ANALYSIS AND MEASUREMENT FOR THE DYNAMIC ERRORS OF COORDINATE MEASURING MACHINES

The analysis and calculating method of dynamic errors of CMMs during probing are discussed.To relate the dynamic displacement errors with the dynamic rotational errors a method for obtaining the displacement errors at the probing position from dynamic rotational errors is presented.It is pointed out that the finite element method might be used for modeling dynamic errors.However,dynamic errors are difficult to be modeled so a combined practical and theoretical approach is needed.In addition,the dynamic errors are measured with inductive position sensors.

Coordinate unification method of high-precision composite measurement in two dimensions

Multi-sensor coordinate unification in dimensional metrology is used in order to get holistic, more accurate and reliable information about a workpiece based on several or multiple measurement values from one or more sensors. Because of the problem that standard ball is deficient as a standard artifact in the coordinate unification of high-precision composite measurement in two dimensions （2D） , a new method is proposed in this paper which uses angle gauge blocks as standard artifacts to achieve coordinate unification between the image sensor and the tactile probe. By comparing the standard ball with the angle gauge block as a standard artifact, theoretical analysis and experimental results are given to prove that it is more precise and more convenient to use angle gauge blocks as standard artifacts to achieve coordinate unification of high-precision composite measurement in two dimensions.

Multiple Measurement Models of Articulated Arm Coordinate Measuring Machines

The existing articulated arm coordinate measuring machines（AACMM） with one measurement model are easy to cause low measurement accuracy because the whole sampling space is much bigger than the result in the unstable calibration parameters. To compensate for the deficiency of one measurement model, the multiple measurement models are built by the Denavit-Hartenberg＇s notation, the homemade standard rod components are used as a calibration tool and the Levenberg-Marquardt calibration algorithm is applied to solve the structural parameters in the measurement models. During the tests of multiple measurement models, the sample areas are selected in two situations. It is found that the measurement errors＇ sigma value（0.083 4 ram） dealt with one measurement model is nearly two times larger than that of the multiple measurement models（0.043 1 ram） in the same sample area. While in the different sample area, the measurement errors＇ sigma value（0.054 0 ram） dealt with the multiple measurement models is about 40% of one measurement model（0.137 3 mm）. The preliminary results suggest that the measurement accuracy of AACMM dealt with multiple measurement models is superior to the accuracy of the existing machine with one measurement model. This paper proposes the multiple measurement models to improve the measurement accuracy of AACMM without increasing any hardware cost.

Surface form inspection with contact coordinate measurement:a review

Parts with high-quality freeform surfaces have been widely used in industries,which require strict quality control during the manufacturing process.Among all the industrial inspection methods,contact measurement with coordinate measuring machines or computer numerical control machine tool is a fundamental technique due to its high accuracy,robustness,and universality.In this paper,the existing research in the contact measurement field is systematically reviewed.First,different configurations of the measuring machines are introduced in detail,which may have influence on the corresponding sampling and inspection path generation criteria.Then,the entire inspection pipeline is divided into two stages,namely the pre-inspection and post-inspection stages.The typical methods of each sub-stage are systematically overviewed and classified,including sampling,accessibility analysis,inspection path generation,probe tip radius compensation,surface reconstruction,and uncertainty analysis.Apart from those classical research,the applications of the emerging deep learning technique in some specific tasks of measurement are introduced.Furthermore,some potential and promising trends are provided for future investigation.

Robot Vision System for Coordinate Measurement of Feature Points on Large Scale Automobile Part

In this paper,we present a robot vision based system for coordinate measurement of feature points on large scale automobile parts.Our system consists of an industrial 6-DOF robot mounted with a CCD camera and a PC.The system controls the robot into the area of feature points.The images of measuring feature points are acquired by the camera mounted on the robot.3D positions of the feature points are obtained from a model based pose estimation that applies to the images.The measured positions of all feature points are then transformed to the reference coordinate of feature points whose positions are obtained from the coordinate measuring machine（CMM）.Finally,the point-to-point distances between the measured feature points and the reference feature points are calculated and reported.The results show that the root mean square error（RMSE） of measure values obtained by our system is less than 0.5 mm.Our system is adequate for automobile assembly and can perform faster than conventional methods.

GUIDELESS SPATIAL COORDINATE MEASUREMENT TECHNOLOGY BASED ON CODING POLE

A new method of guideless spatial coordinate measurement technology based on coding pole and vision measurement is proposed. Unequal spacing of bar code is adopted to pole, so that the code combination of pole image in measuring field is unique. Holographic characteristics of numeric coding pole are adopted to obtain pole pose and pole probe position by any section of bar code on the pole. Spatial coordinates of measuring points can be obtained by coordinate transform. The contradiction between high resolution and large visual field of image sensor is resolved, thereby providing a new concept for surface shape measurement of large objects with high precision. The measurement principles of the system are expounded and mathematic model is established. The measurement equation is evaluated by simulation experiments and the measurement precision is analyzed. Theoretical analysis and simulation experiments prove that this system is characterized by simple structure and wide measurement range. Therefore it can be used in the 3-dimentional coordinate measurement of large objects.

