Kinematics and Dynamics of Multibody Systems

The main goal of this research is to develop mathematical procedures, or "formulations", that automatically generate the equations of motion for complex systems of rigid and flexible bodies, given only a description of the system as input. By encoding these formulations into computer algorithms, powerful computer-aided tools for dynamic analysis are created. Applications include mechanisms, serial and parallel robots, road and rail vehicles, biomechanics, sports equipment, and satellites.  Some ongoing research challenges include the modelling of impacts, friction, and large multibody systems through a decomposition into subsystems.

By using graph-theoretic methods (GTM) to represent the system topology, very efficient and systematic formulations are obtained. A unique and powerful feature of a GTM formulation is that a user is able to select the set of coordinates in terms of which the equations of motion are automatically generated. This has both practical and pedagogical advantages over conventional formulations.

Selected Publications:

• A. Izadbakhsh, J. McPhee, and S. Birkett, Dynamic Modeling and Experimental Testing of a Piano Action Mechanism with a Flexible Hammer Shank, to appear in ASME J. Comp. Non. Dyn., v.3, 2008.
• M. Leger, and J. McPhee, Selection of Modeling Coordinates for Forward Dynamic Multibody Simulations, Multibody Syst. Dyn., v.18, 277-297, 2007.
• Y. Gonthier, J. McPhee, and C. Lange, On the Implementation of Coulomb Friction in a Volumetric-Based Model for Contact Dynamics, Proc. ASME IDETC, Las Vegas, Nevada, 10 pages, 2007.
• J. McPhee and S. Redmond, Modelling Multibody Systems with Indirect Coordinates, Comp. Meth. Appl. Mech. Eng., v.195, 6942-6957, 2006.
• J. McPhee, Unified Modelling Theories for the Dynamics of Multidisciplinary Multibody Systems, to appear in Advances in Computational Multibody Systems, J. Ambrosio, ed., Springer-Verlag, 2005, pp.129-158.
  
• C. Schmitke and J. McPhee, Modelling Mechatronic Multibody Systems using Symbolic Subsystem Models, submitted to Multibody System Dynamics, 2003.
  
• J. McPhee, Virtual Prototyping of Multibody Systems with Linear Graph Theory and Symbolic Computing, in Virtual Nonlinear Multibody Systems, W. Schiehlen and M. Valasek, eds., Kluwer Academic, 2003, pp.37-56.
  
• J. McPhee, Two Different Methods for Simulating the Motion of Variable-Mass Multibody Systems, in Advanced Multibody System Dynamics: Simulation and Software Tools, W. Schiehlen, ed., Kluwer Academic, 1993, pp.385-390.
  
• J. McPhee, C. Schmitke, and S. Redmond, Dynamic Modelling of Mechatronic Multibody Systems with Symbolic Computing and Linear Graph Theory, Mathematical and Computer Modelling of Dynamical Systems, vol.10, no.1, 2004, pp.1-23.
  
• Y. Gonthier, J. McPhee, J.-C. Piedboeuf, and C. Lange, A Regularized Contact Model with Asymmetric Damping and Dwell-Time Dependent Friction, Multibody System Dynamics, vol.11, no.3, 2004, pp.209-233.
  
• C. Schmitke and J. McPhee, Effective use of Subsystem Models in Multibody and Mechatronic System Dynamics, International Journal for Multiscale Computational Engineering, vol.1, no.2, 2003, pp.139-159.
  
• E. Zahariev and J. McPhee, Stabilization of Constraints of Multibody System Dynamics, Mechanics of Structures and Machines, vol.31, no.1, 2003, pp.25-55.
  
• Y. He and J. McPhee, Design Optimization of Rail Vehicles with Passive and Active Suspensions: A Combined Approach using Genetic Algorithms and Multibody Dynamics, Vehicle System Dynamics, vol.37 Supplement, 2003, pp.397-408.
  
• S. Redmond and J. McPhee, Modelling Multibody Systems with Indirect Coordinates, submitted to Computer Methods in Applied Mechanics and Engineering, 2004.
  
