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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 320276, 13 pages
A Differential Algebraic Method to Approximate Nonsmooth Mechanical Systems by Ordinary Differential Equations
Department of Mechanical Engineering, Kyushu University, Motooka 744, Nishi-ku, Fukuoka 819-0395, Japan
Received 28 September 2012; Revised 1 April 2013; Accepted 3 April 2013
Academic Editor: Jitao Sun
Copyright © 2013 Xiaogang Xiong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. Anitescu, “A fixed time-step approach for multibody dynamics with contact and friction,” in Proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '03), pp. 3725–3731, Las Vegas, NV, USA, October 2003.
- Z. Qi, X. Luo, and Z. Huang, “Frictional contact analysis of spatial prismatic joints in multibody systems,” Multibody System Dynamics, vol. 26, no. 4, pp. 441–468, 2011.
- P. Song, P. Kraus, V. Kumar, and P. Dupont, “Analysis of rigid-body dynamic models for simulation of systems with frictional contacts,” Journal of Applied Mechanics, vol. 68, no. 1, pp. 118–128, 2001.
- G. D. Hart and M. Anitescu, “A hard-constraint time-stepping approach for rigid multibody dynamics with joints, contact, and friction,” in Proceedings of the Richard Tapia Celebration of Diversity in Computing Conference (Tapia '03),, pp. 34–40, Atlanta, GA, USA, October 2003.
- P. Dahl, “A solid friction model,” Tech. Rep., Aerospace Corporation, El Segundo, Calif, USA, 1968.
- C. Canudas de Wit, H. Olsson, K. J. Åström, and P. Lischinsky, “A new model for control of systems with friction,” IEEE Transactions on Automatic Control, vol. 40, no. 3, pp. 419–425, 1995.
- F. A. Tariku and R. J. Rogers, “Improved dynamic friction models for simulation of one-dimensional and two-dimensional stick-slip motion,” Journal of Tribology, vol. 123, no. 4, pp. 661–669, 2001.
- D. D. Quinn, “A new regularization of Coulomb friction,” Journal of Vibration and Acoustics, vol. 126, no. 3, pp. 391–397, 2004.
- F. Al-Bender, V. Lampaert, and J. Swevers, “The generalized Maxwell-slip model: a novel model for friction simulation and compensation,” IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1883–1887, 2005.
- L. Luo and M. Nahon, “Development and validation of geometry-based compliant contact models,” Journal of Computational and Nonlinear Dynamics, vol. 6, no. 1, Article ID 011004, 2011.
- Y. Gonthier, J. McPhee, C. Lange, and J. C. Piedbœuf, “A regularized contact model with asymmetric damping and dwell-time dependent friction,” Multibody System Dynamics, vol. 11, no. 3, pp. 209–233, 2004.
- D. W. Marhefka and D. E. Orin, “A compliant contact model with nonlinear damping for simulation of robotic systems,” IEEE Transactions on Systems, Man, and Cybernetics A, vol. 29, no. 6, pp. 566–572, 1999.
- K. H. Hunt and F. R. E. Crossley, “Coefficient of restitution interpreted as damping in vibroimpact,” Journal of Applied Mechanics, vol. 42, no. 2, pp. 440–445, 1975.
- M. Anitescu, F. A. Potra, and D. E. Stewart, “Time-stepping for three-dimensional rigid body dynamics,” Computer Methods in Applied Mechanics and Engineering, vol. 177, no. 3-4, pp. 183–197, 1999.
- M. Anitescu and F. A. Potra, “Formulating dynamic multi-rigid-body contact problems with friction as solvable linear complementarity problems,” Nonlinear Dynamics, vol. 14, no. 3, pp. 231–247, 1997.
- C. Glocker and C. Studer, “Formulation and preparation for numerical evaluation of linear complementarity systems in dynamics,” Multibody System Dynamics, vol. 13, no. 4, pp. 447–463, 2005.
- D. E. Stewart, “Rigid-body dynamics with friction and impact,” SIAM Review, vol. 42, no. 1, pp. 3–39, 2000.
- M. Anitescu and G. D. Hart, “A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contact and friction,” International Journal for Numerical Methods in Engineering, vol. 60, no. 14, pp. 2335–2371, 2004.
- F. A. Potra and M. Anitescu, “A time-stepping method for stiff multibody dynamics with contact and friction,” International Journal for Numerical Methods in Engineering, vol. 55, no. 7, pp. 753–784, 2002.
- F. A. Potra, M. Anitescu, B. Gavrea, and J. Trinkle, “A linearly implicit trapezoidal method for integrating stiff multibody dynamics with contact, joints, and friction,” International Journal for Numerical Methods in Engineering, vol. 66, no. 7, pp. 1079–1124, 2006.
