Abstract
This paper presents a new dissipation principle for resolving post-impact tangential velocities after simultaneous impact events on a system composed of interconnected rigid bodies. In this work, contact is considered as a succession of impacts so that simultaneous contacts and impacts can be treated using the same framework. This treatment includes Coulomb friction and considers hard impacts where deformation of the impacting surfaces is negligible. The impact problem is addressed using the complementarity conditions which lead to an investigation of the relationship between post-impact velocities and feasible coefficients of friction. These conditions do not define a unique post-impact velocity so a dissipation principle is proposed which is encoded as an optimization problem. This solution preserves the discontinuity between the static and dynamic coefficients of friction. The approach is illustrated on a bicycle-like structure with elliptical wheels.
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Gilardi, G., Sharf, I.: Literature survey of contact dynamics modeling. Mech. Mach. Theory 37(10), 1213–1239 (2002)
Flores, P., Ambrosio, J., Claro, J., Lankarani, H.: Influence of the contact–impact force model on the dynamic response of multi-body systems. Proc. Inst. Mech. Eng., Part K: J. Multi-Body Dyn. 220(1), 21–34 (2006)
Modarres Najafabadi, S.A., Kovecses, J., Angeles, J.: Impacts in multibody systems: modeling and experiments. Multibody Syst. Dyn. 20(2), 163–176 (2008)
Djerassi, S.: Collision with friction; Part B: Poisson’s and Stornge’s hypotheses. Multibody Syst. Dyn. 21(1), 55–70 (2009)
Stewart, D.E.: Rigid-body dynamics with friction and impact. SIAM Rev. 42(1), 3–39 (2000)
Moreau, J.J.: Numerical aspects of the sweeping process. Comput. Methods Appl. Mech. Eng. 177(3–4), 329–349 (1999)
Brogliato, B., Ten Dam, A., Paoli, L., Génot, F., Abadie, M.: Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. Appl. Mech. Rev. 55(2), 107–149 (2002)
Liu, T., Wang, M.Y., Low, K.H.: Non-jamming conditions in multi-contact rigid-body dynamics. Multibody Syst. Dyn. 22(3), 269–295 (2009)
Stoianovici, D., Hurmuzlu, Y.: A critical study of the applicability of rigid body collision theory. ASME J. Appl. Mech. 63(2), 307–316 (1996)
Hurmuzlu, Y.: An energy based coefficient of restitution for planar impacts of slender bars with massive external surfaces. ASME J. Appl. Mech. 65(4), 952–952 (1998)
Kim, H.-J., Yoo, W.-S., Ok, J.-K., Kang, D.-W.: Parameter identification of damping models in multibody dynamic simulation of mechanical systems. Multibody Syst. Dyn. (2009)
Djerassi, S.: Collision with friction; part a: Newton’s hypothesis. Multibody Syst. Dyn. 21(1), 37–54 (2009)
Karnopp, D.: Computer simulation of stick-slip friction in mechanical dynamic systems. J. Dyn. Syst. Meas. Control 107(1), 100–103 (1985)
Haessig, D.A., Jr.: Friedland, B.: On the modeling and simulation of friction. J. Dyn. Syst. Meas. Control 113(3), 354–362 (1991)
Ambrósio, J., Verissimo, P.: Improved bushing models for general multibody systems and vehicle dynamics. Multibody Syst. Dyn. (2009)
Aoustin, Y., Formal’Skii, A.: Ball on a beam: stabilization under saturated input control with large basin of attraction. Multibody Syst. Dyn. 21(1), 71–89 (2009)
Bowling, A., Flickinger, D.M., Harmeyer, S.: Energetically consistent simulation of simultaneous impacts and contacts in multibody systems with friction. Multibody Syst. Dyn. 22(1), 27–45 (2009)
Bowling, A.P.: Impact forces and agility in legged robot locomotion. J. Vib. Control (2009, in press)
Craig, J.J.: Introduction to Robotics: Mechanics and Control, 2nd edn. Addison-Wesley, Reading (1989)
Glocker, C., Studer, C.: Formulation and preparation for numerical evaluation of linear complementarity systems in dynamics. Multibody Syst. Dyn. 13(4), 447–463 (2005)
Han, I., Gilmore, B.J.: Multi-body impact motion with friction—analysis, simulation, and experimental validation. J. Mech. Des. 115(3), 412–422 (1993)
Mouri, T., Yamada, T., Iwai, A., Mimura, N., Funahashi, Y.: Identification of contact conditions from contaminated data of contact force and moment. In: Proceedings IEEE International Conference on Robotics and Automation, vol. 1, pp. 597–603 (2001)
Bowling, A.: Dynamic performance, mobility, and agility of multi-legged robots. J. Dyn. Syst. Meas. Control 128(4), 765–777 (2006)
Brach, R.: Friction, restitution, and energy loss in planar collisions. J. Appl. Mech. 51(1), 164–170 (1984)
Brach, R.: Mechanical Impact Dynamics: Rigid Body Collisions. Wiley, New York (1991)
Brogliato, B.: Nonsmooth Mechanics: Models, Dynamics and Control. Springer, London (1999), p. 128
Brach, R.: Formulation of rigid body impact problems using generalized coordinates. Int. J. Eng. Sci. 36(1), 61–71 (1998)
Becker, V., Schwager, T.: Coefficient of tangential restitution for the linear dashpot model. Phys. Rev. E 77(1), 011304–1–011304–12 (2008)
Schiehlen, W., Seifried, R.: Three approaches for elastodynamic contact in multibody systems. Multibody Syst. Dyn. 12(1), 1–16 (2004)
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Flickinger, D.M., Bowling, A. Simultaneous oblique impacts and contacts in multibody systems with friction. Multibody Syst Dyn 23, 249–261 (2010). https://doi.org/10.1007/s11044-009-9182-2
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DOI: https://doi.org/10.1007/s11044-009-9182-2