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Article contents
Multibody dynamics in robotics with focus on contact events
Part of:
The 40th Anniversary of Robotica
Published online by Cambridge University Press: 16 April 2024
Abstract
Multibody dynamics methodologies have been fundamental tools utilized to model and simulate robotic systems that experience contact conditions with the surrounding environment, such as in the case of feet and ground interactions. In addressing such problems, it is of paramount importance to accurately and efficiently handle the large body displacement associated with locomotion of robots, as well as the dynamic response related to contact-impact events. Thus, a generic computational approach, based on the Newton–Euler formulation, to represent the gross motion of robotic systems, is revisited in this work. The main kinematic and dynamic features, necessary to obtain the equations of motion, are discussed. A numerical procedure suitable to solve the equations of motion is also presented. The problem of modeling contacts in dynamical systems involves two main tasks, namely, the contact detection and the contact resolution, which take into account for the kinematics and dynamics of the contacting bodies, constituting the general framework for the process of modeling and simulating complex contact scenarios. In order to properly model the contact interactions, the contact kinematic properties are established based on the geometry of contacting bodies, which allow to perform the contact detection task. The contact dynamics is represented by continuous contact force models, both in terms of normal and tangential contact directions. Finally, the presented formulations are demonstrated by the application to several robotics systems that involve contact and impact events with surrounding environment. Special emphasis is put on the systems’ dynamic behavior, in terms of performance and stability.
Keywords
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press
References
Antonya, C. and Boboc, R. G., “Computational efficiency of multi-body systems dynamic models,” Robotica 39(12), 2333–2348 (2021).CrossRefGoogle Scholar
Li, Z., Li, C., Li, S., Zhu, S. and Samani, H., “A sparsity-based method for fault-tolerant manipulation of a redundant robot,” Robotica 40(10), 3396–3414 (2022).CrossRefGoogle Scholar
Zhang, P., Zhang, J. and Elsabbagh, A., “Fuzzy radial-based impedance controller design for lower limb exoskeleton robot,” Robotica 41(1), 326–345 (2023).CrossRefGoogle Scholar
You, P., Liu, Z. and Ma, Z., “Multibody dynamic modeling and analysis of cable-driven snake robot considering clearance and friction based on ALE method,” Mech Mach Theory 184, 105313 (2023).CrossRefGoogle Scholar
Grazioso, A., Ugenti, A., Galati, R., Mantriota, G. and Reina, G., “Modeling and validation of a novel tracked robot via multibody dynamics,” Robotica 41(10), 3211–3232 (2023).CrossRefGoogle Scholar
Mucchi, E., Fiorati, S., Di Gregorio, R. and Dalpiaz, G., “Multibody modeling and vibration testing of 3R planar manipulators: Effects of flexible installation frames,” Robotica 31(8), 1209–1220 (2013).CrossRefGoogle Scholar
Bascetta, L., Ferretti, G. and Scaglioni, B., “Closed form Newton-Euler dynamic model of flexible manipulators,” Robotica 35(5), 1006–1030 (2017).CrossRefGoogle Scholar
Chang, X., An, H. and Ma, H., “Modeling and base parameters identification of legged robots,” Robotica 40(3), 747–761 (2022).CrossRefGoogle Scholar
Vasileiou, C., Smyrli, A., Drogosis, A. and Papadopoulos, E., “Development of a passive biped robot digital twin using analysis, experiments, and a multibody simulation environment,” Mech Mach Theory 163, 104346 (2021).CrossRefGoogle Scholar
Safartoobi, M., Dardel, M. and Daniali, H. M., “Gait cycles of passive walking biped robot model with flexible legs,” Mech Mach Theory 159, 10429 (2021).CrossRefGoogle Scholar
Kim, M., Moon, W., Bae, D. and Park, I., “Dynamic simulations of electromechanical robotic systems driven by DC motors,” Robotica 22(5), 523–531 (2004).CrossRefGoogle Scholar
Ingrosso, R., De Palma, D., Avanzini, G. and Indiveri, G., “Dynamic modeling of underwater multi-hull vehicles,” Robotica 38(9), 1682–1702 (2020).CrossRefGoogle Scholar
Coelho, J., Ribeiro, F., Dias, B., Lopes, G. and Flores, P., “Trends in the control of hexapod robots: A survey,” Robotics 10(3), 100 (2021).CrossRefGoogle Scholar
Di Vito, D., De Palma, D., Simetti, E., Indiveri, G. and Antonelli, G., “Experimental validation of the modeling and control of a multibody underwater vehicle manipulator system for sea mining exploration,” J Field Robot 38(2), 171–191 (2021).CrossRefGoogle Scholar
Wadi, A. and Mukhopadhyay, S., “A novel localization-free approach to system identification for underwater vehicles using a universal adaptive stabilizer,” Ocean Eng 274, 114013 (2023).CrossRefGoogle Scholar
Kim, J. H., Yang, J. and Abdel-Malek, K., “Planning load-effective dynamic motions of highly articulated human model for generic tasks,” Robotica 27(05), 739–747 (2009).CrossRefGoogle Scholar
Zhang, P. and Zhang, J., “Lower limb exoskeleton robots’ dynamics parameters identification based on improved beetle swarm optimization algorithm,” Robotica 40(8), 2716–2731 (2022).CrossRefGoogle Scholar
Gonçalves, F., Ribeiro, T., Ribeiro, A. F., Lopes, G. and Flores, P., “Dynamic Modeling of a Human-Inspired Robot Based on a Newton-Euler Approach,” In: CISM International Centre for Mechanical Sciences, Courses and Lectures, Vol. 606 (Springer, Cham, 2022) pp. 79–90.Google Scholar
Gonçalves, F., Ribeiro, T., Ribeiro, A. F., Lopes, G. and Flores, P., “A recursive algorithm for the forward kinematic analysis of robotic systems using euler angles,” Robotics 11(1), 15 (2022).CrossRefGoogle Scholar
Transeth, A. A., Pettersen, K. Y. and Liljebäck, P., “A survey on snake robot modeling and locomotion,” Robotica 27(7), 999–1015 (2009).CrossRefGoogle Scholar
Vossoughi, G., Pendar, H., Heidari, Z. and Mohammadi, S., “Assisted passive snake-like robots: Conception and dynamic modeling using Gibbs-Appell method,” Robotica 26(3), 267–276 (2008).CrossRefGoogle Scholar
Mirtaheri, S. M. and Zohoor, H., “Efficient formulation of the Gibbs-Appell equations for constrained multibody systems,” Multibody Syst Dyn 53(3), 303–325 (2021).CrossRefGoogle Scholar
