Formulation and Implementation of Nonholonomic Constraints in the Analysis of Multibody Systems Using Joint Coordinates

1996 ◽  
Author(s):  
Claus Balling
Keyword(s):  
Multibody Systems ◽  
Relative Velocity ◽  
Nonholonomic Constraint ◽  
Nonholonomic Constraints ◽  
General Purpose ◽  
Mutual Interaction ◽  
Cartesian Coordinates ◽  
Joint Coordinates ◽  
Moving Points ◽  
Two Bodies

Abstract A general formulation for analysis of spatial multibody systems subjected to nonholonomic constraints is presented. Nonholonomic constraints are usually formulated in Cartesian coordinates constraining the relative velocity or acceleration between some (fixed or moving) points on two bodies in mutual interaction or a point on one body with respect to ground. The formulation involves a specific type of nonholonomic constraint (rolling disk on a surface) in terms of joint coordinates and perform the implementation in a general purpose program.

A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations

1986 ◽  
Vol 108 (2) ◽  
pp. 176-182 ◽  
Author(s):  
S. S. Kim ◽  
M. J. Vanderploeg
Keyword(s):  
Equations Of Motion ◽  
General Purpose ◽  
Rigid Bodies ◽  
Transformation Matrix ◽  
Cartesian Coordinates ◽  
Velocity Transformation ◽  
Joint Coordinates ◽  
Relative Coordinates ◽  
General Purpose Computer ◽  
New Formulation

This paper presents a new formulation for the equations of motion of interconnected rigid bodies. This formulation initially uses Cartesian coordinates to define the position of the system, the kinematic joints between bodies, and forcing functions on and between bodies. This makes initial system definition straightforward. The equations of motion are then derived in terms of relative joint coordinates through the use of a velocity transformation matrix. The velocity transformation matrix relates relative coordinates to Cartesian coordinates. It is derived using kinematic relationships for each joint type and graph theory for identifying the system topology. By using relative coordinates, the equations of motion are efficiently integrated. Use of both Cartesian and relative coordinates produces an efficient set of equations without loss of generality. The algorithm just described is implemented in a general purpose computer program. Examples are used to demonstrate the generality and efficiency of the algorithms.

Direct Sensitivity Analysis of Multibody Systems: A Vehicle Dynamics Benchmark

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Alfonso Callejo ◽  
Daniel Dopico
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Automatic Differentiation ◽  
Time Integration ◽  
General Purpose ◽  
Contact Forces ◽  
Design Parameters ◽  
Computational Techniques ◽  
Computationally Efficient ◽  
Integration Algorithm

Algorithms for the sensitivity analysis of multibody systems are quickly maturing as computational and software resources grow. Indeed, the area has made substantial progress since the first academic methods and examples were developed. Today, sensitivity analysis tools aimed at gradient-based design optimization are required to be as computationally efficient and scalable as possible. This paper presents extensive verification of one of the most popular sensitivity analysis techniques, namely the direct differentiation method (DDM). Usage of such method is recommended when the number of design parameters relative to the number of outputs is small and when the time integration algorithm is sensitive to accumulation errors. Verification is hereby accomplished through two radically different computational techniques, namely manual differentiation and automatic differentiation, which are used to compute the necessary partial derivatives. Experiments are conducted on an 18-degree-of-freedom, 366-dependent-coordinate bus model with realistic geometry and tire contact forces, which constitutes an unusually large system within general-purpose sensitivity analysis of multibody systems. The results are in good agreement; the manual technique provides shorter runtimes, whereas the automatic differentiation technique is easier to implement. The presented results highlight the potential of manual and automatic differentiation approaches within general-purpose simulation packages, and the importance of formulation benchmarking.

scholarly journals Simulation of Multibody Systems with Nonholonomic Constraints

PAMM ◽  
2003 ◽  
Vol 2 (1) ◽  
pp. 132-133
Author(s):  
G. Kielau ◽  
P. Maißer
Keyword(s):  
Multibody Systems ◽  
Nonholonomic Constraints

Constrained Multibody Dynamics With Python: From Symbolic Equation Generation to Publication

2013 ◽  
Author(s):  
Gilbert Gede ◽  
Dale L. Peterson ◽  
Angadh S. Nanjangud ◽  
Jason K. Moore ◽  
Mont Hubbard
Keyword(s):  
Open Source ◽  
Undergraduate Students ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Academic Research ◽  
General Purpose ◽  
Engineering Software ◽  
Symbolic Equations Of Motion ◽  
High Level

Symbolic equations of motion (EOMs) for multibody systems are desirable for simulation, stability analyses, control system design, and parameter studies. Despite this, the majority of engineering software designed to analyze multibody systems are numeric in nature (or present a purely numeric user interface). To our knowledge, none of the existing software packages are 1) fully symbolic, 2) open source, and 3) implemented in a popular, general, purpose high level programming language. In response, we extended SymPy (an existing computer algebra system implemented in Python) with functionality for derivation of symbolic EOMs for constrained multibody systems with many degrees of freedom. We present the design and implementation of the software and cover the basic usage and workflow for solving and analyzing problems. The intended audience is the academic research community, graduate and advanced undergraduate students, and those in industry analyzing multibody systems. We demonstrate the software by deriving the EOMs of a N-link pendulum, show its capabilities for LATEX output, and how it integrates with other Python scientific libraries — allowing for numerical simulation, publication quality plotting, animation, and online notebooks designed for sharing results. This software fills a unique role in dynamics and is attractive to academics and industry because of its BSD open source license which permits open source or commercial use of the code.

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