Helical angle measurement of worm by a coordinate measuring machine and its uncertainty evaluation

The purpose of the study concerns the measurement of worm's helical angle by a coordinate measurement machine in the ambient industrial environment. The novel measurement method and sampling strategy were described firstly. This method used the coordinate measurement machine to measure both of the worm gear's left and right surfaces. The worm surface was reconstructed based on the measured data of all the sampling points. Then a middle cylinder was established to truncate the fitted worm surfaces, and the truncated spiral lines were straightened to calculate the helical angle. The measurement uncertainty of worm's helical angle was evaluated by taking the difference of calculated helical angles along the truncated spiral lines on both the left and right side surfaces of the worm. Twenty-four measurement experiments show that the maximum measurement error of the proposed method is 0.105, and the measurement error ratios are all less than 3.5%. The result means that the measurement method can realize the precision measurement of worm's helical angle and can be employed in the generally industrial application.

Theoretical analysis and verification of uncertainty of measurement on a cantilever coordinate measuring machine

A cantilever coordinate measuring machine(CCMM)is proposed according to the in-situ measurement requirement of workpieces with complex structures limited by the finite space of the5-axes computerized numerical control(CNC)processing site.Factors affecting uncertainty of measurement(UM)are classified and analyzed on the basis of uncertainty evaluation criteria,and the estimation technique of UM for measuring systems is presented.UM of the CCMM is estimated from the factors such as temperature,error motions as well as the mechanism deformations.Measurement results show that the actual measurement error is smaller than that of measurement requirement.

THEORETICAL ANALYSIS OF COORDINATES MEASUREMENT BY FLEXIBLE 3D MEASURING SYSTEM

The system mathematical model of flexible 3D measuring system is built by theoretical analysis, and the theoretical formula for measuring space point coordinate is also derived. Frog-jumping based coordinate transform method is put forward in order to solve measuring problem for large size parts. The frog-jumping method is discussed, and the coordinate transform mathematical model is method of the space point coordinate compared to original value, and an advanced method is provided, Form the space point coordinate transform formula can derive the calculation measuring method for measuring large size parts.

Measurement of Urban Economic Gravity of China’s Three Major Agglomerations and Its Implications for the Coordinated Development of the Beijing-Tianjin-Hebei Region

This paper adopts the perspective of urban economic linkage and the modified urban economic gravity model to conduct a comparative analysis of the economic gravity among cities in China’s three major urban agglomerations,including the Beijing-Tianjin-Hebei region,the Yangtze River Delta,and the Pearl River Delta.The results show that,despite the ever-tightening economic linkages among cities in the urban agglomerations,the development of the Beijing-Tianjin-Hebei region falls behind that of the Yangtze River Delta and the Pearl River Delta in terms of coordination,closeness,and balance.The economic linkages among cities in the Beijing-Tianjin-Hebei region are not as cohesive as they could be and display a significant“siphon effect”through Beijing and Tianjin as well as a prominently unidirectional economic flow.This study suggests that efforts should be put into directing the orderly flow of resources from Beijing and Tianjin to cities in Hebei and promoting a balanced economic flow among cities,thus facilitating the coordination of regional development.

Application of NURBS for Obtaining Free Form Curves and Surfaces in Spur and Helical Gears by Using CMM （Coordinate Measurement Machine）

Currently, engineering processes require reduced manufacturing time and low cost, in addition to the growing demand for workpieces with high accuracy. Workpieces with complex geometries and free forms has been a common practice in industries from different sectors such as： automotive, aeronautics, bioengineering among others. One way to satisfy the market requirements satisfactorily is making measurements more efficient to make the production process faster, in other words, it is necessary to make the inspection system more accurate and flexible. The coordinate measuring evolved over the past three decades and today it is the technology that best meets the requirements of modem manufacturing through CMMs （coordinate measurement machines）. The CMMs are important tool for design, fabrication and inspection of manufactured products, also used in the application of reverse engineering. These machines are also used by engineers in order to produce an accurate digital model in a virtual space for later use in CAD （computer-aided design）/CAM （computer-aided manufacturing）. It is worth mentioning that the accuracy of the modeling process of given piece depends on the number of control points that are captured on the workpiece surface. Consequently, the laser inspection systems are the best tools for use in reverse engineering, but more expensive when compared to contact measurement systems that use the TTP （touch trigger probe）, also used by CMMs. In this case, this paper aims to present an approach based on NURBS （non-uniform rational B-splines） to obtain free form curves and surfaces from a group of points obtained by using a contact sensor, the touch trigger probe. NURBS is an important mathematical tool and consists of generalizations of Bezier curves and surfaces and B-splines. The approach proposed in this paper can be applied for obtaining free form curves and surfaces in spur and helical gears. Experimental results obtained by measuring spur gears showed that the NURBS technique contributes for application of CMMs with touch trigger probe in reverse engineering.