Talaeizadeh, A., Forootan, M., Zabihi, M. and Pishkenari, H. N., “Comparison of kane’s and Lagrange’s methods in analysis of constrained dynamical systems,” Robotica 38(12), 2138–2150 (2020).CrossRefGoogle Scholar
Saunders, F., Golden, E., White, R. D. and Rife, J., “Experimental verification of soft-robot gaits evolved using a lumped dynamic model,” Robotica 29(6), 823–830 (2011).CrossRefGoogle Scholar
Zou, J., Lin, Y., Ji, C. and Yang, H., “A reconfigurable omnidirectional soft robot based on caterpillar locomotion,” Soft Robot 5(2), 164–174 (2018).CrossRefGoogle ScholarPubMed
Jia, J., Cheng, P., Ye, Y., Xie, Q. and Wu, C., “A novel soft-rigid wheeled crawling robot with high payload and passing capability,” Robotica 40(11), 3930–3951 (2022).CrossRefGoogle Scholar
Banerjee, A., Chanda, A. and Das, R., “Historical origin and recent development on normal directional impact models for rigid body contact simulation: A critical review,” Arch Comput Method Eng 24(2), 397–422 (2017).CrossRefGoogle Scholar
Skrinjar, L., Slavič, J. and Boltežar, M., “A review of continuous contact-force models in multibody dynamics,” Int J Mech Sci 145, 171–187 (2018).CrossRefGoogle Scholar
Machado, M., Moreira, P., Flores, P. and Lankarani, H. M., “Compliant contact force models in multibody dynamics: Evolution of the hertz contact theory,” Mech Mach Theory 53, 99–121 (2012).CrossRefGoogle Scholar
Marques, F., Flores, P., Pimenta Claro, J. C. and Lankarani, H. M., “A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems,” Nonline Dynam 86(3), 1407–1443 (2016).CrossRefGoogle Scholar
Marques, F., Flores, P., Claro, J. C. P. and Lankarani, H. M., “Modeling and analysis of friction including rolling effects in multibody dynamics: A review,” Multibody Syst Dyn 45(2), 223–244 (2019).CrossRefGoogle Scholar
Pennestrì, E., Rossi, V., Salvini, P. and Valentini, P. P., “Review and comparison of dry friction force models,” Nonlinear Dyn 83(4), 1785–1801 (2016).CrossRefGoogle Scholar
Vukobratović, M. K. and Potkonjak, V., “Dynamics of contact tasks in robotics. Part I: General model of robot interacting with environment,” Mech Mach Theory 34(6), 923–942 (1999).CrossRefGoogle Scholar
Saraiva, L., Rodrigues da Silva, M., Marques, F., Tavares da Silva, M. and Flores, P., “A review on foot-ground contact modeling strategies for human motion analysis,” Mech Mach Theory 177, 105046 (2022).CrossRefGoogle Scholar
Vukobratovic, M., Potkonjak, V. and Matijevic, V., “Contribution to the study of dynamics and dynamic control of robots interacting with dynamic environment,” Robotica 19(2), 149–161 (2001).CrossRefGoogle Scholar
Loganathan, A. and Ahmad, N. S., “A systematic review on recent advances in autonomous mobile robot navigation,” Eng Sci Tech Int J 40, 101343 (2023).Google Scholar
Dottore, E. D., Sadeghi, A., Mondini, A., Mattoli, V. and Mazzolai, B., “Toward growing robots: A historical evolution from cellular to plant-inspired robotics,” Front Robot AI 5, 16 (2018).CrossRefGoogle ScholarPubMed
Napp, N. and Nagpal, R., “Distributed amorphous ramp construction in unstructured environments,” Robotica 32(2), 279–290 (2014).CrossRefGoogle Scholar
Mehdian, M. and Rahnejat, H., “An intelligent part sorting robot in unstructured manufacturing environments,” Robotica 10(2), 155–164 (1992).CrossRefGoogle Scholar
Varedi-Koulaei, S. M., Daniali, H. M. and Farajtabar, M., “The effects of joint clearance on the dynamics of the 3RRR planar parallel manipulator,” Robotica 35(6), 1223–1242 (2017).CrossRefGoogle Scholar
Guo, F., Cheng, G., Wang, S. and Li, J., “Rigid-flexible coupling dynamics analysis with joint clearance for a 5-DOF hybrid polishing robot,” Robotica 40(7), 2168–2188 (2022).CrossRefGoogle Scholar
Tian, X., Lv, M., Sun, J., Zhao, H., Jiang, Z., Han, J., Gu, W. and Cheng, G., “An adaptive impedance control method for polishing system of an optical mirror processing robot,” Robotica 42(1), 21–39 (2024).CrossRefGoogle Scholar
Zahedi, A., Shafei, A. M. and Shamsi, M., “Kinetics of planar constrained robotic mechanisms with multiple closed loops: An experimental study,” Mech Mach Theory 183, 105250 (2023).CrossRefGoogle Scholar
Farhat, N., Mata, V., Page, Á. and Díaz-Rodríguez, M., “Dynamic simulation of a parallel robot: Coulomb friction and stick-slip in robot joints,” Robotica 28(1), 35–45 (2010).CrossRefGoogle Scholar
Ahmadizadeh, M., Shafei, A. M. and Fooladi, M., “A recursive algorithm for dynamics of multiple frictionless impact-contacts in open-loop robotic mechanisms,” Mech Mach Theory 146, 103745 (2020).CrossRefGoogle Scholar
Schiehlen, W., “Energy-optimal design of walking machines,” Multibody Syst Dyn 13(1), 129–141 (2005).CrossRefGoogle Scholar
Taheri, H. and Mozayani, N., “A study on quadruped mobile robots,” Mech Mach Theory 190, 105448 (2023).CrossRefGoogle Scholar
Mahapatra, A., Roy, S. S. and Pratihar, D. K., “Study on feet forces’ distributions, energy consumption and dynamic stability measure of hexapod robot during crab walking,” Appl Math Model 65, 717–744 (2019).CrossRefGoogle Scholar
He, J. and Ren, G., “A multibody dynamics approach to limit cycle walking,” Robotica 37(10), 1804–1822 (2019).CrossRefGoogle Scholar
Liu, Z., Gao, J., Rao, X., Ding, S. and Liu, D., “Complex dynamics of the passive biped robot with flat feet: Gait bifurcation, intermittency and crisis,” Mech Mach Theory 191, 105500 (2024).CrossRefGoogle Scholar
Tang, Y., Zhang, J. M. and Zhang, D., “A new comprehensive performance optimization approach for Earth-contact mechanism based on terrain-adaptability task,” Robotica 41(1), 193–214 (2023).CrossRefGoogle Scholar
Hu, Y. and Guo, W., “A new concept of contact joint to model the geometric foot-environment contacts for efficiently determining possible stances for legged robots,” Mech Mach Theory 162, 104327 (2021).CrossRefGoogle Scholar
Tang, H., Li, Y., Zhang, J. W., Zhang, D. and Yu, H., “Design and optimization of a novel sagittal-plane knee exoskeleton with remote-center-of-motion mechanism,” Mech Mach Theory 194, 105570 (2024).CrossRefGoogle Scholar
David, A. and Bruneau, O., “Bipedal walking gait generation based on the sequential method of analytical potential (SMAP),” Multibody Syst Dyn 26(4), 367–395 (2011).CrossRefGoogle Scholar
Kherici, N. and Mohamed Ben Ali, Y., “Using PSO for a walk of a biped robot,” J Comput Sci 5(5), 743–749 (2014).CrossRefGoogle Scholar
