.. Problem, 84 4.2.2 Static equilibrium configuration for serial chain in the loaded mode Stiffness matrix of serial chain in the loaded mode, pp.4-7

.. Problem, 89 4.3.2 Static equilibrium equations for serial chain with auxiliary loadings Static equilibrium configuration for serial chain with auxiliary loadings Stiffness matrix for serial chain with auxiliary loadings, ., pp.91-95

.. Stability-criterion-for-kinematic-chain-configuration, 95 4.5 Stiffness model of parallel manipulators in loaded mode

P. Conclusions, 133 Contributions of the thesis 133 Limitations of obtained results, Further investigations and Perspectives, p.136

. Analytical and .. Of-cartesian-stiffness-matrix, 61 3.3.1 Extended stiffness mapping equation Stiffness matrix properties

.. Problem, 84 4.2.2 Static equilibrium configuration for serial chain in the loaded mode Stiffness matrix of serial chain in the loaded mode, pp.4-7

.. Problem, 89 4.3.2 Static equilibrium equations for serial chain with auxiliary loadings Static equilibrium configuration for serial chain with auxiliary loadings Stiffness matrix for serial chain with auxiliary loadings, ., pp.91-95

.. Stability-criterion-for-kinematic-chain-configuration, 95 4.5 Stiffness model of parallel manipulators in loaded mode

]. A. Pashkevich, A. Klimchik, D. Chablat, . Ph, and . Wenger, Stiffness analysis of multichain parallel robotic systems with loading, Journal of Automation Mobile Robotics & Intelligent Systems, vol.3, issue.3, pp.75-82, 2009.

]. A. Pashkevich, A. Klimchik, and D. Chablat, Enhanced stiffness modeling of manipulators with passive joints, Mechanism and Machine Theory, pp.662-679, 2011.

]. A. Pashkevich, D. Chablat, and A. Klimchik, Enhanced stiffness modeling of serial manipulators with passive joints, pp.331-360, 2010.
DOI : 10.5772/9539

]. A. Pashkevich, A. Klimchik, D. Chablat, . Ph, and . Wenger, Accuracy Improvement for Stiffness Modeling of Parallel Manipulators, Proceedings of 42nd CIRP Conference on Manufacturing Systems, pp.CD-proceedings, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00414207

]. A. Pashkevich, A. Klimchik, and ;. Chablat, Nonlinear effect in stiffness modeling of robotic manipulators, Proceedings of International Conference on Computer and Automation Technology, pp.168-173, 2009.

]. A. Pashkevich, A. Klimchik, S. Caro, and D. Chablat, Stiffness modelling of parallelogrambased parallel manipulators, 3-rd, European Conference on Mechanism Science Mechanisms and Machine Science, vol.1, issue.5, pp.675-682, 2010.

]. A. Pashkevich, A. Klimchik, and D. Chablat, Stiffness Analysis of Parallel Manipulators with Preloaded Passive Joints, 12th International Symposium Advances in Robot Kinematics 2010 Advances in Robot Kinematics: Motion in Man and Machine, pp.465-474, 2010.
DOI : 10.1007/978-90-481-9262-5_50

URL : https://hal.archives-ouvertes.fr/hal-00544851

]. A. Pashkevich, A. Klimchik, S. Briot, and D. Chablat, Performance Evaluation of Parallel Manipulators for Milling Application, 2010.
DOI : 10.1007/978-3-642-15973-2_62

URL : https://hal.archives-ouvertes.fr/hal-00544855

. France, Global Product Development, pp.619-629, 2010.

]. A. Pashkevich, A. Klimchik, S. Caro, and D. Chablat, Cartesian stiffness matrix of manipulators with passive joints: Analytical approach, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2011.
DOI : 10.1109/IROS.2011.6094419

URL : https://hal.archives-ouvertes.fr/hal-00610306

]. Klimchik, S. Caro, and A. Pashkevich, Stiffness modeling of manipulators with auxiliary loadings, 12e congres annuel de la ROADEF, Saint-Etienne, pp.765-766, 2011.

]. E. Abele-2007, M. Abele, S. Weigold, and . Rothenbücher, Modeling and Identification of an Industrial Robot for Machining Applications, CIRP Annals - Manufacturing Technology, vol.56, issue.1, pp.387-390, 2007.
DOI : 10.1016/j.cirp.2007.05.090

J. E. Akin, B. Alici, and . Shirinzadeh, Finite Element Analysis With Error Estimators: An Introduction to the FEM and Adaptive Error Analysis for Engineering Students Elsevier Enhanced stiffness modeling, identification and characterization for robot manipulators, Proceedings of IEEE Transactions on Robotics, pp.554-564, 2005.

