近年來，CNC robot不斷推陳出新，其功用之廣泛且穩定已使其成為在眾多機器人中成為相當具有潛力的一種，然而在一系列加工流程中，量測為一核心且極具影響力的項目，在許多在精度方面要求甚高的工業中，量測為期提供了品質保證、誤差判定的功效，如在航太業上，飛機機翼是一精度要求極高的大型加工件，且其獨特的設計考量了氣流、風力、風阻等多項因素，一點點加工上的誤差便會改變飛機在空中的穩定性，直接影響了上百人的安全，在小型加工件方面，如齒輪，些微的誤差都會容易造成齒輪旋轉過程中卡住，破壞機械結構使整台機器故障甚至報廢，由已上便可知道量測在加工中是如此重要。此篇碩論提出一就由裝置高精度探針的多軸量測機來玩成對複雜曲面之量測。
多自由度之測量機台搭配冗餘度的特性後可在空間中有著相當大的工作範圍及自由性，其末端點可以在位置不動的情況下改變旋轉以此來確定末端點之探針探測工件表面的的點做量測時可以保證其以法向量觸碰，藉此得到準確的量測數據，大多數的測量機台由於沒有多自由度之特性，常常在以非法向量的方式量測後再額外進行計算出真正的觸碰點位置，此方法的缺點為由於無法真正準確地知道觸碰點與探針末端點的關係，導致難以準確補償物差造成精確度下降。而在量測技術方面，對於ㄧ有複雜曲面之工件的量測往往會由於缺乏參考點而無法找出量測點，此篇碩論中一提出一針對複雜曲面之量測流程，其包括之內容有物件定位、探針半徑補償、曲面量測點取樣、曲面重建、誤差分析及曲面精度分析等。

For these years, CNC(Computer Numerical Control) machine has been developed at an incredibly high speed. Because of its high stability and wide applicability, this kind of machine is considered as the most powerful potential in the future development. In the series of machining procedure, measurement is a core and certainly influential item. For many industries which require extremely high precision of a workpiece, measurement provides the insurance of quality and error decision for each workpiece. Take aerospace industry for example, the airfoil is a large machined part which requires extremely high precision, which is specially designed that considers a lot of factors such as air flow, air mechanics, windage, and so on. Any small error may incredibly influence the characteristics above and decrease the flying stability. Another great example is gear. Stuck is happened while the precision cannot be promised, which may furthermore destroy the whole equipment. This paper proposed a method for measuring a complex surface by a precise probing system mounted on the end-effector of measurement machine with high DoF.
For some measuring strategy, they use different sides of the end-effector to measure the points because of the limitation of lower degree of freedom. The merit of the strategy is effectively reflected on lower cost of hardware. However, the difficulty is increased because extra computation is needed for points with inaccessible orientation and position. What’s more, since the error of the end-effector is inevitably affects the real position and command position, the accuracy of measuring value must be much lower. This paper presents an algorithm to explain how to get the normal vector of each point located on the surface of a workpiece and how to avoid the dangerous points which may lead to collision during measuring is presented as well. Finally, the algorithm is implemented on a 7-DoF measurement machine. Thanks to high reliability and high degree of freedom, the machine has extremely wide workspace and a redundant angle to make the end-effector can reach the target even an obstacle exists that may disturb the path of the manipulator. In the measurement technique aspect, a series of measurement procedure will be introduced and explained, including workpiece localization, probe radius compensation, complex surface sampling, surface reconstruction, error analysis and precision analysis of real workpiece.