Nikravesh, P. E.. Computer-aided analysis of mechanical systems (Prentice Hall, Englewood Cliffs, New Jersey, 1988).Google Scholar
Askari, E., Flores, P., Dabirrahmani, D. and Appleyard, R., “Dynamic modeling and analysis of wear in spatial hard-on-hard couple hip replacements using multibody systems methodologies,” Nonlinear Dynam 82(1-2), 1039–1058 (2015).CrossRefGoogle Scholar
Rodrigues da Silva, M., Marques, F., Tavares da Silva, M. and Flores, P., “A comparison of spherical joint models in the dynamic analysis of rigid mechanical systems: Ideal, dry, hydrodynamic and bushing approaches,” Multibody Syst Dyn 56(3), 221–266 (2022).CrossRefGoogle Scholar
Flores, P., “A methodology for quantifying the kinematic position errors due to manufacturing and assembly tolerances,” Strojniski Vestnik/J Mech Eng 57(6), 457–467 (2011).CrossRefGoogle Scholar
Marques, F., Roupa, I., Silva, M. T., Flores, P. and Lankarani, H. M., “Examination and comparison of different methods to model closed loop kinematic chains using lagrangian formulation with cut joint, clearance joint constraint and elastic joint approaches,” Mech Mach Theory 160, 104294 (2021).CrossRefGoogle Scholar
Nikravesh, P. E., “Initial condition correction in multibody dynamics,” Multibody Syst Dyn 18(1), 107–115 (2007).CrossRefGoogle Scholar
Neto, M. A. and Ambrósio, J., “Stabilization methods for the integration of DAE in the presence of redundant constraints,” Multibody Syst Dyn 10(1), 81–105 (2003).CrossRefGoogle Scholar
Marques, F., Souto, A. P. and Flores, P., “On the constraints violation in forward dynamics of multibody systems,” Multibody Syst Dyn 39(4), 385–419 (2017).CrossRefGoogle Scholar
Nikravesh, P. E., “Newtonian-based methodologies in multi-body dynamics,” Proceed Inst Mech Engin Part K: J Multi-body Dyna 222(4), 277–288 (2008).Google Scholar
Baumgarte, J., “Stabilization of constraints and integrals of motion in dynamical systems,” Comput Method Appl M 1(1), 1–16 (1972).CrossRefGoogle Scholar
Chang, C. O. and Nikravesh, P. E., “An adaptive constraint violation stabilization method for dynamic analysis of mechanical systems,” J Mech Design 107(4), 488–492 (1985).Google Scholar
Lin, S.-T. and Huang, J.-N., “Stabilization of baumgarte’s method using the runge-kutta approach,” J Mech Design 124(4), 633–641 (2002).CrossRefGoogle Scholar
Flores, P., Machado, M., Seabra, E. and Tavares da Silva, M., “A parametric study on the baumgarte stabilization method for forward dynamics of constrained multibody systems,” J Comput Nonlin Dyn 6(1), 011019 (2011).CrossRefGoogle Scholar
Khoshnazar, M., Dastranj, M., Azimi, A., Aghdam, M. M. and Flores, P., “Application of the bezier integration technique with enhanced stability in forward dynamics of constrained multibody systems with baumgarte stabilization method,” Eng Comput, (2023). doi: 10.1007/s00366-023-01884-x.CrossRefGoogle Scholar
Flores, P. and Nikravesh, P. E., “Comparison of Different Methods to Control Constraints Violation in Forward Multibody Dynamics,” In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, 55966, (2013) p. V07AT10A028.Google Scholar
Wehage, R. A. and Haug, E. J., “Generalized coordinate partitioning for dimension reduction in analysis of constrained systems,” J Mech Design 104(1), 247–255 (1982).CrossRefGoogle Scholar
de Jalón, J. G. and Bayo, E. Kinematic and Dynamic Simulations of Multibody Systems: The Real-Time Challenge (Springer, New York, 1994).CrossRefGoogle Scholar
Bayo, E. and Ledesma, R., “Augmented Lagrangian and mass-orthogonal projection methods for constrained multibody dynamics,” Nonlinear Dynam 9(1-2), 113–130 (1996).CrossRefGoogle Scholar
Glocker, C., “On frictionless impact models in rigid-body systems,” Philo Trans Royal Society: Math, Phys Eng Sci 359(1789), 2385–2404 (2001).CrossRefGoogle Scholar
Machado, M., Flores, P., Ambrosio, J. and Completo, A., “Influence of the contact model on the dynamic response of the human knee joint,” Proceed Inst Mech Eng”, Part K: J Multi-body Dyna 225(4), 344–358 (2011).Google Scholar
Flores, P., Ambrósio, J. and Lankarani, H. M., “Contact-impact events with friction in multibody dynamics: Back to basics,” Mech Mach Theory 184, 105305 (2023).CrossRefGoogle Scholar
Flores, P. and Ambrósio, J., “On the contact detection for contact-impact analysis in multibody systems,” Multibody Syst Dyn 24(1), 103–122 (2010).CrossRefGoogle Scholar
Lankarani, H. M. and Nikravesh, P. E., “A contact force model with hysteresis damping for impact analysis of multibody systems,” J Mech Design 112(3), 369–376 (1990).CrossRefGoogle Scholar
Askari, E., Flores, P., Dabirrahmani, D. and Appleyard, R., “A review of squeaking in ceramic total hip prostheses,” Tribol Int 93, 239–256 (2015).CrossRefGoogle Scholar
Costa, J., Peixoto, J., Moreira, P., Flores, P., Souto, A. P. and Lankarani, H. M., “Influence of the hip joint modeling approaches on the kinematics of human gait,” J Tribo 138(3), 031201 (2016).CrossRefGoogle Scholar
Pfeiffer, F., “Non-smooth engineering dynamics,” Meccanica 51(12), 3167–3184 (2016).CrossRefGoogle Scholar
Lopes, D. S., Silva, M. T., Ambrósio, J. A. and Flores, P., “A mathematical framework for rigid contact detection between quadric and superquadric surfaces,” Multibody Syst Dyn 24(3), 255–280 (2010).CrossRefGoogle Scholar
Machado, M., Flores, P. and Ambrósio, J., “A lookup-table-based approach for spatial analysis of contact problems,” J Comput Nonlin Dyn 9(4), 041010 (2014).CrossRefGoogle Scholar
Marques, F., Magalhães, H., Liu, B., Pombo, J., Flores, P., Ambrósio, J., Piotrowski, J. and Bruni, S., “On the generation of enhanced lookup tables for wheel-rail contact models,” Wear 434-435, 202993 (2019).CrossRefGoogle Scholar
Moreno, R. G., Marques, F., Abad, E. C., Alonso, J. M., Flores, P. and Castejon, C., “Enhanced modelling of planar radial-loaded deep groove ball bearings with smooth-contact formulation,” Multibody Syst Dyn 60(1), 121–159 (2024).Google Scholar
Machado, M., Flores, P., Claro, J. C. P., Ambrósio, J., Silva, M., Completo, A. and Lankarani, H. M., “Development of a planar multi-body model of the human knee joint,” Nonlinear Dynam 60(3), 459–478 (2010).CrossRefGoogle Scholar
Flores, P. and Ambrósio, J., “Revolute joints with clearance in multibody systems,” Comput Struc 82(17-19), 1359–1369 (2004).CrossRefGoogle Scholar
