Higher-order derivatives of rigid body dynamics with application to the dynamic balance of spatial linkages

de Jong, J. J.; Müller, A.; Herder, J.L.

doi:10.1016/j.mechmachtheory.2020.104059

Higher-order derivatives of rigid body dynamics with application to the dynamic balance of spatial linkages

Title

Higher-order derivatives of rigid body dynamics with application to the dynamic balance of spatial linkages

Author

de Jong, J. J. (University of Twente)
Müller, A. (Johannes Kepler University Linz)
Herder, J.L. (TU Delft Precision and Microsystems Engineering)

Department

Precision and Microsystems Engineering

Date

2021

Abstract

Dynamic balance eliminates the fluctuating reaction forces and moments induced by high-speed robots that would otherwise cause undesired base vibrations, noise and accuracy loss. Many balancing procedures, such as the addition of counter-rotating inertia wheels, increase the complexity and motor torques. There exist, however, a small set of closed-loop linkages that can be balanced by a specific design of the links' mass distribution, potentially leading to simpler and cost-effective solutions. Yet, the intricacy of the balance conditions hinder the extension of this set of linkages. Namely, these conditions contain complex closed-form kinematic models to express them in minimal coordinates. This paper presents an alternative approach by satisfying all higher-order derivatives of the balance conditions, thus avoiding finite closed-form kinematic models while providing a full solution for arbitrary linkages. The resulting dynamic balance conditions are linear in the inertia parameters such that a null space operation, either numeric or symbolic, yield the full design space. The concept of inertia transfer provides a graphical interpretation to retain intuition. A novel dynamically balanced 3-RSR spatially moving mechanism is presented together with known examples to illustrate the method.

Subject

Dynamic balance
Higher-order derivatives
Momentum
Multipole representation
Parallel mechanisms
Parameter-linear form
Rigid body dynamics
Screw theory

To reference this document use:

http://resolver.tudelft.nl/uuid:f9dc24fc-5660-4a34-ae0b-12cb9efd7c53

DOI

https://doi.org/10.1016/j.mechmachtheory.2020.104059

ISSN

0094-114X

Source

Mechanism and Machine Theory, 155

Part of collection

Institutional Repository