誌謝 i
中文摘要 ii
ABSTRACT iii
CONTENTS v
LIST OF FIGURES viii
LIST OF TABLES xi
Chapter 1 Introduction 1
1.1 Era of Coordinate Measurement Machine 1
1.2 Freeform Surface Inspection and Validation 5
1.3 CAD Model Representation 6
1.3.1 IGES File Specification 6
1.3.2 IGES File Specification 7
1.4 Proposed Measurement and Validation Procedure 8
Chapter 2 Scenario 9
2.1 Scenario Introduction 9
2.2 Coordinate Measurement Machine in iCeiRA 10
2.2.1 Mechanism Design of Multi-axis CNC Robot 10
2.2.2 Anti-collision sensor and Home sensor 15
2.2.3 High accuracy probe 16
2.3 Measured Workpiece 17
2.4 Geometrical Data Extraction 18
2.4.1 NURBS Specification 18
2.4.2 Data Extraction from CAD model 19
2.4.3 Geometrical Characteristics Computation 21
2.5 Simulation Workspace 24
Chapter 3 CMM Kinematics 26
3.1 Spatial Descriptions and Transformation 26
3.1.1 Three-Angle Representation 27
3.1.2 Angle–Axis Representation 28
3.1.3 Unit Quaternions 29
3.2 Differential Motion 32
3.3 CMM Kinematics 34
3.3.1 Forward Kinematics of CMM 34
3.3.2 Velocity Relationship: The Manipulator Jacobian 36
3.4 Forward Kinematics Model of iCeiRA CNC robot 38
3.5 Inverse Kinematics Model of iCeiRA CNC robot 40
3.5.1 Numerical Solution - The Jacobian Transpose Method 40
3.5.2 Analytic Solution – Closed-Form Solution 41
3.6 Linear Blending Motion 44
Chapter 4 Workpiece Registration 45
4.1 Description 45
4.2 Reference-based Registration 47
4.3 Algorithm-based Registration 51
Chapter 5 Freeform Surface Measurement and Validation 55
5.1 Concept of Proposed Measurement Process 55
5.2 Measured point generation 56
5.3 Working Consideration 57
5.3.1 Joint Limit Consideration 58
5.3.2 Collision Detection 58
5.4 Measurement Trajectory Generation 62
5.4.1 Probing Posture Determination 62
5.4.2 Initial Trajectory generation 64
5.4.3 Joint Limit Response 67
5.4.4 Collision Response 69
5.5 Error Consideration 72
5.5.1 Pretraveling problem 73
5.5.2 Radius Compensation 74
5.6 Surface Validation 75
5.6.1 Localization Uncertainties 77
5.6.2 Reconstruction Uncertainty 79
5.6.3 Surface Validation 80
Chapter 6 Experiment 82
6.1 Localization Experiment 82
6.2 Freeform Surface Measurement Experiment 84
6.3 Data Analysis and Surface Validation 87
Chapter 7 Conclusion 90
REFERENCE 91
VITA 95

[1]I. Ainsworth, M. Ristic and D. Brujic, "CAD-Based Measurement Path Planning for Free-Form Shapes Using Contact Probes", International Journal of Advanced Manufacturing Technology, vol. 16, no. 1, pp. 23-31, 2000.
[2]T. Woo, R. Liang, C. Hsieh and N. Lee, "Efficient sampling for surface measurements", Journal of Manufacturing Systems, vol. 14, no. 5, pp. 345-354, 1995.
[3]S. Obeidat and S. Raman, "An intelligent sampling method for inspecting free-form surfaces", The International Journal of Advanced Manufacturing Technology, vol. 40, no. 11-12, pp. 1125-1136, 2008.
[4]X. He, Y. Xue, M. Ni, C. Hua and C. Li, "Adaptive measuring algorithm for CMM based on 5-th Bezier curve", IEEE ICCA 2010, 2010.
[5]A. Zhou, J. Guo and W. Shao, "Automated inspection planning of freeform surfaces for manufacturing applications", 2011 IEEE International Conference on Mechatronics and Automation, 2011.
[6]L. Mu, Z. Yin and Y. Xiong, "Sampling Method for Similar Section Surface Inspection", 2011 First International Conference on Instrumentation, Measurement, Computer, Communication and Control, 2011.
[7]X. Lin, S. Jiang, X. Liu and K. Yang, "The CMM Measurement Path Planning for Blade Surface Based on the Contour Measurement", 2011 Second International Conference on Digital Manufacturing & Automation, 2011.
[8]Bai Yuewei, Wei Shuangyu, Liu Kai and Wang Xiaogang, "A strategy to automatically planning measuring path with CMM offline", 2010 International Conference on Mechanic Automation and Control Engineering, 2010.
[9]M. Yu, Y. Zhang, Y. Li and D. Zhang, "Adaptive sampling method for inspection planning on CMM for free-form surfaces", The International Journal of Advanced Manufacturing Technology, vol. 67, no. 9-12, pp. 1967-1975, 2012.
[10]Y. Li and Z. Liu, "Method for determining the probing points for efficient measurement and reconstruction of freeform surfaces", Measurement Science and Technology, vol. 14, no. 8, pp. 1280-1288, 2003.
[11]Y. Chen, Z. Ma and H. Xu, "Key technologies of 3D surface inspection for complex workpiece using OMP60 probe", 2009 IEEE International Conference on Automation and Logistics, 2009.