]. J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, 2007.
DOI : 10.1007/b97597

]. J. Angeles and F. Park, Performance Evaluation and Design Criteria, Handbook of robotics, pp.229-243, 2008.
DOI : 10.1007/978-3-540-30301-5_11

]. H. Arumugam, R. M. Voyles, and S. Bapat, Stiffness analysis of a class of parallel mechanisms for micro-positioning applications, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566), pp.1826-1831, 2004.
DOI : 10.1109/IROS.2004.1389662

]. F. Benamar, P. Bidaud, and F. L. Menn, Generic differential kinematic modeling of articulated mobile robots, Mechanism and Machine Theory, pp.997-1012, 2010.

]. D. Bennett, J. M. Hollerbach, and D. Geiger, Autonomous Robot Calibration for Hand-Eye Coordination, The International Journal of Robotics Research, vol.10, issue.5, pp.550-559, 1991.
DOI : 10.1177/027836499101000510

]. T. Bera, K. A. Desai, and P. V. Rao, Error compensation in flexible end milling of tubular geometries, Journal of Materials Processing Technology, vol.211, issue.1, pp.24-34, 2011.
DOI : 10.1016/j.jmatprotec.2010.08.013

]. I. Bogdan and G. , Abba: Identification of the servomechanism used for micro-displacement, IROS, vol.2009, pp.1986-1991, 2009.

]. B. Bouzgarrou, J. C. Fauroux, G. Gogu, and Y. Heerah, Rigidity analysis of T3R1 parallel robot with uncoupled kinematics, Proc. Of the 35th International Symposium on Robotics, 2004.

]. E. Budak, Analytical models for high performance milling. Part I: Cutting forces, structural deformations and tolerance integrity, International Journal of Machine Tools and Manufacture, vol.46, issue.12-13, pp.12-13, 2006.
DOI : 10.1016/j.ijmachtools.2005.09.009

]. M. Carricato, J. Duffy, and V. Parenti-castelli, Catastrophe analysis of a planar system with flexural pivots, Mechanism and Machine Theory, pp.37-693, 2002.

]. K. Castelino, R. D. Souza, and P. K. Wright, Toolpath optimization for minimizing airtime during machining, Journal of Manufacturing Systems, vol.22, issue.3, pp.173-180, 2003.
DOI : 10.1016/S0278-6125(03)90018-5

]. D. Chablat and P. Wenger, Architecture optimization of a 3-DOF translational parallel mechanism for machining applications, the orthoglide, IEEE Transactions on Robotics and Automation, vol.19, issue.3, pp.403-410, 2003.
DOI : 10.1109/TRA.2003.810242

URL : https://hal.archives-ouvertes.fr/hal-00168179

]. V. Cheboxarov, V. F. Filaretov, and M. Vukobratoviimage, Raising the stiffness of manipulators with lightweight links, Mechanism and Machine Theory, pp.1-13, 2000.

]. Chen and I. Kao, Conservative congruence transformation of stiffness control in robotic grasping and manipulation, the 9th International Symposium on Robotics Research, pp.7-14, 1999.

]. S. Chen and I. Kao, Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers, The International Journal of Robotics Research, vol.19, issue.9, pp.835-847, 2000.
DOI : 10.1177/02783640022067201

]. S. Chen and I. Kao, Simulation of Conservative Congruence Transformation: Conservative Properties in the Joint and Cartesian Spaces, pp.1283-1288, 2000.

I. Chen and . Kao, Geometrical Approach to The Conservative Congruence Transformation (CCT) for Robotic Stiffness Control, Proceedings of the 2002 IEEE lntemational Conference on Robotics and Automation, pp.544-549, 2002.

]. J. Chen and F. Lan, Instantaneous stiffness analysis and simulation for hexapod machines, Simulation Modelling Practice and Theory, pp.419-428, 2008.

]. N. Ciblak and H. Lipkin, Asymmetric Cartesian stiffness for the modeling of compliant robotic systems, Proc. 23rd Biennial ASME Mechanisms Conference, 1994.

]. N. Ciblak and H. Lipkin, Synthesis of stiffness by springs, Proceedings of DETC'98, 1998.

]. R. Clavel, DELTA, a fast robot with parallel geometry, Proceedings, of the 18th International Symposium of Robotic Manipulators, pp.91-100, 1988.