CAD Model-Based Intelligent Inspection Planning for Coordinate Measuring Machines

As the market competition among enterprises grows intensively and the demand for high quality products increases rapidly, product quality inspection and control has become one of the most important issues of manufacturing, and improving the efficiency and accuracy of inspection is also one of problems which enterprises must solve. It is particularly important to establish rational inspection planning for parts before inspecting product quality correctly. The traditional inspection methods have been difficult to satisfy the requirements on the speed and accuracy of modern manufacturing, so CAD-based computer-aided inspection planning （CAIP） system with the coordinate measuring machines （CMM） came into being. In this paper, an algorithm for adaptive sampling and collision-free inspection path generation is proposed, aiming at the CAD model-based inspection planning for coordinate measuring machines （CMM）. Firstly, using the method of step adaptive subdivision and iteration , the sampling points for the specified number with even distribution will be generated automatically. Then, it generates the initial path by planning the inspection sequence of measurement points according to the values of each point＇s weight sum of parameters, and detects collision by constructing section lines between the probe swept-volume surfaces and the part surfaces, with axis-aligned bounding box （AABB） filtering to improve the detection efficiency. For collided path segments, it implements collision avoidance firstly aiming at the possible outer-circle features, and then at other collisions, for which the obstacle-avoiding movements are planned with the heuristic rules, and combined with a designed expanded AABB to set the obstacle-avoiding points. The computer experimental results show that the presented algorithm can plan sampling points＇ locations with strong adaptability for different complexity of general surfaces, and generate efficient optimum path in a short time and avoid collision effectively.

Single Camera 3-D Coordinate Measuring System Based on Optical Probe Imaging

A new vision coordinate measuring system--single camera 3 D coordinate measuring system based on optical probe imaging is presented. A new idea in vision coordinate measurement is proposed. A linear model is deduced which can distinguish six freedom degrees of optical probe to realize coordinate measurement of the object surface. The effects of some factors on the resolution of the system are analyzed. The simulating experiments have shown that the system model is available.

ERROR COMPENSATION OF COORDINATE MEASURING MACHINES WITH LOW STIFFNESS

A technique for compensating the errors of coordinate measuring machines (CMMs) with low stiffness is proposed. Some additional items related with the force deformation are introduced to the error compensation aquations. The research was carried on a moving colunm horizontal arm CMM. Experimental results show that both the effects of systematic components of error motions and force deformations are greatly reduced, which shows the effectiveness of proposed technique.

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.

COORDINATE MEASURING MACHINE PROBING ACCESSIBILITY

The accessibility of coordinate measuring machines (CMMs) in dimensional inspection is studied. The problem of computing the global accessibility cone is solved using a method of angle representation. Otherwise, the length and volume of probe are considered sufficiently so that all the feasible probe orientations could be determined for the inspection of a workpiece when a touch trigger probe is used and the shortcoming of abstracting a probe as an infinite half line could be overcome completely. In the end, an example is given to explain the method.

Determination of the workspace of a new coordinate-measuring machine using parallel-link mechanism

Presents the detailed algorithm established for determination of workspace for a 3-DOF coordinate measuring machine using parallel link mechanism by constructing the inverse kinematic model first and then reviewing the physical and kinematical constraints from the structural characteristics of the parallel link mechanism, and discusses the actual geometries of workspace and the factors having effect on workspace through computer simulation thereby providing necessary theoretical basis for the research and development of coordinate measuring machines using parallel link mechanism.

Light pen whole space coordinate measuring system based on a tracking turntable

Light pen coordinate measuring system(LPCMS)is a kind of portable coordinate measuring technique based on vision metrology.In classical LPCMS,the measuring range is limited to the camera’s field of view.To overcome this defect,a new LPCMS is designed in this paper to fulfil whole space coordinate measurement.The camera is installed on a turntable instead of a tripod,so that the camera can rotate to track the movement of the light pen.The new system can be applied to large scale onsite measurement,and therefore it notably extends the application of LPCMS.To guarantee the accuracy of the new system,a method to calibrate the parameters of the tracking turntable is also proposed.Fixing the light pen at a stationary position,and changing the azimuth angles of the turntable’s two shafts,so that the camera can capture the images of the light pen from different view angles.According to the invariant spatial relationship between the camera and the pedestal of the tracking turntable,a system of nonlinear equations can be established to solve the parameters of the turntable.Experimental results show that the whole space coordinate measuring accuracy of the new system can reach 0.25 mm within 10 m.It can be concluded that the newly designed system can significantly expand the measuring range of LPCMS without losing too much accuracy.

Development of Flexible Spherical Actuator with 3D Coordinate Measuring Device

Rehabilitation devices help to recover the physical abilities of patients. This study aims to develop a portable rehabilitation device that is safe to use when?patients are holding it by hands. In a previous study, to realize a home rehabilitation device, a flexible spherical actuator that can provide motion to patients was developed. In this study, to measure the relative position between both handling stages, a 3D coordinate measuring device using three wire-type linear potentiometers and an embedded controller was proposed and tested. In this paper, the spherical actuator with built-in 3D coordinate measuring device is described. The measuring method and experimental results obtained are also presented. The tracking position control of the actuator using the measuring device was carried out. As a result, the position of the handling stages can be successfully controlled using the feedback signal from the tested?measuring device.