Dynamics of a rope modeled as a multi-body system with elastic joints

Abstract

A discrete model of a rope with spiral springs in joints is considered, the aim being to include transverse elasticity of the rope. Elastic characteristic of the springs is derived on the basis of simple geometrical formulas and the classical curvature-bending moment relationship for beams. Lagrange's equations of motion are presented and their complexity is discussed from the computational point of view. Numerical experiments are performed for a system with both scleronomic and rheonomic constraints. The influence of the elasticity on behaviour of the model is analyzed. Results validity is examined in terms of basic energy principles.

Targeting the user experience in the development of mobile machinery using real-time multibody simulation

“…20 In this approach, the chain is assumed to be made of n rigid components of uniform length l and mass m. These components are coupled together via rotational joints. As discussed in Fritzkowski and Kaminski, 20 the elasticity of chain in transverse direction is modelled using theory of elastic bending and basic geometric relationship between generalized coordinates. The viscoelastic behaviour of chain in longitudinal direction renders realistic sensation to the users in real-time simulation application.…”

“…The bending theory and geometrical relationships between the repeating units were selected such that visual performance chain resamples behaviour of real structure. 20 Few studies have dealt with combining the semirecursive approach, hydraulic actuators, LuGre friction and tyre models in the real-time simulation of rigid and flexible MBSs. [21][22][23][24] The real-time simulation of the pulley and chain mechanism has not yet been studied with hydraulics, contacts and tyres in the framework of MBS dynamics.…”

Real-time simulation of cable pay-out and reel-in with towed fishing gears

“…Modelling the system with natural coordinates has significant advantages compared to other coordinate choices used in multibody cable models described in the literature [15,24,34]. In the first place, the Coriolis and velocity-dependent forces term is absent from the dynamics equations and the mass matrix M is constant.…”

“…In fishing assemblies, the range of cable tensions and moderate torsion and curvature radius make these simplifications acceptable [50]. Often, simplified models discretize the cable as a sequence of segments connected by joints that allow them to rotate with respect to each other; bending stiffness can be modelled with torsion springs between bars [15]. These segments can be flexible or rigid along their longitudinal axis, or a combination of both [14].…”

“…This method neglects the axial flexibility of the cable, which can be a valid assumption for stiff cables. The rope model described in [15] is a 2D example of this second approach; only a few publications exist that use 3D multibody modelling in practical marine applications [24], especially in the context of towed fishing gears [34].…”