]. O. Company, S. Krut, and F. Pierrot, Modelling and preliminary design issues of a four-axis parallel machine for heavy parts handling, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, vol.216, issue.1, pp.1-11, 2002.
DOI : 10.1177/146441930221600102

]. O. Company, F. Pierrot, and J. Fauroux, A Method for Modeling Analytical Stiffness of a Lower Mobility Parallel Manipulator, Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp.3232-3237, 2005.
DOI : 10.1109/ROBOT.2005.1570608

URL : https://hal.archives-ouvertes.fr/lirmm-00105965

]. J. Connor, Analysis of Structural Member Systems, 1976.

]. M. Ceccarelli and G. Carbone, A stiffness analysis for CaPaMan (Cassino Parallel Manipulator), Mechanism and Machine Theory, pp.427-439, 2002.
DOI : 10.1016/S0094-114X(02)00006-X

C. Corradini, J. C. Fauroux, S. Krut, and O. Company, Evaluation of a 4 degree of freedom parallel manipulator stiffness, Proc of the 11th World Cong. in Mechanism & Machine Science, 2004.

H. Cui and Z. Zhu, Error Modeling and Accuracy of Parallel Industrial Robots, Source: Industrial-Robotics-Theory-Modelling-Control, ARS/plV, pp.964-573, 2006.

M. Dadfarnia, N. Jalili, Z. Liu, and D. M. Dawson, An observer-based piezoelectric control of flexible Cartesian robot arms: theory and experiment, Control Engineering Practice, vol.12, issue.8, pp.1041-1053, 2004.
DOI : 10.1016/j.conengprac.2003.09.003

]. D. Daney, N. Andreff, G. Chabert, and Y. Papegay, Interval method for calibration of parallel robots: Vision-based experiments, Mechanism and Machine Theory, pp.929-944, 2006.

]. M. Das and L. C. Dülger, Mathematical modelling, simulation and experimental verification of a scara robot, Simulation Modelling Practice and Theory, pp.257-271, 2005.

]. D. Deblaise, X. Hernot, and P. Maurine, A systematic analytical method for PKM stiffness matrix calculation, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006., pp.4213-4219, 2006.
DOI : 10.1109/ROBOT.2006.1642350

. Ph, J. Dépincé, and . Hascoët, Active integration of tool deflection effects in end milling, International Journal of Machine Tools and Manufacture, vol.46, issue.9, pp.945-956, 2006.

]. J. Dolinsky, I. D. Jenkinson, and G. J. Colquhoun, Application of genetic programming to the calibration of industrial robots, Computers in Industry, pp.255-264, 2007.

T. A. Dow, E. L. Miller, and K. Garrard, Tool force and deflection compensation for small milling tools, Precision Engineering, pp.31-45, 2004.
DOI : 10.1016/s0141-6359(03)00072-2

]. P. Drouet, S. Dubowsky, and C. Mavroidis, Compensation of Geometric and Elastic Deflection Errors in Large Manipulators Based on Experimental Measurements: Application to a High Accuracy Medical Manipulator, submitted to the 6th International Symposium on Advances in Robot Kinematics Methodology for Joint Stiffness Identification of Serial Robots, Intelligent Robots and Systems (IROS) IEEE/RSJ International Conference on, pp.464-469, 1998.
DOI : 10.1007/978-94-015-9064-8_52

]. J. Duffy, Statics and Kinematics with Applications to Robotics, 1996.
DOI : 10.1017/CBO9780511530173

P. M. El-khasawneh and . Ferreira, Computation of stiffness and stiffness bounds for parallel link manipulators, International Journal of Machine Tools and Manufacture, vol.39, issue.2, pp.321-342, 1999.
DOI : 10.1016/S0890-6955(98)00039-X

L. P. Elatta, F. Gen, Y. Liang-zhi, L. Daoyuan, and . Fei, An Overview of Robot Calibration, Information Technology Journal, vol.3, issue.1, pp.74-78, 2004.