• J. McPhee, Graph-Theoretic Modelling of Multibody Systems , invited lecture for NATO ASI Workshop on Virtual Nonlinear Multibody Systems , Prague, Czech Republic, June 2002.
  
• C. Schmitke and J. McPhee, Effective Use of Subsystem Models in Multibody and Mechatronic System Dynamics, submitted to International Journal of Computational Civil and Structural Engineering, 2002.
  
• E. Zahariev and J. McPhee, Dynamics of Multibody Systems with Multiple Constraints, submitted to Mathematical and Computer Modelling of Dynamical Systems, 2002.
  
• J. McPhee, P. Shi, and J.-C. Piedboeuf, Dynamics of Multibody Systems using Virtual Work and Symbolic Programming , Mathematical and Computer Modelling of Dynamical Systems , vol.8, no.2, 2002, pp.137-156.
  
• Y. Gonthier, J. McPhee, J.-C. Piedboeuf, and C. Lange, A Regularized Contact Model with Asymmetric Damping and Dwell-Time Dependent Friction, submitted to Multibody System Dynamics, 2002.
  
• E. Zahariev and J. McPhee, Stabilization of Constraints of Multibody System Dynamics, to appear in Mechanics of Structures and Machines, 2002.
  
• T. Geike and J. McPhee, On the Automatic Generation of Inverse Dynamic Solutions for Parallel Manipulators, Proceedings of Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators , Quebec City, Canada, October 2002.
  
• P. Shi, J. McPhee, and G. Heppler, A Deformation Field for Euler-Bernoulli Beams with Application to Flexible Multibody Dynamics, Multibody System Dynamics, vol.5, pp.79-104, 2001.
  
• J. McPhee, A Unified Formulation of Multibody Kinematic Equations in Terms of Absolute, Joint, and Indirect Coordinates , CD-ROM Proceedings of the ASME Design Engineering Technical Conference, Pittsburgh U.S.A., September 2001.
  
• P. Shi and J. McPhee, Dynamics of Flexible Multibody Systems using Virtual Work and Linear Graph Theory, Multibody System Dynamics, vol.4, pp.355-381, 2000.
  
• J. McPhee and P. Shi, Inverse Dynamics of Multibody Systems using Virtual Work and Graph Theory, Proceedings of 10th World Congress on the Theory of Machines and Mechanisms, Oulu, Finland, 20-24 June, 1999, pp.1258-1263.
  
• J.J. McPhee, Automatic Generation of Motion Equations for Planar Mechanical Systems Using the New Set of ``Branch Co-ordinates'' , Mechanism and Machine Theory , vol.33, no.6, pp.805-823, 1998.
  
• J.J. McPhee, A Unified Graph-Theoretic Approach to Formulating Multibody Dynamics Equations in Absolute or Joint Coordinates , Journal of the Franklin Institute, vol.334B, no.3, pp.431-445, 1997.
  
• J.J. McPhee, On the Use of Linear Graph Theory in Multibody System Dynamics, Nonlinear Dynamics, vol.9, pp.73-90, 1996.
  
• J.J. McPhee, M.G. Ishac, and G.C. Andrews, Wittenburg's Formulation of Multibody Dynamics Equations from a Graph-Theoretic Perspective, Mechanism and Machine Theory , vol.31, no.2, pp.201-213, 1996.
  
• J.J. McPhee, Two Different Methods for Simulating the Motion of Variable-Mass Multibody Systems, in Advanced Multibody System Dynamics: Simulation and Software Tools , edited by W. Schiehlen, Kluwer Academic, pp.385-390, 1993.
  
• J.J. McPhee and R.N. Dubey, Dynamic Analysis and Computer Simulation of Variable-Mass Multi-Rigid-Body Systems, International Journal for Numerical Methods in Engineering , vol.32, no.8, pp.1711-1725, 1991.
  
• J.J. McPhee and R.N. Dubey, Dynamics of Multibody Systems with Known Configuration Changes, Journal of Applied Mechanics, vol.58, no.1, pp.215-221, 1991.