Flores, P., Ambrósio, J., Claro, J. C. P. and Lankarani, H. M., “Influence of the contact-impact force model on the dynamic response of multi-body systems,” Proceed Inst Mech Eng, Part K: J Multi-body Dyn 220(1), 21–34 (2006).Google Scholar
Glocker, C., “Concepts for modeling impacts without friction,” Acta Mech 168(1-2), 1–19 (2004).CrossRefGoogle Scholar
Pombo, J. and Ambrósio, J., “Application of a wheel-rail contact model to railway dynamics in small radius curved tracks,” Multibody Syst Dyn 19(1-2), 91–114 (2008).CrossRefGoogle Scholar
Schiehlen, W. and Seifried, R., “Three approaches for elastodynamic contact in multibody systems,” Multibody Syst Dyn 12(1), 1–16 (2004).CrossRefGoogle Scholar
Flores, P., Machado, M., Silva, M. T. and Martins, J. M., “On the continuous contact force models for soft materials in multibody dynamics,” Multibody Syst Dyn 25(3), 357–375 (2011).CrossRefGoogle Scholar
Flores, P., “Contact mechanics for dynamical systems: A comprehensive review,” Multibody Syst Dyn 54(2), 127–177 (2022).CrossRefGoogle Scholar
Nikravesh, P. E. and Poursina, M., “Determination of effective mass for continuous contact models in multibody dynamics,” Multibody Syst Dyn 58(3-4), 253–273 (2023).CrossRefGoogle Scholar
Ding, S., Jian, B., Zhang, Y., Xia, R. and Hu, G., “A normal contact force model for viscoelastic bodies and its finite element modeling verification,” Mech Mach Theory 181, 105202 (2023).CrossRefGoogle Scholar
Wang, K. and Tian, Q., “A nonsmooth method for spatial frictional contact dynamics of flexible multibody systems with large deformation,” Int J Numer Meth Eng 124(3), 752–779 (2023).CrossRefGoogle Scholar
Wang, G., Ma, D., Liu, C. and Liu, Y., “Development of a compliant dashpot model with nonlinear and linear behaviors for the contact of multibody systems,” Mech Syst Signal Pr 185, 109785 (2023).CrossRefGoogle Scholar
Ma, J., Wang, J., Han, Y., Dong, S., Yin, L. and Xiao, Y., “Towards data-driven modeling for complex contact phenomena via self-optimized artificial neural network methodology,” Mech Mach Theory 182, 3023 (2023).CrossRefGoogle Scholar
Lankarani, H. M., “A poisson-based formulation for frictional impact analysis of multibody mechanical systems with open or closed kinematic chains,” J Mech Design 122(4), 489–497 (2000).CrossRefGoogle Scholar
Lankarani, H. M. and Pereira, M. F. O. S., “Treatment of impact with friction in planar multibody mechanical systems,” Multibody Syst Dyn 6(3), 203–227 (2001).CrossRefGoogle Scholar
Piazza, S. J. and Delp, S. L., “Three-dimensional dynamic simulation of total knee replacement motion during a step-up task,” J Biomech Eng 123(6), 599–606 (2001).CrossRefGoogle ScholarPubMed
Pfeiffer, F. and Glocker, C.. Multibody Dynamics with Unilateral Constraints (John Wiley and Sons, New York, 1996).CrossRefGoogle Scholar
Glocker, C. H. and Pfeiffer, F., “Dynamical systems with unilateral contacts,” Nonlinear Dynam 3(4), 245–259 (1992).CrossRefGoogle Scholar
Leine, R. I., Van Campen, D. H. and Glocker, C. H., “Nonlinear dynamics and modeling of various wooden toys with impact and friction,” J Vib Control 9(1-2), 25–78 (2003).CrossRefGoogle Scholar
Klisch, T., “Contact mechanics in multibody dynamics,” Mech Mach Theory 34(5), 665–675 (1999).CrossRefGoogle Scholar
Ravn, P., “A continuous analysis method for planar multibody systems with joint clearance,” Multibody Syst Dyn 2(1), 1–24 (1998).CrossRefGoogle Scholar
Peng, P., Di, C., Qian, L. and Chen, G., “Parameter identification and experimental investigation of sphere-plane contact impact dynamics”2,” Exp Techniques 41(5), 547–555 (2017).CrossRefGoogle Scholar
Chen, S. and Zhang, Z., “Modification of friction for straightforward implementation of friction law,” Multibody Syst Dyn 48(2), 239–257 (2020).CrossRefGoogle Scholar
Qian, Z., Zhang, D. and Jin, C., “A regularized approach for frictional impact dynamics of flexible multi-link manipulator arms considering the dynamic stiffening effect,” Multibody Syst Dyn 43(3), 229–255 (2018).CrossRefGoogle Scholar
Marques, F., Woliński, Łukasz, Wojtyra, M., Flores, P. and Lankarani, H. M., “An investigation of a novel LuGre-based friction force model,” Mech Mach Theory 166, 104493 (2021).CrossRefGoogle Scholar
Verscheure, D., Sharf, I., Bruyninckx, H., Swevers, J. and De Schutter, J., “Identification of contact parameters from stiff multi-point contact robotic operations,” Int J Rob Res 29(4), 367–385 (2010).CrossRefGoogle Scholar
Roy, A. and Carretero, J. A., “A damping term based on material properties for the volume-based contact dynamics model,” Int J Nonlin Mech 47(3), 103–112 (2012).CrossRefGoogle Scholar
Pfeiffer, F. and Glocker, C., “Contacts in multibody systems,” J Appl Math Mech 64(5), 773–782 (2000).CrossRefGoogle Scholar
Pfeiffer, F., “On non-smooth multibody dynamics,” Proceed Inst Mech Eng Part K: J Multi-body Dyn 226(2), 147–177 (2012).Google Scholar
Kwak, B. M., “Complementarity problem formulation of three-dimensional frictional contact,” J Appl Mech 58(1), 134–140 (1991).CrossRefGoogle Scholar
Pang, J.-S. and Trinkle, J. C., “Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction,” Math Program 73(2), 199–226 (1996).CrossRefGoogle Scholar
Pfeiffer, F., “The idea of complementarity in multibody dynamics,” Arch Appl Mech 72(11), 807–816 (2003).CrossRefGoogle Scholar
Signorini, A., Sopra alcune questioni di elastostatica, (Atti della società italiana per il progresso delle scienze, (1993).Google Scholar
Trinkle, J. C., Tzitzouris, J. A. and Pang, J. S., “Dynamic multi-rigid-body systems with concurrent distributed contacts,” Philo Trans: Math, Phys Eng Sci 359(1789), 2575–2593 (2001).CrossRefGoogle Scholar
Studer, C., “Numerics of Unilateral Contacts and Friction,” In: Modeling and Numerical Time Integration in Non-Smooth Dynamics, (Lecture Notes in Applied and Computational Mechanics. vol. 47 (Springer, Berlin, 2009).Google Scholar
Klisch, T., “Contact mechanics in multibody systems,” Multibody Syst Dyn 2(4), 335–354 (1998).CrossRefGoogle Scholar
Leine, R. I., Brogliato, B. and Nijmeijer, H., “Periodic motion and bifurcations induced by the painlevé paradox,” European J Mech - A/Solids 21(5), 869–896 (2002).CrossRefGoogle Scholar
Pfeiffer, F., “Impacts with friction: Structures, energy, measurements,” Arch Appl Mech 86(1-2), 281–301 (2016).CrossRefGoogle Scholar