]. Fassi and G. J. Wiens, Multiaxis Machining: PKMs and Traditional Machining Centers, Journal of Manufacturing Processes, vol.2, issue.1, pp.1-14, 2000.
DOI : 10.1016/S1526-6125(00)70008-9

URL : http://ufdc.ufl.edu/LS00001599/00001

]. M. Geldart, P. Webb, H. Larsson, M. Backstrom, N. Gindy et al., A direct comparison of the machining performance of a variax 5 axis parallel kinetic machining centre with conventional 3 and 5 axis machine tools, Theory of matrices, pp.1107-1116, 1959.
DOI : 10.1016/S0890-6955(03)00119-6

]. C. Gong, J. Yuan, and J. Ni, Nongeometric error identification and compensation for robotic system by inverse calibration, International Journal of Machine Tools and Manufacture, vol.40, issue.14, pp.2119-2137, 2000.
DOI : 10.1016/S0890-6955(00)00023-7

]. C. Gosselin and D. Zhang, Stiffness analysis of parallel mechanisms using a lumped model, Int. J. of Robotics and Automation, vol.17, pp.17-27, 2002.

J. Goto and O. Krauss, Maffei Injection Moulding Machine--OSP KM-5000 With Computerized Numerical Control, Jpn. Plast. Age, vol.23, issue.205, pp.35-38, 1985.

]. J. Gower and G. B. Dijksterhuis, Procrustes Problems handbook of mechanical engineering, 2004.

]. R. Hines, D. Marsh, and J. Duffy, Catastrophe Analysis of the Planar Two-Spring Mechanism, The International Journal of Robotics Research, vol.17, issue.1, pp.89-101, 1998.
DOI : 10.1177/027836499801700108

]. S. Howard, M. Zefran, and V. Kumar, On the 6 ?? 6 cartesian stiffness matrix for three-dimensional motions, Mechanism and Machine Theory, vol.33, issue.4, pp.389-408, 1998.
DOI : 10.1016/S0094-114X(97)00040-2

W. H. Huang, I. Hung, and . Kao, New Conservative Stiffness Mapping for the Stewart-Gough Platform, Proceedings of the 2002 IEEE International Conference on Robotics & Automation, pp.823-828, 2002.

P. Daniel-kanaan, D. Wenger, and . Chablat, Kinematic analysis of a serial?parallel machine tool: The VERNE machine, Mechanism and Machine Theory, pp.487-498, 2009.

I. Kao and C. Ngo, Properties of the Grasp Stiffness Matrix and Conservative Control Strategies, The International Journal of Robotics Research, vol.18, issue.2, pp.159-167, 1999.
DOI : 10.1177/027836499901800204

]. B. Kaya, C. Oysu, and H. M. Ertunc, Force-torque based on-line tool wear estimation system for CNC milling of Inconel 718 using neural networks, Advances in Engineering Software, vol.42, issue.3, pp.76-84, 2011.
DOI : 10.1016/j.advengsoft.2010.12.002

K. L. Conrad, P. S. Shiakolas, and T. C. Yih, Robotic calibration issues: accuracy, repeatability and calibration, 2000.

]. W. Khalil and S. Besnard, Geometric Calibration of Robots with Flexible Joints and Links, Journal of Intelligent and Robotic Systems, vol.34, issue.4, pp.357-379, 2002.
DOI : 10.1023/A:1019687400225

E. Khalil and . Dombre, Geometric calibration of robots, Modeling, Identification and Control of Robots, pp.257-289, 2004.

J. Kim, C. Park, J. Kim, and F. C. Park, Performance Analysis of Parallel Manipulator Architectures for CNC Machining Applications, Proc. IMECE Symp. On Machine Tools, 1997.

Y. Koseki, T. Tanikawa, N. Koyachi, and T. Arai, Kinematic Analysis of Translational 3- DOF Micro Parallel Mechanism Using Matrix Method The stiffness matrix in elastically articulated rigid-body systems, Proc. of IROS J. Kövecses, J. Angeles Multibody System Dynamics, vol.18, issue.12, pp.786-169, 2000.

P. C. Krause, Analysis of Electrical Machinery Cutting force estimation in sculptured surface milling, International Journal of Machine Tools & Manufacture, vol.44, pp.1511-1526, 1984.

J. A. Soren-larsson and . Kjellander, Motion control and data capturing for laser scanning with an industrial robot, Robotics and Autonomous Systems, vol.54, issue.6, pp.453-460, 2006.
DOI : 10.1016/j.robot.2006.02.002

Y. Li and I. Kao, On the Stiffness Control and Congruence Transformation Using the Conservative Congruence Transformation (CCT), Proceedings, pp.3937-3942, 2001.

]. Y. Li-2002a, S. Li-1, I. Chen, and . Kao, Stiffness Control and Transformation for Robotic Systems With Coordinate and Non-Coordinate Bases, Proceedings of the 2002 IEEE lntemational Conference on Robotics 8 Automation (ICRA), pp.550-555, 2002.

