Dynamics of a rope as a rigid multibody system

This paper presents a new approach to the problem of determining the frequencies and mode shapes of Euler–Bernoulli tapered cantilever beams with a tip mass and a spring at the free end. The approach is based on the replacement of the flexible beam by a rigid multibody system. Beams with constant thickness and exponentially and linearly tapered width, as well as double-tapered cantilever beams are considered. The influence of the tip mass, stiffness of the spring, and taper on the frequencies of the free transverse vibrations of tapered cantilever beams are examined. Numerical examples with results confirming the convergence and accuracy of the approach are given.

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A Modular Dynamic Model for Multibody System Adapted to Interactive Simulation

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2003/vib-48311 ◽

2003 ◽

Cited By ~ 1

Author(s):

N. Seguy ◽

P. Joli ◽

Z. Q. Feng ◽

M. Pascal

Keyword(s):

Computer Aided Design ◽

Multibody System ◽

Integration Scheme ◽

Interactive Simulation ◽

Modular Model ◽

Numerical Integration Scheme ◽

Aided Design ◽

Rigid Multibody ◽

Augmented Lagrangian Formulation ◽

Made In

This paper presents a modular model of rigid multibody system using the acceleration-based augmented Lagrangian formulation. An important effort on the formulation of the governing equations has been made in order to meet the requirements for interactive simulation in computer aided design. Each body has been considered as an independent numerical component with its own numerical parameters, own mechanical parameters and own numerical integration scheme. Non-holonomic and holonomic constraints have been implemented in this formulation. This present work can be considered as an extended formulation of Bayo et al. [1] to the problem of interactive design and particular attention is paid to define the criteria of numerical stability.

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Structure Preserving Simulation of Monopedal Jumping

Archive of Mechanical Engineering ◽

10.2478/meceng-2013-0008 ◽

2013 ◽

Vol 60 (1) ◽

pp. 127-146 ◽

Cited By ~ 8

Author(s):

Michael W. Koch ◽

Sigrid Leyendecker

Keyword(s):

Optimal Control ◽

Multibody System ◽

Three Dimensional ◽

Smooth Approximation ◽

Dynamic Simulations ◽

Human Environment ◽

Structure Preserving ◽

Variational Integrator ◽

Different Types ◽

Rigid Multibody

The human environment consists of a large variety of mechanical and biomechanical systems in which different types of contact can occur. In this work, we consider a monopedal jumper modelled as a three-dimensional rigid multibody system with contact and simulate its dynamics using a structure preserving method. The applied mechanical integrator is based on a constrained version of the Lagranged’Alembert principle. The resulting variational integrator preserves the symplecticity and momentum maps of the multibody dynamics. To ensure the structure preservation and the geometric correctness, we solve the non-smooth problem including the computation of the contact configuration, time and force instead of relying on a smooth approximation of the contact problem via a penalty potential. In addition to the formulation of non-smooth problems in forward dynamic simulations, we are interested in the optimal control of the monopedal high jump. The optimal control problem is solved using a direct transcription method transforming it into a constrained optimisation problem, see [14].

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Special Coordinates Associated With Recursive Forward Dynamics Algorithm for Open Loop Rigid Multibody Systems

Journal of Applied Mechanics ◽

10.1115/1.2936923 ◽

2008 ◽

Vol 75 (5) ◽

Author(s):

Sangamesh R. Deepak ◽

Ashitava Ghosal

Keyword(s):

Multibody Systems ◽

Multibody System ◽

Equations Of Motion ◽

Special Property ◽

Open Loop ◽

Forward Dynamics ◽

Rigid Multibody Systems ◽

Two Stages ◽

Rigid Multibody ◽

General Tree

The recursive forward dynamics algorithm (RFDA) for a tree structured rigid multibody system has two stages. In the first stage, while going down the tree, certain equations are associated with each node. These equations are decoupled from the equations related to the node’s descendants. We refer them as the equations of RFDA of the node and the current paper derives them in a new way. In the new derivation, associated with each node, we recursively obtain the coordinates, which describe the system consisting of the node and all its descendants. The special property of these coordinates is that a portion of the equations of motion with respect to these coordinates is actually the equations of RFDA associated with the node. We first show the derivation for a two noded system and then extend to a general tree structure. Two examples are used to illustrate the derivation. While the derivation conclusively shows that equations of RFDA are part of equations of motion, it most importantly gives the associated coordinates and the left out portion of the equations of motion. These are significant insights into the RFDA.

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