[12]E. Wang, Y. Gao, C. Su, P. Yu, M. Jiang and Y. Liu, "New algorithm of measuring the cone section with the coordinate machine measurement", 2012 International Conference on Optoelectronics and Microelectronics, 2012.
[13]H. Aoyama, M. Kawai, T. Kishinami and N. Taniguchi, "A New Method for Detecting the Contact Point between a Touch Probe and a Surface", CIRP Annals - Manufacturing Technology, vol. 38, no. 1, pp. 517-520, 1989.
[14]C. Menq and F. Chen, "Curve and surface approximation from CMM measurement data", Computers & Industrial Engineering, vol. 30, no. 2, pp. 211-225, 1996.
[15]R. Johnson, Qingping Yang and C. Butler, "Dynamic error characteristics of touch trigger probes fitted to coordinate measuring machines", IEEE Transactions on Instrumentation and Measurement, vol. 47, no. 5, pp. 1168-1172, 1998.
[16]M. Ristic, I. Ainsworth and D. Brujic, "Contact probe radius compensation using computer aided design models", Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 215, no. 6, pp. 819-834, 2001.
[17]Y. Lin and W. Sun, "Probe Radius Compensated by the Multi-Cross Product Method in Freeform Surface Measurement with Touch Trigger Probe CMM", The International Journal of Advanced Manufacturing Technology, vol. 21, no. 10-11, pp. 902-909, 2003.
[18]F. Zhang, J. Lu, S. Tang, Y. Yan and H. Sun, "Analytic model of machining errors for thin walled parts based on the deformation of the workpiece-fixture system", 2009 IEEE International Conference on Industrial Engineering and Engineering Management, 2009.
[19]A. Nafi, J. Mayer and A. Wozniak, "Novel CMM-based implementation of the multi-step method for the separation of machine and probe errors", Precision Engineering, vol. 35, no. 2, pp. 318-328, 2011.
[20]L. Laaouina, A. Nafi and A. Mouchtachi, "Application of CMM separation method for identifying absolute values of probe errors and machine errors", 2016 International Conference on Engineering & MIS (ICEMIS), 2016.
[21]Z. Mei, "CMM Measurement Error Model Based on High-order Lagrange Interpolation", Information Technology Journal, vol. 12, no. 15, pp. 3457-3461, 2013.
[22]J. Mayer, Y. Mir, F. Trochu, A. Vafaeesefat and M. Balazinski, "Touch probe radius compensation for coordinate measurement using kriging interpolation", Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 211, no. 1, pp. 11-18, 1997.
[23]Zexiang Li, Jianbo Gou and Yunxian Chu, "Geometric algorithms for workpiece localization", IEEE Transactions on Robotics and Automation, vol. 14, no. 6, pp. 864-878, 1998.
[24]Z. Xiong and Z. Li, "Error compensation of workpiece localization", Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).
[25]Z. Xiong, M. Wang and Z. Li, "A Near-Optimal Probing Strategy for Workpiece Localization", IEEE Transactions on Robotics, vol. 20, no. 4, pp. 668-676, 2004.
[26]K. Morishige, K. Kase and Y. Takeuchi, "Collision-free tool path generation using 2-dimensional C-space for 5-axis control machining", The International Journal of Advanced Manufacturing Technology, vol. 13, no. 6, pp. 393-400, 1997.
[27]Jin Bao, Wang Shuguo and Yili Fu, "Sensor-based motion planning for robot manipulators in unknown environments", 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005.
[28]A. Ademovic and B. Lacevic, "Path planning for robotic manipulators using expanded bubbles of free C-space", 2016 IEEE International Conference on Robotics and Automation (ICRA), 2016.
[29]M. Ngom and F. Nagata, "Detection of workpieces on a CNC machining table for measurement and automatic tool positioning", 2014 14th International Conference on Control, Automation and Systems (ICCAS 2014), 2014.
[30]V. Mehrad, D. Xue and P. Gu, "Inspection of freeform surfaces considering uncertainties in measurement, localization and surface reconstruction", Measurement Science and Technology, vol. 24, no. 8, p. 085008, 2013.
[31]T. Möller, "A Fast Triangle-Triangle Intersection Test", Journal of Graphics Tools, vol. 2, no. 2, pp. 25-30, 1997.
[32]N. Gelfand, L. Ikemoto, S. Rusinkiewicz and M. Levoy, "Geometrically stable sampling for the ICP algorithm", Fourth International Conference on 3-D Digital Imaging and Modeling, 2003. 3DIM 2003. Proceedings.