]. Y. Li, J. S. Wang, and L. P. Wang, Stiffness analysis of a Stewart platform-based parallel kinematic machine, Proceedings of IEEE International Conference on Robotics and Automation (ICRA), pp.2002-3672, 2002.

Y. Li and Q. Xu, Stiffness analysis for a 3-PUU parallel kinematic machine, Mechanism and Machine Theory, pp.186-200, 2008.

L. Lin, C. Yang, J. Lu, L. Ying, and E. Weinan, A Fast Parallel Algorithm for Selected Inversion of Structured Sparse Matrices with Application to 2D Electronic Structure Calculations Minimization of maximum lateness on parallel machines with sequence-dependent setup times and job release dates, Computers & Operations Research38, pp.46-52, 2009.

C. Lo, CNC machine tool surface interpolator for ball-end milling of free-form surfaces, International Journal of Machine Tools and Manufacture, vol.40, issue.3, pp.307-326, 2000.
DOI : 10.1016/S0890-6955(99)00071-1

]. C. Long, J. A. Snyman, and A. A. Groenwold, Optimal structural design of a planar parallel platform for machining, Applied Mathematical Modelling, vol.27, issue.8, pp.581-609, 2003.
DOI : 10.1016/S0307-904X(03)00070-2

T. Lu, G. C. Lin, and J. R. He, Neural-network-based 3D force/torque sensor calibration for robot applications, Engineering Applications of Artificial Intelligence, vol.10, issue.1, pp.87-97, 1997.
DOI : 10.1016/S0952-1976(96)00069-3

]. A. De-luca and W. Book, Robots with Flexible Elements, Handbook of robotics, pp.287-319, 2008.

]. F. Majou, Kinetostatic analysis of translational parallel kinematic machines, 2004.

]. F. Majou, C. Gosselin, P. Wenger, and D. Chablat, Parametric stiffness analysis of the Orthoglide, Mechanism and Machine Theory, pp.296-311, 2007.
DOI : 10.1016/j.mechmachtheory.2006.03.018

URL : https://hal.archives-ouvertes.fr/hal-00168332

H. C. Martin, Introduction to matrix methods of structural analysis High-speed end milling of an articulated robot and its characteristics, Journal of Materials Processing Technology, vol.95, pp.1-3, 1966.

M. A. Meggiolaro, C. Mavroidis, and S. Dubowsky, Identification and compensation of geometric and elastic errors in large manipulators: application to a high accuracy medical robot, Proceedings of DETC1998: 1998 ASME Design Engineering Technical Conference, pp.1-7, 1998.

M. A. , S. Dubowsky, and C. , Mavroidis, Error identification and compensation in large manipulators with application in cancer proton therapy, Fev. e Março, pp.71-77, 2004.

M. A. Meggiolaro, C. Dubowsky, and . Mavroidis, Geometric and elastic error calibration of a high accuracy patient positioning system, Mechanism and Machine Theory, pp.40-415, 2005.

]. Merlet and C. Gosselin, Parallel Mechanisms and Robots, Handbook of robotics, pp.269-285, 2008.
DOI : 10.1007/978-3-540-30301-5_13

C. R. Mirman and K. C. Gupta, Compensation of Robot joint variables using special Jacobian matrices, Journal of Robotic Systems, vol.8, issue.4, pp.133-137, 1992.
DOI : 10.1002/rob.4620090107

]. A. Nektarios and N. A. Aspragathos, Optimal location of a general position and orientation end-effector's path relative to manipulator's base, considering velocity performance, Robotics and Computer-Integrated Manufacturing, pp.162-173, 2010.

R. Neugebauer, F. Wieland, M. Schwaar, Z. Karczewski, and C. Hochmuth, Erfahrungen mit dem Mikromat Hexapod 6X (1998), Internationales Parallelkinematik-Kolloquium, pp.65-79, 1998.

]. K. Neumann, United State Patent no, p.732625, 1988.