- M. Förg, F. Pfeiffer, and H. Ulbrich, “Simulation of unilateral constrained systems with many bodies,” Multibody System Dynamics, vol. 14, no. 2, pp. 137–154, 2005.
- P. Flores, R. Leine, and C. Glocker, “Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach,” Multibody System Dynamics, vol. 23, no. 2, pp. 165–190, 2010.
- R. Kikuuwe, N. Takesue, A. Sano, H. Mochiyama, and H. Fujimoto, “Admittance and impedance representations of friction based on implicit Euler integration,” IEEE Transactions on Robotics, vol. 22, no. 6, pp. 1176–1188, 2006.
- V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems, vol. 35 of Lecture Notes in Applied and Computational Mechanics, Springer, Berlin, Germany, 2008.
- R. Kikuuwe and H. Fujimoto, “Incorporating geometric algorithms in impedance- and admittance-type haptic rendering,” in Proceedings of the 2nd Joint Eurohaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems (WHC '07), pp. 249–254, Tsukuba, Japan, March 2007.
- D. E. Stewart, “A numerical method for friction problems with multiple contacts,” Australian Mathematical Society B, vol. 37, no. 3, pp. 288–308, 1996.
- R. Kikuuwe, S. Yasukouchi, H. Fujimoto, and M. Yamamoto, “Proxy-based sliding mode control: a safer extension of PID position control,” IEEE Transactions on Robotics, vol. 26, no. 4, pp. 670–683, 2010.
- R. Kikuuwe, M. Yamamoto, and H. Fujimoto, “Velocity-bounding stiff position controller,” in Proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '06), pp. 3050–3055, Beijing, China, October 2006.
- V. Acary, O. Bonnefon, and B. Brogliato, “Time-stepping numerical simulation of switched circuits within the nonsmooth dynamical systems approach,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 29, no. 7, pp. 1042–1055, 2010.
- B. Brogliato, A. Daniilidis, C. Lemaréchal, and V. Acary, “On the equivalence between complementarity systems, projected systems and differential inclusions,” Systems & Control Letters, vol. 55, no. 1, pp. 45–51, 2006.
- D. Karnopp, “Computer simulation of stick-slip friction in mechanical dynamic systems,” Journal of Dynamic Systems, Measurement and Control, vol. 107, no. 1, pp. 100–103, 1985.
- P. Dupont, V. Hayward, B. Armstrong, and F. Altpeter, “Single state elastoplastic friction models,” IEEE Transactions on Automatic Control, vol. 47, no. 5, pp. 787–792, 2002.
- J. Bastien and C. H. Lamarque, “Persoz's gephyroidal model described by a maximal monotone differential inclusion,” Archive of Applied Mechanics, vol. 78, no. 5, pp. 393–407, 2008.
- R. Kikuuwe and M. Yamamoto, “A modular software architecture for simulating mechanical systems involving coulomb friction integrable by the Runge-Kutta method,” in Proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '08), pp. 2277–2282, Nice, France, September 2008.
- M. K. Vukobratović and V. Potkonjak, “Dynamics of contact tasks in robotics. I. General model of robot interacting with environment,” Mechanism and Machine Theory, vol. 34, no. 6, pp. 923–942, 1999.
- P. Flores and J. Ambrósio, “On the contact detection for contact-impact analysis in multibody systems,” Multibody System Dynamics, vol. 24, no. 1, pp. 103–122, 2010.
- Y. Zhang and I. Sharf, “Validation of nonlinear viscoelastic contact force models for low speed impact,” Journal of Applied Mechanics, vol. 76, no. 5, Article ID 051002, pp. 1–12, 2009.
- S. E. Sørensen, M. R. Hansen, M. Ebbesen, and O. Mouritsen, “Implicit identification of contact parameters in a continuous chain model,” Modeling, Identification and Control, vol. 32, no. 1, pp. 1–15, 2011.
- Ch. Glocker and F. Pfeiffer, “Multiple impacts with friction in rigid multibody systems,” Nonlinear Dynamics, vol. 7, no. 4, pp. 471–497, 1995.
- J. Baumgarte, “Stabilization of constraints and integrals of motion in dynamical systems,” Computer Methods in Applied Mechanics and Engineering, vol. 1, pp. 1–16, 1972.
- J. Awrejcewicz, M. Fečkan, and P. Olejnik, “On continuous approximation of discontinuous systems,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 62, no. 7, pp. 1317–1331, 2005.