Index-3 augmented Lagrangian formulations with projections of velocities and accelerations represent an efficient and robust method to carry out the forward-dynamics simulation of multibody systems modeled in dependent coordinates. Existing formalisms, however, were only established for holonomic systems, for which the expression of the constraints at the position-level is known. In this work, an extension of the original algorithms for nonholonomic systems is introduced. Moreover, projections of velocities and accelerations have two side effects: they modify the kinetic energy of the system and they contribute to the constraint reaction forces. Although the effects of the projections on the energy have been studied by several authors, their role in the calculation of the reaction forces has not been described so far. In this work, expressions to determine the constraint reactions from the Lagrange multipliers of the dynamic equations and the Lagrange multipliers of the velocity and acceleration projections are introduced. Simulation results show that the proposed strategy can be used to expand the capabilities of index-3 augmented Lagrangian algorithms, making them able to deal with nonholonomic constraints and provide correct reaction efforts.
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October 2014
Research-Article
Determination of Holonomic and Nonholonomic Constraint Reactions in an Index-3 Augmented Lagrangian Formulation With Velocity and Acceleration Projections
Daniel Dopico,
Daniel Dopico
1
Department of Computer Science and
Department of Mechanical Engineering,
e-mail: ddopico@udc.es
Department of Mechanical Engineering,
Virginia Tech
,2200 Kraft Drive
,Blacksburg, VA 24060
e-mail: ddopico@udc.es
1Corresponding author.
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Francisco González,
Francisco González
Department of Mechanical Engineering
and Centre for Intelligent Machines,
e-mail: franglez@cim.mcgill.ca
and Centre for Intelligent Machines,
McGill University
,817 Sherbrooke Street West
,Montréal, QC H3A 0C3
, Canada
e-mail: franglez@cim.mcgill.ca
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Javier Cuadrado,
Javier Cuadrado
Laboratorio de Ingeniería Mecánica,
e-mail: javicuad@cdf.udc.es
University of La Coruña
,Mendizábal s/n
,Ferrol 15403
, Spain
e-mail: javicuad@cdf.udc.es
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József Kövecses
József Kövecses
Department of Mechanical Engineering and Centre for Intelligent Machines,
e-mail: jozsef.kovecses@mcgill.ca
McGill University
,817 Sherbrooke Street West
,Montréal, QC H3A 0C3
, Canada
e-mail: jozsef.kovecses@mcgill.ca
Search for other works by this author on:
Daniel Dopico
Department of Computer Science and
Department of Mechanical Engineering,
e-mail: ddopico@udc.es
Department of Mechanical Engineering,
Virginia Tech
,2200 Kraft Drive
,Blacksburg, VA 24060
e-mail: ddopico@udc.es
Francisco González
Department of Mechanical Engineering
and Centre for Intelligent Machines,
e-mail: franglez@cim.mcgill.ca
and Centre for Intelligent Machines,
McGill University
,817 Sherbrooke Street West
,Montréal, QC H3A 0C3
, Canada
e-mail: franglez@cim.mcgill.ca
Javier Cuadrado
Laboratorio de Ingeniería Mecánica,
e-mail: javicuad@cdf.udc.es
University of La Coruña
,Mendizábal s/n
,Ferrol 15403
, Spain
e-mail: javicuad@cdf.udc.es
József Kövecses
Department of Mechanical Engineering and Centre for Intelligent Machines,
e-mail: jozsef.kovecses@mcgill.ca
McGill University
,817 Sherbrooke Street West
,Montréal, QC H3A 0C3
, Canada
e-mail: jozsef.kovecses@mcgill.ca
1Corresponding author.
Manuscript received July 20, 2013; final manuscript received May 9, 2014; published online July 11, 2014. Assoc. Editor: Dan Negrut.
J. Comput. Nonlinear Dynam. Oct 2014, 9(4): 041006 (9 pages)
Published Online: July 11, 2014
Article history
Received:
July 20, 2013
Revision Received:
May 9, 2014
Citation
Dopico, D., González, F., Cuadrado, J., and Kövecses, J. (July 11, 2014). "Determination of Holonomic and Nonholonomic Constraint Reactions in an Index-3 Augmented Lagrangian Formulation With Velocity and Acceleration Projections." ASME. J. Comput. Nonlinear Dynam. October 2014; 9(4): 041006. https://doi.org/10.1115/1.4027671
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