]. S. Newmana, A. Nassehi, X. W. Xu, R. S. Jr, L. Wang et al., Strategic advantages of interoperability for global manufacturing using CNC technology, Robotics and Computer-Integrated Manufacturing, vol.24, issue.6, pp.699-708, 2008.
DOI : 10.1016/j.rcim.2008.03.002

A. Olabi, R. Béarée, and O. Gibaru, Feedrate planning for machining with industrial six-axis robots, Control Engineering Practice, vol.18, issue.5, pp.471-482, 2010.
DOI : 10.1016/j.conengprac.2010.01.004

URL : https://hal.archives-ouvertes.fr/hal-00992192

]. C. Ozgur and J. R. Brown, A two-stage traveling salesman procedure for the single machine sequence-dependent scheduling problem, Omega, vol.23, issue.2, 1995.
DOI : 10.1016/0305-0483(94)00057-H

]. H. Paris-2007, D. Paris, A. Brissaud, and . Gouskov, A More Realistic Cutting Force Model at Uncut Chip Thickness Close to Zero, CIRP Annals - Manufacturing Technology, vol.56, issue.1, pp.415-418, 2007.
DOI : 10.1016/j.cirp.2007.05.096

]. J. Park, B. Kim, J. Song, and H. Kim, Safe link mechanism based on nonlinear stiffness for collision safety, Mechanism and Machine Theory, vol.43, issue.10, pp.1332-1348, 2008.
DOI : 10.1016/j.mechmachtheory.2007.10.004

]. A. Pashkevich, P. Wenger, and D. Chablat, Design strategies for the geometric synthesis of Orthoglide-type mechanisms, Mechanism and Machine Theory, vol.40, issue.8, pp.907-930, 2005.
DOI : 10.1016/j.mechmachtheory.2004.12.006

URL : https://hal.archives-ouvertes.fr/hal-00168494

A. Pashkevich, D. Chablat, and P. Wenger, Stiffness analysis of 3-d.o.f. overconstrained translational parallel manipulators, 2008 IEEE International Conference on Robotics and Automation, pp.1562-1567, 2008.
DOI : 10.1109/ROBOT.2008.4543424

URL : https://hal.archives-ouvertes.fr/hal-00257728

A. Pashkevich, D. Chablat, and P. Wenger, Stiffness analysis of overconstrained parallel manipulators, Mechanism and Machine Theory, pp.966-982, 2008.

. Fabricio-tadeu-paziani, R. H. Benedito-di-giacomo, and . Tsunaki, Robot measuring form, Robotics and Computer-Integrated Manufacturing, pp.168-177, 2009.

F. Pierrot, P. Dauchez, and A. Fournier, HEXA: a fast six-DOF fully-parallel robot, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments, pp.1158-1163, 1991.
DOI : 10.1109/ICAR.1991.240399

]. F. Pierrot and T. Shibukawa, From Hexa to previous termHexaM.next term, 1999.

K. S. Molinari-tosatti and . Smith, Editors, Parallel kinematic previous termmachines:next term theoretical aspects and industrial requirements, pp.357-364, 1999.

F. Pierrot, V. Nabat, O. Company, and S. Krut, Optimal Design of a 4-DOF Parallel Manipulator: From Academia to Industry, IEEE Transactions on Robotics, vol.25, issue.2, pp.213-224, 2009.
DOI : 10.1109/TRO.2008.2011412

URL : https://hal.archives-ouvertes.fr/lirmm-00385724

T. Pigoski, M. Griffis, and J. Duffy, Stiffness mappings employing different frames of reference, Mechanism and Machine Theory, vol.33, issue.6, pp.825-838, 1998.
DOI : 10.1016/S0094-114X(97)00083-9

C. Quennouelle and C. M. Gosselin, Stiffness Matrix of Compliant Parallel Mechanisms, Springer Advances in Robot Kinematics: Analysis and Design, pp.331-341, 2008.
DOI : 10.1007/978-1-4020-8600-7_35

]. C. Quennouelle and C. M. Gosselin, Instantaneous Kinemato-Static Model of Planar Compliant Parallel Mechanisms, Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B, 2008.
DOI : 10.1115/DETC2008-49265

]. R. Ramesh, M. A. Mannan, and A. N. Poo, Error compensation in machine tools ??? a review, International Journal of Machine Tools and Manufacture, vol.40, issue.9, pp.1235-1256, 2000.
DOI : 10.1016/S0890-6955(00)00009-2

F. Rehsteiner, R. Neugebauer, S. Spiewak, and F. Wieland, Putting Parallel Kinematics Machines (PKM) to Productive Work, CIRP Annals - Manufacturing Technology, vol.48, issue.1, pp.345-350, 1999.
DOI : 10.1016/S0007-8506(07)63199-0

]. R. Rizk, J. C. Fauroux, M. Mumteanu, and G. Gogu, A comparative stiffness analysis of a reconfigurable parallel machine with three or four degrees of mobility, Journal of Machine Engineering, vol.6, issue.2, pp.45-55, 2006.