Pfeiffer, F., “On the structure of frictional impacts,” Acta Mech 229(2), 629–644 (2018).CrossRefGoogle Scholar
Kraus, P. R. and Kumar, V., “Compliant Contact Models For Rigid Body Collisions,” In: IEEE International Conference on Robotics and Automation, Albuquerque, NM, USA (1997) pp. 1382–1387.Google Scholar
Cataldo, E. and Sampaio, R., “A brief review and a new treatment for rigid bodies collision models,” J Braz Soc Mech Sci 23(1), 63–78 (2001).CrossRefGoogle Scholar
Font-Llagunes, J. M., Barjau, A., Pàmies-Vilà, R. and Kövecses, J., “Dynamic analysis of impact in swing-through crutch gait using impulsive and continuous contact models,” Multibody Syst Dyn 28(3), 257–282 (2012).CrossRefGoogle Scholar
Pazouki, A., Kwarta, M., Williams, K., Likos, W., Serban, R., Jayakumar, P. and Negrut, D., “Compliant contact versus rigid contact: A comparison in the context of granular dynamics,” Phys Rev E 96(4), 042905 (2017).CrossRefGoogle ScholarPubMed
Melanz, D., Fang, L., Jayakumar, P. and Negrut, D., “A comparison of numerical methods for solving multibody dynamics problems with frictional contact modeled via differential variational inequalities,” Comput Method Appl Mech Eng 320, 668–693 (2017).CrossRefGoogle Scholar
Khadiv, M., Moosavian, S. A. A., Yousefi-Koma, A., Sadedel, M., Ehsani-Seresht, A. and Mansouri, S., “Rigid vs compliant contact: An experimental study on biped walking,” Multibody Syst Dyn 45(4), 379–401 (2019).CrossRefGoogle Scholar
Johnson, K. L.. Contact Mechanics (Cambridge University Press, England, 1985).CrossRefGoogle Scholar
Jian, B., Hu, G. M., Fang, Z. Q., Zhou, H. J. and Xia, R., “Comparative behavior of damping terms of viscoelastic contact force models with consideration on relaxation time,” Powder Technol 356, 735–749 (2019).CrossRefGoogle Scholar
Serrancolí, G., Kinney, A. L. and Fregly, B. J., “Influence of musculoskeletal model parameter values on prediction of accurate knee contact forces during walking,” Med Eng Phys 85, 35–47 (2020).CrossRefGoogle ScholarPubMed
Wan, Q., Liu, G., Song, C., Zhou, Y., Ma, S. and Tong, R., “Study on the dynamic interaction of multiple clearance joints for flap actuation system with a modified contact force model,” J Mech Sci Technol 34, 2701–2713 (2020).CrossRefGoogle Scholar
Kildashti, K., Dong, K. and Samali, B., “An accurate geometric contact force model for super-quadric particles,” Comput Method Appl Mech Eng 360, 112774 (2020).CrossRefGoogle Scholar
Ma, J., Chen, G., Ji, L., Qian, L. and Dong, S., “A general methodology to establish the contact force model for complex contacting surfaces,” Mech Syst Signal Process 140, 106678 (2020).CrossRefGoogle Scholar
Ambrósio, J., “A general formulation for the contact between superellipsoid surfaces and nodal points,” Multibody Syst Dyn 50, 415–434 (2020).CrossRefGoogle Scholar
Brogliato, B., Kovecses, J. and Acary, V., “The contact problem in Lagrangian systems with redundant frictional bilateral and unilateral constraints and singular mass matrix. The all-sticking contacts problem,” Multibody Syst Dyn 48(2), 151–192 (2020).CrossRefGoogle Scholar
Paraskevopoulos, E., Passas, P. and Natsiavas, S., “A novel return map in non-flat configuration spaces οf multibody systems with impact,” Int J Solids Struct 202, 822–834 (2020).CrossRefGoogle Scholar
Kelly, C., Olsen, N. and Negrut, D., “Billion degree of freedom granular dynamics simulation on commodity hardware via heterogeneous data-type representation,” Multibody Syst Dyn 50(4), 355–379 (2020).CrossRefGoogle Scholar
Wang, K., Tian, Q. and Hu, H., “Nonsmooth spatial frictional contact dynamics of multibody systems,” Multibody Syst Dyn 53(1), 1–27 (2021).CrossRefGoogle Scholar
Wittenberg, J.. Dynamics of Systems of Rigid Bodies (B. G. Teubner, Stuttgart, Germany, 1977).CrossRefGoogle Scholar
Wehage, R. W.. Generalized Coordinate Partitioning in Dynamic Analysis of Mechanical Systems (PhD Dissertation) (The University of Iowa, USA, (1980).Google Scholar
Khulief, Y. A., Haug, E. J. and Shabana, A. A., Dynamic analysis of large scale mechanical systems with intermittent motion, The University of Iowa, USA, (1983). (Technical Report No. CCAD-83-10.Google Scholar
Wehage, R. A. and Haug, E. J., “Dynamic analysis of mechanical systems with intermittent motion,” J Mech Design 104(4), 778–784 (1982).CrossRefGoogle Scholar
Khulief, Y. A. and Shabana, A. A., “Dynamic analysis of constrained system of rigid and flexible bodies with intermittent motion,” J Mech Trans Automat Design 108, 38–45 (1986).CrossRefGoogle Scholar
Khulief, Y. A., “Restitution and Friction in Impact Analysis of Multibody Systems Executing Plane Motion,” In: ASME Design Engineering Technical Conference, Paper, Columbus, Ohio, 86-DET-50 (1986).Google Scholar
Batlle, J. A. and Condomines, A. B., “Rough collisions in multibody systems,” Mech Mach Theory 26(6), 565–577 (1991).Google Scholar
Lankarani, H. M. and Nikravesh, P. E., “Canonical impulse-momentum equations for impact analysis of multibody systems,” J Mech Design 114(1), 180–186 (1992).CrossRefGoogle Scholar
Haug, E. J., Wu, S. C. and Yang, S. M., “Dynamics of mechanical systems with coulomb friction, stiction, impact and constraint addition-deletion – I theory,” Mech Mach Theory 21(5), 401–406 (1986).CrossRefGoogle Scholar
Wang, Y.-T. and Kumar, V., “Simulation of mechanical systems with multiple frictional contacts,” J Mech Design 116(2), 571–580 (1994).CrossRefGoogle Scholar
Anitescu, M., Cremer, J. F. and Potra, F. A., “Formulating three-dimensional contact dynamics problems,” Mech Struct Mach 24(4), 405–437 (1996).CrossRefGoogle Scholar
Ghafoor, A., Dai, J. S. and Duffy, J., “Stiffness modelling of the soft-finger contact in robotic grasping,” J Mech Design 126(4), 646–656 (2004).CrossRefGoogle Scholar
Cui, L., Sun, J. and Dai, J. S., “In-hand forward and inverse kinematics with rolling contact,” Robotica 35(12), 2381–2399 (2017).CrossRefGoogle Scholar
Dong, H., Qiu, C., Prasad, D. K., Pan, Y., Dai, J. S. and Chen, I. M., “Enabling grasp action: Generalized quality evaluation of grasp stability via contact stiffness from contact mechanics insight,” Mech Mach Theory 134, 625–644 (2019).CrossRefGoogle Scholar
Liu, X.-F., Cai, G.-P., Wang, M.-M. and Chen, W.-J., “Contact control for grasping a non-cooperative satellite by a space robot,” Multibody Syst Dyn 50(2), 119–141 (2020).CrossRefGoogle Scholar
