### Abstract

The dynamic equations of motion for constrained multibody systems are frequently formulated using the Newton- Euler's approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. It is known that the standard resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general review of the main methods commonly used to control or eliminate the violation of the constraint equations in the context of multibody dynamics formulation is presented and discussed. Furthermore, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is also presented. The basic idea of this approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations.

Original language | English (US) |
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Title of host publication | Proceedings of the ASME Design Engineering Technical Conference |

Publisher | American Society of Mechanical Engineers |

Volume | 7 A |

ISBN (Print) | 9780791855966 |

DOIs | |

State | Published - 2013 |

Event | ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013 - Portland, OR, United States Duration: Aug 4 2013 → Aug 7 2013 |

### Other

Other | ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013 |
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Country | United States |

City | Portland, OR |

Period | 8/4/13 → 8/7/13 |

### Fingerprint

### Keywords

- Augmented Lagrangian formulation
- Baumgarte method
- Constraints violation
- Coordinate partitioning method
- Direct correction
- Multibody dynamics
- Penalty approach

### ASJC Scopus subject areas

- Mechanical Engineering
- Computer Graphics and Computer-Aided Design
- Computer Science Applications
- Modeling and Simulation

### Cite this

*Proceedings of the ASME Design Engineering Technical Conference*(Vol. 7 A). American Society of Mechanical Engineers. https://doi.org/10.1115/DETC2013-12591

**Comparison of different methods to control constraints violation in forward multibody dynamics.** / Flores, Paulo; Nikravesh, Parviz E.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the ASME Design Engineering Technical Conference.*vol. 7 A, American Society of Mechanical Engineers, ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013, Portland, OR, United States, 8/4/13. https://doi.org/10.1115/DETC2013-12591

}

TY - GEN

T1 - Comparison of different methods to control constraints violation in forward multibody dynamics

AU - Flores, Paulo

AU - Nikravesh, Parviz E

PY - 2013

Y1 - 2013

N2 - The dynamic equations of motion for constrained multibody systems are frequently formulated using the Newton- Euler's approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. It is known that the standard resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general review of the main methods commonly used to control or eliminate the violation of the constraint equations in the context of multibody dynamics formulation is presented and discussed. Furthermore, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is also presented. The basic idea of this approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations.

AB - The dynamic equations of motion for constrained multibody systems are frequently formulated using the Newton- Euler's approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. It is known that the standard resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general review of the main methods commonly used to control or eliminate the violation of the constraint equations in the context of multibody dynamics formulation is presented and discussed. Furthermore, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is also presented. The basic idea of this approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations.

KW - Augmented Lagrangian formulation

KW - Baumgarte method

KW - Constraints violation

KW - Coordinate partitioning method

KW - Direct correction

KW - Multibody dynamics

KW - Penalty approach

UR - http://www.scopus.com/inward/record.url?scp=84897015336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897015336&partnerID=8YFLogxK

U2 - 10.1115/DETC2013-12591

DO - 10.1115/DETC2013-12591

M3 - Conference contribution

AN - SCOPUS:84897015336

SN - 9780791855966

VL - 7 A

BT - Proceedings of the ASME Design Engineering Technical Conference

PB - American Society of Mechanical Engineers

ER -