### Abstract

In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

Original language | English |
---|---|

Title of host publication | Interdisciplinary Applications of Kinematics - Proceedings of the International Conference |

Publisher | Kluwer Academic Publishers |

Pages | 179-197 |

Number of pages | 19 |

Volume | 26 |

ISBN (Electronic) | 9783319107226 |

DOIs | |

Publication status | Published - Jan 2015 |

Externally published | Yes |

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### Cite this

*Interdisciplinary Applications of Kinematics - Proceedings of the International Conference*(Vol. 26, pp. 179-197). Kluwer Academic Publishers. https://doi.org/10.1007/978-3-319-10723-3_19

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*Interdisciplinary Applications of Kinematics - Proceedings of the International Conference.*vol. 26, Kluwer Academic Publishers, pp. 179-197. https://doi.org/10.1007/978-3-319-10723-3_19

**On the Requirements of Interpolating Polynomials for Path Motion Constraints.** / Pombo, Joao; Ambrósio, Jorge; Antunes, Pedro; Pombo, Joaão.

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

TY - GEN

T1 - On the Requirements of Interpolating Polynomials for Path Motion Constraints

AU - Pombo, Joao

AU - Ambrósio, Jorge

AU - Antunes, Pedro

AU - Pombo, Joaão

PY - 2015/1

Y1 - 2015/1

N2 - In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

AB - In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

KW - Constraint Stabilization

KW - Constraint Violations

KW - Moving Frames

KW - Multibody Dynamics

UR - http://www.scopus.com/inward/record.url?scp=84916607975&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-10723-3_19

DO - 10.1007/978-3-319-10723-3_19

M3 - Conference contribution

AN - SCOPUS:84916607975

VL - 26

SP - 179

EP - 197

BT - Interdisciplinary Applications of Kinematics - Proceedings of the International Conference

PB - Kluwer Academic Publishers

ER -