Hao, K. A. and Nichols, J. A., “Simulating finger-tip force using two common contact models: Hunt-crossley and elastic foundation,” J Biomech 119, 110334 (2021).CrossRefGoogle ScholarPubMed
Marhefka, D. W. and Orin, D. E., “A compliant contact model with nonlinear damping for simulation of robotic systems,” IEEE Trans Syst, Man, Cyber - Part A: Syst Humans 29(6), 566–572 (1999).CrossRefGoogle Scholar
Bi, S.-S., Zhou, X.-D. and Marghitu, D. B., “Impact modelling and analysis of the compliant legged robots,” Proceed Inst Mech Eng, Part K: J Multi-body Dyn 226(2), 85–94 (2012).Google Scholar
Chen, Z., Gao, F., Sun, Q., Tian, Y., Liu, J. and Zhao, Y., “Ball-on-plate motion planning for six-parallel-legged robots walking on irregular terrains using pure haptic information,” Mech Mach Theory 141, 136–150 (2019).CrossRefGoogle Scholar
Liu, Y. and Ben-Tzvi, P., “Dynamic modeling, analysis, and comparative study of a quadruped with bio-inspired robotic tails,” Multibody Syst Dyn 51(2), 195–219 (2021).CrossRefGoogle Scholar
Ambrósio, J. and Verissimo, P., “Improved bushing models for general multibody systems and vehicle dynamics,” Multibody Syst Dyn 22(4), 341–365 (2009).CrossRefGoogle Scholar
Tay, Y. Y., Bhonge, P. S. and Lankarani, H. M., “Crash simulations of aircraft fuselage section in water impact and comparison with solid surface impact,” Int J Crashworthines 20(5), 464–482 (2015).CrossRefGoogle Scholar
Guida, M., Manzoni, A., Zuppardi, A., Caputo, F., Marulo, F. and De Luca, A., “Development of a multibody system for crashworthiness certification of aircraft seat,” Multibody Syst Dyn 44(2), 191–221 (2018).CrossRefGoogle Scholar
Tay, Y. Y., Flores, P. and Lankarani, H., “Crashworthiness analysis of an aircraft fuselage section with an auxiliary fuel tank using a hybrid multibody/plastic hinge approach,” Int J Crashworthines 25(1), 95–105 (2020).CrossRefGoogle Scholar
Shabana, A. A., Zaazaa, K. E., Escalona, J. L. and Sany, J. R., “Development of elastic force model for wheel/rail contact problems,” J Sound Vib 269(1-2), 295–325 (2004).CrossRefGoogle Scholar
Malvezzi, M., Meli, E., Falomi, S. and Rindi, A., “Determination of wheel-rail contact points with semianalytic methods,” Multibody Syst Dyn 20(4), 327–358 (2008).CrossRefGoogle Scholar
Piotrowski, J., Liu, B. and Bruni, S., “The Kalker book of tables for non-hertzian contact of wheel and rail,” Vehicle Syst Dyn 55(6), 875–901 (2017).CrossRefGoogle Scholar
Song, Y., Antunes, P., Pombo, J. and Liu, Z., “A methodology to study high-speed pantograph-catenary interaction with realistic contact wire irregularities,” Mech Mach Theory 152, 103940 (2020).CrossRefGoogle Scholar
Magalhães, H., Marques, F., Liu, B., Antunes, P., Pombo, J., Flores, P., Ambrósio, J., Piotrowski, J. and Bruni, S., “Implementation of a non-hertzian contact model for railway dynamic application,” Multibody Syst Dyn 48(1), 41–78 (2020).CrossRefGoogle Scholar
Vollebregt, E., “Detailed wheel/rail geometry processing with the conformal contact approach,” Multibody Syst Dyn 52(2), 135–167 (2021).CrossRefGoogle Scholar
Modenese, L. and Phillips, A. T. M., “Prediction of hip contact forces and muscle activations during walking at different speeds,” Multibody Syst Dyn 28(1-2), 157–168 (2012).CrossRefGoogle Scholar
Gerus, P., Sartori, M., Besier, T. F., Fregly, B. J., Delp, S. L., Banks, S. A., Pandy, M. G., D’Lima, D. D. and Lloyd, D. G., “Subject-specific knee joint geometry improves predictions of medial tibiofemoral contact forces,” J Biomech 46(16), 2778–2786 (2013).CrossRefGoogle ScholarPubMed
Askari, E., Flores, P., Dabirrahmani, D. and Appleyard, R., “Nonlinear vibration and dynamics of ceramic on ceramic artificial hip joints: A spatial multibody modelling,” Nonlinear Dynam 76(2), 1365–1377 (2014).CrossRefGoogle Scholar
Askari, E., Flores, P., Dabirrahmani, D. and Appleyard, R., “A computational analysis of squeaking hip prostheses,” J Comput Nonlin Dyn 10(2), 024502 (2015).CrossRefGoogle Scholar
Shourijeh, M. S. and McPhee, J., “Foot-ground contact modeling within human gait simulations: From Kelvin-Voigt to hyper-volumetric models,” Multibody Syst Dyn 35(4), 393–407 (2015).CrossRefGoogle Scholar
Ezati, M., Brown, P., Ghannadi, B. and McPhee, J., “Comparison of direct collocation optimal control to trajectory optimization for parameter identification of an ellipsoidal foot-ground contact model,” Multibody Syst Dyn 49(1), 71–93 (2020).CrossRefGoogle Scholar
Mouzo, F., Michaud, F., Lugris, U. and Cuadrado, J., “Leg-orthosis contact force estimation from gait analysis,” Mech Mach Theory 148, 103800 (2020).CrossRefGoogle Scholar
Schwab, A. L., Meijaard, J. P. and Meijers, P., “A comparison of revolute joint clearance models in the dynamic analysis of rigid and elastic mechanical systems,” Mech Mach Theory 37(9), 895–913 (2002).CrossRefGoogle Scholar
Liu, C., Zhang, K. and Yang, L., “Compliance contact model of cylindrical joints with clearances,” Act Mech Sinica/Lixue Xuebao 21(5), 451–458 (2005).CrossRefGoogle Scholar
Marques, F., Isaac, F., Dourado, N., Souto, A. P., Flores, P. and Lankarani, H. M., “A study on the dynamics of spatial mechanisms with frictional spherical clearance joints,” J Comput Nonlin Dyn 12(5), 051013 (2017).CrossRefGoogle Scholar
Akhadkar, N., Acary, V. and Brogliato, B., “Multibody systems with 3D revolute joints with clearances: An industrial case study with an experimental validation,” Multibody Syst Dyn 42(3), 249–282 (2018).CrossRefGoogle Scholar
Ambrósio, J. and Pombo, J., “A unified formulation for mechanical joints with and without clearances/bushings and/or stops in the framework of multibody systems,” Multibody Syst Dyn 42(3), 317–345 (2018).CrossRefGoogle Scholar
Isaac, F., Marques, F., Dourado, N. and Flores, P., “A finite element model of a 3D dry revolute joint incorporated in a multibody dynamic analysis,” Multibody Syst Dyn 45(3), 293–313 (2019).CrossRefGoogle Scholar
Cirelli, M., Valentini, P. P. and Pennestrì, E., “A study of the non-linear dynamic response of spur gear using a multibody contact based model with flexible teeth,” J Sound Vib 445, 148–167 (2019).CrossRefGoogle Scholar
Hu, X. H., Cao, L., Luo, Y., Chen, A., Zhang, E. and Zhang, W. J., “A novel methodology for comprehensive modeling of the kinetic behavior of steerable catheters,” IEEE/ASME Trans Mech 24(4), 1785–1797 (2019).CrossRefGoogle Scholar
