Modeling Flexible Multi-Body Systems Within the Udwadia–Kalaba Framework, a Lumped Parameter Approach

Abstract

It is common practice within Multi-Body Dynamic (MBD) modelling to assume that individual bodies are rigid however this can be an oversimplification especially when slender bodies are present resulting in inaccurate estimations of the system's natural frequencies and overall behaviour. To address this shortfall, we extend the Udwadia-Kalaba (U-K) MBD formulation in this paper to model flexible multibody systems for purposes of exploring system natural frequencies. To model the flexibility, a lumped parameter approach is proposed, which in this work idealises a flexible beam as a series of discrete rigid elements connected by torsional springs. In the U-K formulation, a mechanical system can also be discretised into rigid elements and adapted. This is viewed as a benefit for incorporating a lumped parameter approach within the U-K formulation to model flexible multibody systems. A flexible crank-slider mechanism is introduced and modelled within the Udwadia-Kalaba formulation to capture the dynamics of flexibility through linkage compliance. The model is validated against an alternatively formulated MBD model and system natural frequencies and mode shapes numerically predicted. Results of the study show the effectiveness and potential of extending the application of the Udwadia-Kalaba modelling approach to dynamically model flexible multibody systems. Results also highlight the importance of considering flexible body modes within dynamic analysis of multibody systems, which would otherwise be overlooked under rigid body assumption models.

Advances in Flexible Robotic Manipulator Systems—Part I: Overview and Dynamics Modeling Methods

“…Sarkhel et al [73] used LPM to model a fishing-rod-like flexible manipulator, the free end of which is linked to the payload via a string, thus yielding sudden and sinusoidal loadings. Yap et al [74] used LPM to model a flexible multibody system. Khajiyeva et al [75] used LPM to model the nonlinear vibrations of flexible drill strings in a supersonic gas flow.…”