]. R. Rizk, N. Andreff, J. C. Fauroux, J. M. Lavest, and G. Gogu, Precision Study of a Decoupled Four Degrees of Freedom Parallel Robot Including Manufacturing and Assembling Errors, Advances in Integrated Design and Manufacturing in Mechanical, Engineering II, pp.111-127, 2007.

]. P. Rocco, G. Ferretti, and G. Magnani, Implicit force control for industrial robots in contact with stiff surfaces, Automatica, vol.33, issue.11, 1997.
DOI : 10.1016/S0005-1098(97)00113-1

Z. Roth, B. Mooring, and B. Ravani, An overview of robot calibration, IEEE Journal on Robotics and Automation, vol.3, issue.5, 1987.
DOI : 10.1109/JRA.1987.1087124

]. J. Salisbury, Active stiffness control of a manipulator in cartesian coordinates, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, pp.87-97, 1980.
DOI : 10.1109/CDC.1980.272026

T. E. Seo, Intégration des effets de déformation d'outil en génération de trajectoires d'usinage, Thèse de doctorat, 1998.

I. R. Sharma, Latest Trends in machining 209 pages, 2001.

T. Son, S. E. Kim, A. Sarma, and . Slocum, A hybrid 5-axis CNC milling machine, Precision Engineering, pp.430-446, 2009.
DOI : 10.1016/j.precisioneng.2008.12.001

H. Su, J. Mccartny, and . Mc, A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms, Journal of Mechanical Design, vol.128, issue.4, pp.776-786, 2006.
DOI : 10.1115/1.2202137

]. J. Sulzer and I. Kova?, Enhancement of positioning accuracy of industrial robots with a reconfigurable fine-positioning module, Precision Engineering, pp.201-217, 2010.

]. D. Surdilovic and M. Vukobratovi, Deflection compensation for large flexible manipulators, Mechanism and Machine Theory, vol.31, issue.3, pp.317-329, 1996.
DOI : 10.1016/0094-114X(95)00073-8

]. M. Svinin, S. Nosoe, and M. Uchiyama, On the stiffness and stability of Gough-Stewart platforms, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164), pp.3268-3273, 2001.
DOI : 10.1109/ROBOT.2001.933122

A. Taghvaeipour, J. Angeles, and L. Lessard, Online computation of the stiffness matrix in robotic structures using finite elements analysis, Report TR-CIM-10-05 Department of mechanical engineering and center for intelligent machines, 2010.

A. Dugas and J. Hascoet, Qualification of parallel kinematics machines in high-speed milling on free form surfaces, International Journal of Machine Tools & Manufacture, vol.44, pp.865-877, 2004.

J. Tlusty, J. Ziegert, and S. Ridgeway, Fundamental Comparison of the Use of Serial and Parallel Kinematics for Machines Tools, CIRP Annals - Manufacturing Technology, vol.48, issue.1, pp.351-356, 1999.
DOI : 10.1016/S0007-8506(07)63200-4

L. W. Tsai and S. Joshi, Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator, Journal of Mechanical Design, vol.122, issue.4, pp.439-446, 2000.
DOI : 10.1115/1.1311612

]. Tsai and Y. Liao, Prediction of cutting forces in ball-end milling by means of geometric analysis, journal of materials processing technology, pp.205-229, 2001.

]. I. Tyapin and G. Hovland, Kinematic and elastostatic design optimization of the 3-DOF Gantry- Tau parallel kinamatic manipulator, Modelling, Identification and Control, pp.39-56, 2009.

W. K. Veitchegger and C. H. Wu, Robot accuracy analysis based on kinematics, IEEE Journal on Robotics and Automation, vol.2, issue.3, pp.171-179, 1986.
DOI : 10.1109/JRA.1986.1087054

D. Veeramani and Y. S. Gau, Models for tool-path plan optimization in patch-by-patch machining, International Journal of Production Research, vol.36, issue.6, pp.1633-1651, 1998.
DOI : 10.1080/002075498193200

]. R. Vertechy and V. Parenti-castelli, Static and stiffness analysis of a class of over-constrained parallel manipulators with legs of type US and UPS, Proceedings of IEEE International Conference on Robotics and Automation (ICRA), pp.561-567, 2007.