Ohno, M. and Takeda, Y., “Design of target trajectories for the detection of joint clearances in parallel robot based on the actuation torque measurement,” Mech Mach Theory 155, 104081 (2021).CrossRefGoogle Scholar
Kuwabara, G. and Kono, K., “Restitution coefficient in a collision between two spheres,” Japanese J Appl Phys 26(8), 1230–1233 (1987).CrossRefGoogle Scholar
Renouf, M., Dubois, F. and Alart, P., “A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media,” J Comput Appl Math 168(1-2), 375–382 (2004).CrossRefGoogle Scholar
Tasora, A., Anitescu, M., Negrini, S. and Negrut, D., “A compliant visco-plastic particle contact model based on differential variational inequalities,” Int J Nonlin Mech 53, 2–12 (2013).CrossRefGoogle Scholar
Goldobin, D. S., Susloparov, E. A., Pimenova, A. V. and Brilliantov, N. V., “Collision of viscoelastic bodies: Rigorous derivation of dissipative force,” Eur Phys J E 38(6), 55 (2015).CrossRefGoogle ScholarPubMed
Melanz, D., Jayakumar, P. and Negrut, D., “Experimental validation of a differential variational inequality-based approach for handling friction and contact in vehicle/granular-terrain interaction,” J Terramechanics 65, 1–13 (2016).CrossRefGoogle Scholar
Turner, J. D., “On the simulation of discontinuous functions,” J Appl Mech 68(5), 751–757 (2001).CrossRefGoogle Scholar
Leine, R. I., Glocker, C. and Van Campen, D. H., “Nonlinear dynamics of the woodpecker toy,” In: Proceedings of the ASME Design Engineering Technical Conference, 6C, (2001) pp. 2629–2637.Google Scholar
Slavič, J. and Boltežar, M., “Non-linearity and non-smoothness in multi-body dynamics: Application to woodpecker toy,” Proceed Inst Mech Eng Part C: J Mech Eng Sci 220(3), 285–296 (2006).CrossRefGoogle Scholar
Studer, C., Leine, R. I. and Glocker, C., “Step size adjustment and extrapolation for time-stepping schemes in non-smooth dynamics,” Int J Numer Meth Eng 76(11), 1747–1781 (2008).CrossRefGoogle Scholar
Flores, P., Contact-impact analysis in multibody systems based on the nonsmooth dynamics approach, ETH-Zurich Switzerland, (2009). (Post-Doctoral Report.Google Scholar
Zhang, K. Y. and Xu, Y., “Passive movement modeling of a woodpecker robot,” Appl Mech Mater 415, 23–25 (2013).CrossRefGoogle Scholar
Steinkamp, P., “A statically unstable passive hopper: Design evolution,” J Mech Rob 9(1), 011016–1 (2017).CrossRefGoogle Scholar
Corral, E., García, M. J. G., Castejon, C., Meneses, J. and Gismeros, R., “Dynamic modeling of the dissipative contact and friction forces of a passive biped-walking robot,” Appl Sci 10(7), 2342 (2020).CrossRefGoogle Scholar
Galvez, J., Cosimo, A., Cavalieri, F. J., Cardona, A. and Brüls, O., “A general purpose formulation for nonsmooth dynamics including large rotations: Application to the woodpecker toy,” J Comput Nonlin Dyn 16(3), 031001 (2021).Google Scholar
Jankowski, R., “Non-linear viscoelastic modelling of earthquake-induced structural pounding,” Earthquake Eng Struc Dyn 34(6), 595–611 (2005).CrossRefGoogle Scholar
Muthukumar, S. and DesRoches, R., “A hertz contact model with non-linear damping for pounding simulation,” Earthquake Eng Struc Dyn 35(7), 811–828 (2006).CrossRefGoogle Scholar
DeJong, M. J., De Lorenzis, L., Adams, S. and Ochsendorf, J. A., “Rocking stability of masonry arches in seismic regions,” Earthq Spectra 24(4), 847–865 (2008).CrossRefGoogle Scholar
Mahmoud, S., Chen, X. and Jankowski, R., “Structural pounding models with hertz spring and nonlinear damper,” J Appl Sci 8(10), 1850–1858 (2008).CrossRefGoogle Scholar
Ye, K., Li, L. and Zhu, H., “A modified Kelvin impact model for pounding simulation of base-isolated building with adjacent structures,” Earthq Eng Eng Vib 8(3), 433–446 (2009).CrossRefGoogle Scholar
Ye, K., Li, L. and Zhu, H., “A note on the hertz contact model with nonlinear damping for pounding simulation,” Earthquake Eng Struc Dyn 38(9), 1135–1142 (2009).CrossRefGoogle Scholar
Ajibose, O. K., Wiercigroch, M., Pavlovskaia, E. and Akisanya, A. R., “Global and local dynamics of drifting oscillator for different contact force models,” Int J Nonlin Mech 45(9), 850–858 (2010).CrossRefGoogle Scholar
Banerjee, A., Chanda, A. and Das, R., “Seismic analysis of a curved bridge considering deck-abutment pounding interaction: An analytical investigation on the post-impact response,” Earthquake Eng Struc Dyn 46(2), 267–290 (2017).CrossRefGoogle Scholar
Shi, Z. and Dimitrakopoulos, E. G., “Nonsmooth dynamics prediction of measured bridge response involving deck-abutment pounding,” Earthquake Eng Struc Dyn 46(9), 1431–1452 (2017).CrossRefGoogle Scholar
Beatini, V., Royer-Carfagni, G. and Tasora, A., “A non-smooth-contact-dynamics analysis of Brunelleschi’s cupola: An octagonal vault or a circular dome?,” Meccanica 54(3), 525–547 (2019).CrossRefGoogle Scholar
Avanzini, F., Serafin, S. and Rocchesso, D., “Interactive simulation of rigid body interaction with friction-induced sound generation,” IEEE Trans Speech Audi Pro 13(5), 1073–1080 (2005).CrossRefGoogle Scholar
Papetti, S., Avanzini, F. and Rocchesso, D., “Numerical methods for a nonlinear impact model: A comparative study with closed-form corrections,” IEEE Trans Audi, Speech Lang Pro 19(7), 2146–2158 (2011).CrossRefGoogle Scholar
Masoudi, R., Birkett, S. and McPhee, J., “A mechanistic multibody model for simulating the dynamics of a vertical piano action,” J Comput Nonlin Dyn 9(3), 061004 (2014).Google Scholar
Masoudi, R. and Birkett, S., “Experimental validation of a mechanistic multibody model of a vertical piano action,” J Comput Nonlin Dyn 10(6), 061004 (2015).CrossRefGoogle Scholar
Maunsbach, M. and Serafin, S., “Non-linear contact sound synthesis for real-time audio-visual applications using modal textures”,” In: Proceedings of the Sound and Music Computing Conferences, (2019) pp. 431–436.Google Scholar
Timmermansa, S., Ceulemans, A.-E. and Fisette, P., “Upright and grand piano actions dynamic performances assessments using a multibody approach,” Mech Mach Theory 160, 104296 (2021).CrossRefGoogle Scholar
Dintwa, E., Van Zeebroeck, M., Tijskens, E. and Ramon, H., “Determination of parameters of a tangential contact force model for viscoelastic spheroids (fruits) using a rheometer device,” Biosyst Eng 91(3), 321–327 (2005).CrossRefGoogle Scholar
