibration and non-kinematic error compensation, confirming the effectiveness and correctness of the proposed method.

A Kinematic Calibration Method of the Articulated Arm Coordinate Measuring Machine Using Niching Chaos Optimization Algorithm

Abstract Articulated arm coordinate measuring machine (AACMM) is a kind of portable coordinate measuring equipment, which employs a series of rotating joints. In order to improve the measuring accuracy and repeatability of AACMM, it is essential to calibrate the kinematic parameters of AACMM. The calibration process is a kind of nonlinear optimization problem and can be solved by employing various optimization algorithms most including Levenberg–Marquardt algorithm (LMA) and trust region algorithm. Recently, evolutionary computation (EC) has been extensively studied and applied to many engineering problems, since they have some positive features such as easy implementation, broad applicability and robust mechanism of escaping from the local optimum. Chaos optimization algorithm (COA) is one of the evolutionary computation, which utilizes chaotic numerical sequences. In this article, a new kinematic calibration approach for AACMM is proposed by using niching chaos optimization algorithm (NCOA). A hybrid objective function for kinematic calibration is proposed that reflects the various performance tests including single-point articulation performance test, effective diameter performance test and volumetric performance test. Levenberg–Marquardt algorithm and niching chaos optimization algorithm are applied for calibrating the kinematic parameters. Niching chaos optimization algorithm shows competitive calibration performance to Levenberg–Marquardt algorithm. The experimental results demonstrate that the measurement accuracy calibrated using NCOA has been better than that of using LMA in terms of the root-mean-square deviation. The experimental results demonstrate that the measurement accuracy calibrated using NCOA has been better than that of using LMA in terms of the root-mean-square deviation.

Calibration Method of Parallel Mechanism Type Machine Tools

This paper proposes a calibration method for a parallel mechanism type machine tool (XMINI, Exechon Enterprises L.L.C.). In this method, the kinematic parameters are calculated using forward kinematics and the least squares method from the results obtained by a coordinate measuring machine. By using an articulated arm coordinate measuring machine (AACMM), we can measure a wide space, and the measuring machine position do not have to be determined strictly. This paper provides a solution for the forward kinematics problem to identify the kinematic parameters. The results from the kinematic parameter calculation are evaluated using the experimental results from an actual machine.

Proposition of a periodic verification test for Articulated Arm Coordinate Measuring Machines using a small 3D artefact

This paper proposes a periodic verification/acceptance test for Articulated Arm Coordinate Measuring Machine (AACMM). The verification tests recommended by standards dedicated to AACMM are generally time consuming and require bulky artifacts. In fact, the volumetric test of ISO 10360-12 requires measuring five lengths in seven different directions, ensuring that the largest length covers at least 66% of the working range. The proposed test in the paper requires only small artifacts and takes 20–30 min. The test is designed in a way to move all encoders of the AACMM through their entire angular range, with measurements located in a small area of the working range of the AACMM, thanks to the redundancy of the kinematic structure of AACMMs. To validate the proposed test, a comparison with the ISO 10360-12 volumetric test (in terms of encoders’ error, mechanical deformation errors and the maximal error captured) is presented.

Modelling and compensation of temperature errors for articulated arm coordinate measuring machines

The temperature variation is an important factor affecting the accuracy of the articulated arm coordinate measuring machine (AACMM). This paper addresses the modelling and compensation of temperature errors in AACMMs. Firstly, a temperature field model of AACMMs is established by finite element analysis, based on which the influence of temperature change on single-point repeatability accuracy and spatial distance measuring accuracy for AACMMs are analysed. The results of the analysis show that non-zero linear parameters of AACMMs are influenced by temperature variation greatly, while the angular parameters are almost unchanged. Then, a temperature scaling method is proposed to improve the distance measuring accuracy of AACMMs, and a linear regression temperature error compensation model is established under the simulation environment. Experimental results show that in the presence of temperature scaling method, the average absolute value of distance measuring accuracy is improved by 65.24%.

Design and Validation of a Self-Driven Joint Model for Articulated Arm Coordinate Measuring Machines

Articulated arm coordinate measuring machines (AACMMs) have been developed and applied in industrial measurement fields for more than 30 years. Manual operation is typically required during measurement, which introduces uncertain influences, such as fluctuation of measurement force, speed, and acceleration, and leads to poor reliability and reproducibility. In this paper, a novel self-driven joint model is proposed to realize automatic measurement for AACMMs. A self-driven joint is designed by combining the joint of an AACMM with a robotic arm to realize automatic rotation. A self-driven AACMM is designed using three rolling joints and three pitching joints with assigned parameters. A virtual prototype of the self-driven AACMM is established using the Adams software to simulate the driving moment of each joint. The simulation results demonstrate that the designed mechanical structure and selected devices can meet the preset requirements. Additionally, based on the proposed model, a single physical joint is developed and assembled for performance testing. Experimental results demonstrate that the model can achieve a repeatability of 1.39″ (k = 2) when the rotational velocity is less than 1.53 rad/s. Therefore, the proposed design is suitable for use in AACMMs.

Kinematic parameter identification procedure of an articulated arm coordinate measuring machine based on a metrology platform

A still current challenge of paramount importance for manufacturing metrology is the industry and laboratories’ increasing demand for faster inspection and verification measuring procedures to determine the conformance of products to dimensional or functional requirements. Within this context, a measuring system group that has gained great importance in the field of high precision dimensional verification are the portable coordinate measuring machines (PCMMs) such as articulated arm coordinate measuring machine (AACMM). Nevertheless, an important drawback of these type of instruments are the time-consuming, tedious, and expensive tasks inherent to their verification and kinematic parameter identification procedures. In this work, a kinematic parameter identification procedure of an AACMM by means of an indexed metrology platform is presented. Moreover, the kinematic modeling of the AACMM is developed, and the optimization of the arm kinematic parameters to minimize the measurement error is carried out in terms of eight objective functions. Finally, a comparison between the optimized parameters and the nominal parameters is discussed, showing the advantages of using the indexed metrology platform (IMP) in the optimization procedure.

Rapid and robust on-site evaluation of articulated arm coordinate measuring machine performance

This paper proposes a quick and efficient methodology of uncertainty estimation on measurement results provided by an articulated arm coordinate measuring machine (AACMM). The methodology is highly adapted to industrial applications—a frequent use of these devices—but can also be performed in laboratories. The study stems from an actual need among coordinate measuring arm users to estimate the uncertainty associated with their equipment in specific conditions on the shop floor. It is important to mention that no simple and quick test exists currently to estimate the measurement uncertainty of results obtained with an AACMM in the conditions of the measurement site. In fact, the guidelines and studies addressing measuring machines propose protocols to verify performance or to evaluate uncertainties associated with measurement results, but these protocols are laboratory-type tests (carried out after purchase, re-calibration, etc) and usually take hours to complete.