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.

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.

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.

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.

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.

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.

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.

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.

Cylindrical coordinate measuring machines: probe offset and workpiece clamping error

A cylindrical coordinate measuring machine for the detection of large-size rotational parts is introduced. The measuring machine can simultaneously measure the geometrical dimensions, form and position errors of the inner and outer surfaces. Since the maximum length of the workpiece can reach 2 000 mm , it is difficult to be clamped and adjusted and easy to produce clamping error. The eccentricity can be up to 1.5 mm, which has an interaction effect with the probe mounting offset. We mainly study the probe offset of the measuring machine and the influence of the workpiece clamping error on the measurement. A method of controlling the offset of the measuring probe is proposed. The effect of the clamping error is eliminated through the space coordinate transformation of the workpiece axis, and the axis is fitted by the least square method. Finally, a common fixture can be realized to meet the clamping requirements of the workpiece.

ASSESSING THE DYNAMIC ERRORS OF COORDINATE MEASURING MACHINES

The main factors affecting the dynamic errors of coordinate measuring machines are analyzed. It is pointed out that there are two main contributors to the dynamic errors: One is the rotation of the elements around the joints connected with air bearings and the other is the bending of the elements caused by the dynamic inertial forces. A method for obtaining the displacement errors at the probe position from dynamic rotational errors is presented. The dynamic rotational errors are measured with inductive position sensors and a laser interferometer. The theoretical and experimental results both show that during the process of fast probing, due to the dynamic inertial forces, there are not only large rotation of the elements around the joints connected with air bearings but also large bending of the weak elements themselves.

STUDY OF NON-CONTACT MEASUREMENT OF FREE-FORM SURFACES

A non contact three dimensional measurement method is presented in this paper.This system consists of a laser triangulation probe,a probe head and a coordinate measuring machine (CMM).The measurement principle of the system is discussed,and a system calibration method employing a reference ball is proposed.The geometric model involving four frames is established to calculate the data points based on the reading of the laser probe and position information from the CMM.A measuring experiment for gesso free form surface using this system is carried out.

Multi-Aspect Value of Measuring Systems and Methods Based on the Results of Roundness Measurements

The increase of quality consciousness brings about the growth of significance of metrological systems. Besides the significance, the level of automatization, flexibility, accuracy, et al. have advanced. The modern measuring systems are constructed so that nearly all necessary dimensional characteristics can be measured with them. However, conventional measuring systems are provided for particular mode measurements. This research paper presents and compares several conventional and modem measuring systems and methods. The measured value is roundness, one of the basic shapes of cross section in mechanical engineering. This paper arises in search of answers for the question whether conventional measuring techniques and equipments are made redundant because of the modern ones. In what segments and in which criterion are modem methods preferable？

METHODS OF VISUAL RECOGNITION,POSITIONING AND ORIENTATING OF 3 D SIMPLE GEOMETRIC WORKPIECE

The methods of visual recognition,positioning and orienting with simple 3 D geometric workpieces are presented in this paper.The principle and operating process of multiple orientation run length coding based on general orientation run length coding and visual recognition method are described elaborately.The method of positioning and orientating based on the moment of inertia of the workpiece binary image is stated also.It has been applied in a research on flexible automatic coordinate measuring system formed by integrating computer aided design,computer vision and computer aided inspection planning,with a coordinate measuring machine.The results show that integrating computer vision with measurement system is a feasible and effective approach to improve their flexibility and automation.

Estimation of measuring uncertainty for optical micro-coordinate measuring machine

Based on the evaluation principle of the measuring uncertainty of the traditional coordinate measuring machine (CMM), the analysis and evaluation of the measuring uncertainty for optical micro-CMM have been made. Optical micro-CMM is an integrated measuring system with optical, mechanical, and electronic components, which may influence the measuring uncertainty of the optical micro-CMM. If the influence of laser speckle is taken into account, its longitudinal measuring uncertainty is 2.0 μm, otherwise it is 0.88 μm. It is proved that the estimation of the synthetic uncertainty for optical micro-CMM is correct and reliable by measuring the standard reference materials and simulating the influence of the diameter of laser beam. With Heisenberg's uncertainty principle and quantum mechanics theory, a method for improving the measuring accuracy of optical micro-CMM through adding a diaphragm in the receiving terminal of the light path was proposed, and the measuring results are verified by experiments.

Dynamic Coordination of Uncalibrated Hand/Eye Robotic System Based on Neural Network

A nonlinear visual mapping model is presented to replace the image Jacobian relation for uncalibrated hand/eye coordination. A new visual tracking controller based on artificial neural network is designed. Simulation results show that this method can drive the static tracking error to zero quickly and keep good robustness and adaptability at the same time. In addition, the algorithm is very easy to be implemented with low computational complexity.

Development of an in-situ measuring system for blisk manufacturing

In order to solve the in-situ measurement problem of workpiece with complex structures,a cantilever coordinate measuring machine(CCMM)is proposed to adapt to the finite space constraints of the 5-axis computer numerical control(CNC)processing site.Structure design of dense ball bearing shafting is analyzed and optimized.Factors affecting measurement accuracy of CCMM are analyzed,and measurement accuracy is validated by experiments.Results show that the structure of CCMM is able to satisfy requirements of technical specification,and the in-situ measurement of blisk manufacturing is realized.The CCMM developed is of important significance for machining quantity improvement of blisk and development of large aircraft production.

Design, Development and Geometric Error Analysis of an Aerostatic Rotary Table

Rotary tables are equipments in precision machinery applied in five-axis Machine Tools and CMM （Coordinate Measuring Machines）, offering rotational （C-axis） and tilting motion （A-axis）, allowing the obtaining of several configurations for manufacturing or inspection of parts with complex geometries. The demand for high accuracy, high efficiency and fewer errors in the positioning of the part in precision machines increases every day, thus ensuring their high confidence and the use of aerostatic bearings enable constructive innovations to the equipment. In this context, this work presents the mechanical design, the development and error analysis of a prototype of an aerostatic rotary table. This study emphasizes the analysis of a prototype that uses the air as a working principle for reducing friction between moving parts, increasing the mechanical efficiency, and its influence of motion error is also discussed based on the experimental results. For the geometrical errors analysis, experimental tests were realized in laboratory using a DBB （Double Ballbar）. The tests are performed with only one axis moving, observing the behavior of the system for different feedrate at the C-axis.

Current status and challenges of using geometric tolerance information in intelligent manufacturing systems

Recent development in computer-based manufacturing and inspection has necessitated extended knowledge and usage of geometric tolerances as carriers of design intent. The aim of applying geometrical tolerances in design is to provide function-oriented precise description of part geometry where the conventional size tolerance system fails to address. In view of the current development of computer-aided systems, applying geometric tolerances opens a new research front. This article examines the challenges in applying geometric tolerance information to carry the design intent to other downstream manufacturing processes and intelligently integrate the whole system. Based on the observed practical capabilities and literature studies, it is concluded that the current computer-aided design （CAD） systems cannot effectively provide the appropriate use of geometric tolerances. This article highlights the existing challenges and proposes a scheme of algorithm development for appropriate use of tolerance symbols and conditions at the design specification stage. This, in the long run, enables the CAD model to carry the design intent and opens a window of opportunity for intelligently integrating manufacturing systems.