Kruggel-Emden, H., Wirtz, S. and Scherer, V., “A study on tangential force laws applicable to the discrete element method (DEM) for materials with viscoelastic or plastic behavior,” Chem Eng Sci 63(6), 1523–1541 (2008).CrossRefGoogle Scholar
Ahmadi, E., Ghassemzadeh, H. R., Sadeghi, M., Moghaddam, M. and Neshat, S. Z., “The effect of impact and fruit properties on the bruising of peach,” J Food Eng 97(1), 110–117 (2010).CrossRefGoogle Scholar
Barikloo, H. and Ahmadi, E., “Dynamic properties of golden delicious and red delicious apple under normal contact force models,” J Texture Stud 44(6), 409–417 (2013).CrossRefGoogle Scholar
Scheffler, O. C., Coetzee, C. J. and Opara, U. L., “A discrete element model (DEM) for predicting apple damage during handling,” Biosyst Eng 172, 29–48 (2018).CrossRefGoogle Scholar
Zhang, S., Wang, W., Wang, Y., Fu, H. and Yang, Z., “Improved prediction of litchi impact characteristics with an energy dissipation model,” Postharvest Biol Tec 176, 111508 (2021).CrossRefGoogle Scholar
Glocker, C.. Set-Valued Force Laws: Dynamics of Non-Smooth Systems, (Lecture Notes in Applied Mechanics 1 (Springer-Verlag, Berlin, 2001).CrossRefGoogle Scholar
Leine, R. and Nijmeijer, H., Dynamics and bifurcations of non-smooth mechanical systems (Springer, Berlin, 2004).CrossRefGoogle Scholar
Acary, V. and Brogliato, B., “Numerical Methods for Nonsmooth Dynamical Systems, Applications in Mechanics and Electronics,” In: Lecture Notes in Applied and Computational Mechanics. vol. 35 (Springer, Berlin, 2008).Google Scholar
Flores, P. and Lankarani, H. M., “Contact Force Models for Multibody Dynamics,” In Solid Mechanics and Its Applications (Springer, Berlin, 2016).CrossRefGoogle Scholar
Gilardi, G. and Sharf, I., “Literature survey of contact dynamics modelling,” Mech Mach Theory 37(10), 1213–1239 (2002).CrossRefGoogle Scholar
Seifried, R., Schiehlen, W. and Eberhard, P., “The role of the coefficient of restitution on impact problems in multi-body dynamics,” Proceed Inst Mech Engi, Part K: J Multi-body Dyn 224(3), 279–306 (2010).Google Scholar
Stewart, D. E., “Rigid-body dynamics with friction and impact,” Society Indus Appl Math 42(1), 3–39 (2000).Google Scholar
Shigley, J. E. and Mischke, C. R.. Mechanical engineering design (McGraw-Hill, New York, 1989).Google Scholar
Hertz, H., “On the contact of elastic solids,” Z Reine Angew Mathematik 92, 156–171 (1881).Google Scholar
Goldsmith, W.. Impact – The Theory and Physical Behavior of Colling Solids (Edward Around, London, England, 1960).Google Scholar
Hunt, K. H. and Crossley, F. R. E., “Coefficient of restitution interpreted as damping in vibroimpact,” J Appl Mech 42(2), 440–445 (1975).CrossRefGoogle Scholar
Ambrósio, J., “Selected challenges in realistic multibody modeling of machines and vehicles,” Iutam Bookser 33, 1–39 (2019).CrossRefGoogle Scholar
Marques, F., Magalhães, H., Pombo, J., Ambrósio, J. and Flores, P., “A three-dimensional approach for contact detection between realistic wheel and rail surfaces for improved railway dynamic analysis,” Mech Mach Theory 149, 103825 (2020).CrossRefGoogle Scholar
Liu, Q., Cheng, J., Li, D. and Wei, Q., “A hybrid contact model with experimental validation,” J Dyn Syst Measure Cont 143(9), 094501 (2021).CrossRefGoogle Scholar
Askari, E., “Mathematical models for characterizing non-hertzian contacts,” Appl Math Model 90, 432–447 (2021).CrossRefGoogle Scholar
Corral, E., Moreno, R. G., García, M. J. G. and Castejón, C., “Nonlinear phenomena of contact in multibody systems dynamics: A review,” Nonlinear Dynam 104(2), 1269–1295 (2021).CrossRefGoogle Scholar
Ahmed, S., Lankarani, H. M. and Pereira, M. F. O. S., “Frictional impact analysis in open-loop multibody mechanical systems,” J Mech Design 121(1), 119–127 (1999).CrossRefGoogle Scholar
Hutchings, I. M., “Leonardo da Vinci’s studies of friction,” Wear 360-361, 51–66 (2016).CrossRefGoogle Scholar
Amontons, G., “On the resistance originating in machines”,” In: Proceedings of the French Royal Academy of Sciences, (1699) pp. 206–222.Google Scholar
Coulomb, C. A., “Théorie des machines simples, en ayant égard au frottement de leurs parties, et a la roideur dews cordages,” Memoires de Math Phys Acad Sci 10, 161–331 (1785).Google Scholar
Threlfall, D. C., “The inclusion of coulomb friction in mechanisms programs with particular reference to DRAM,” Mech Mach Theory 13(4), 475–483 (1978).CrossRefGoogle Scholar
Bengisu, M. T. and Akay, A., “Stability of friction-induced vibrations in multi-degree-of-freedom systems,” J Sound Vib 171(4), 557–570 (1994).CrossRefGoogle Scholar
Ambrósio, J. A. C., “Impact of rigid and flexible multibody systems: Deformation description and contact model,” Virt Nonlin Multi Syst 103, 57–81 (2003).CrossRefGoogle Scholar
Dahl, P. R., “Solid friction damping in mechanical vibrations,” AIAA J 14(12), 1675–1682 (1976).CrossRefGoogle Scholar
Bo, L. C. and Pavelescu, D., “The friction-speed relation and its influence on the critical velocity of stick-slip motion,” Wear 82(3), 277–289 (1982).Google Scholar
Karnopp, D., “Computer simulation of stick-slip friction in mechanical dynamic systems,” J Dyn Syst Measure Cont 107(1), 100–103 (1985).CrossRefGoogle Scholar
de Wit, C. C., Olsson, H., Åström, K. J. and Lischinsky, P., “A new model for control of systems with friction,” IEEE Trans Autom Cont 40(3), 419–425 (1995).CrossRefGoogle Scholar
Andersson, S., Söderberg, A. and Björklund, S., “Friction models for sliding dry, boundary and mixed lubricated contacts,” Tribol Int 40(4), 580–587 (2007).CrossRefGoogle Scholar
Awrejcewicz, J., Grzelczyk, D. and Pyryev, Y., “A novel dry friction modeling and its impact on differential equations computation and Lyapunov exponents estimation,” J Vibroeng 10, 475–482 (2008).Google Scholar
Specker, T., Buchholz, M. and Dietmayer, K., “A new approach of dynamic friction modelling for simulation and observation,” IFAC Proceed Vol 47(3), 4523–4528 (2014).CrossRefGoogle Scholar
Coelho, J., Dias, B., Lopes, G., Ribeiro, F. and Flores, P., “Development and implementation of a new approach for posture control of a hexapod robot to walk in irregular terrains,” Robotica 42(3), 792–816 (2024).CrossRefGoogle Scholar
Gonçalves, F., Ribeiro, T., Ribeiro, A. F., Lopes, G. and Flores, P., “Multibody model of the human-inspired robot CHARMIE,” Multibody Syst Dyn 60(1), 93–120 (2024).CrossRefGoogle Scholar