W. Min-wan and . Zhang, Systematic study on cutting force modelling methods for peripheral milling, International Journal of Machine Tools and Manufacture, vol.49, issue.5, pp.424-432, 2009.
DOI : 10.1016/j.ijmachtools.2008.12.004

]. J. Wang, H. Zhang, and T. F. St, Improving machining accuracy with robot deformation compensation, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp.3826-3831, 2009.
DOI : 10.1109/IROS.2009.5353988

]. A. Watanabe-2006, S. Watanabe, K. Sakakibara, M. Ban, G. Yamada et al., A Kinematic Calibration Method for Industrial Robots Using Autonomous Visual Measurement, CIRP Annals -Manufacturing Technology, pp.1-6, 2006.

W. Wei and N. Simaan, Design of Planar Parallel Robots With Preloaded Flexures for Guaranteed Backlash Prevention, Journal of Mechanisms and Robotics, vol.2, issue.1, 2010.
DOI : 10.1115/1.4000522

P. Wenger, C. Gosselin, and B. Maille, A Comparative Study of Serial and Parallel Mechanism Topologies for Machine Tools, Proc. PKM'99, pp.23-32, 1999.

P. Wenger, C. Gosselin, and D. Chablat, A Comparative Study of Parallel Kinematic Architectures for Machining Applications, Proc. Workshop on Computational Kinematics, pp.249-258, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00165167

]. A. Werner, Z. Lechniak, K. Skalski, and K. Keîdzior, Design and manufacture of anatomical hip joint endoprostheses using CAD/CAM systems, Journal of Materials Processing Technology, vol.107, issue.1-3, pp.181-186, 2000.
DOI : 10.1016/S0924-0136(00)00682-8

A. Wiegand, M. Hebsacker, and M. Honegger, Parallele Kanematik und Lineamotoren: Hexaglide -ein neues, hochdynamisches Werkzeugmaschinenkonzept, 1996.

]. F. Xi, D. Zhang, C. M. Mechefske, . Y. Sh, and . Lang, Global kinetostatic modelling of tripod-based parallel kinematic machine, Mechanism and Machine Theory, pp.39-357, 2004.

]. X. Xu and S. T. Newman, Making CNC machine tools more open, interoperable and intelligent???a review of the technologies, Computers in Industry, vol.57, issue.2, pp.141-152, 2006.
DOI : 10.1016/j.compind.2005.06.002

M. Xu, R. B. Jerard, and B. K. Fussell, Energy Based Cutting Force Model Calibration for Milling, Computer-Aided Design and Applications, vol.25, issue.7, pp.1-4, 2007.
DOI : 10.1080/16864360.2007.10738554

B. Yi and R. A. Freeman, Synthesis of Actively Adjustable Springs by Antagonistic Redundant Actuation, Journal of Dynamic Systems, Measurement, and Control, vol.114, issue.3, pp.454-461, 1992.
DOI : 10.1115/1.2897368

]. Yi and R. A. Freeman, Geometric analysis of antagonistic stiffness in redundantly actuated parallel mechanisms, Journal of Robotic Systems, vol.4, issue.5, pp.581-603, 1993.
DOI : 10.1002/rob.4620100504

]. M. ?efran and V. Kumar, Coordinate-Free Formulation of the Cartesian Stiffness Matrix, 5th International Symposium on Advances in Robot Kinematics, pp.119-128, 1996.
DOI : 10.1007/978-94-009-1718-7_12

]. M. Zefran and R. V. Kumar, A Geometrical Approach to the Study of the Cartesian Stiffness Matrix, Journal of Mechanical Design, vol.124, issue.1, pp.30-38, 2002.
DOI : 10.1115/1.1423638

]. D. Zhang and C. M. Gosselin, Kinetostatic modeling of parallel mechanisms with a passive constraining leg and revolute actuators, Mechanism and Machine Theory, pp.599-617, 2002.

]. D. Zhang, F. Xi, C. M. Mechefske, and S. Y. Lang, Analysis of parallel kinematic machine with kinetostatic modelling method, Robotics and Computer-Integrated Manufacturing, vol.20, issue.2, pp.151-165, 2004.
DOI : 10.1016/j.rcim.2003.08.005

]. Zhang and L. Wang, Conceptual development of an enhanced tripod mechanism for machine tool, Robotics and Computer-Integrated Manufacturing, pp.318-327, 2005.

]. Zhong, J. Lewis, and F. L. Nagy, Inverse robot calibration using artificial neural networks, Engineering Applications of Artificial Intelligence, vol.9, issue.1, pp.83-93, 1996.
DOI : 10.1016/0952-1976(95)00069-0