On the Requirements of Interpolating Polynomials for Path Motion Constraints

Joao Pombo, Jorge Ambrósio, Pedro Antunes, Joaão Pombo

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

12 Citations (Scopus)


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 languageEnglish
Title of host publicationInterdisciplinary Applications of Kinematics - Proceedings of the International Conference
PublisherKluwer Academic Publishers
Number of pages19
ISBN (Electronic)9783319107226
Publication statusPublished - Jan 2015
Externally publishedYes


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