scholarly journals A contribution on the modular modelling of multibody systems

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150080 ◽  
Author(s):  
Renato Maia Matarazzo Orsino ◽  
Tarcisio Antonio Hess-Coelho
Keyword(s):  
Programming Languages ◽  
Multibody Systems ◽  
General Purpose ◽  
Analytical Mechanics ◽  
Constraint Forces ◽  
Bicycle Model ◽  
Past Half Century ◽  
Modelling Methodology ◽  
Generalized Constraint ◽  
Modular Modelling

Over the past half-century, the increasing use of computational tools for mathematical modelling and simulation was responsible for significant advances in the area of Multibody System Dynamics. However, there is still a high dependence on the use of proprietary software in this area. Noticing that most of the complex multibody systems share many components and subsystems, this paper aims to propose a modular modelling methodology in which the starting points are some already known mathematical models of subsystems and the corresponding descriptions of the constraints existing among them. The proposed algorithm is based on the computation of some orthogonal complements of Jacobian matrices, derived from the constraint equations among the subsystems, leading to a minimal system of equations without requiring the use of undetermined multipliers or generalized constraint forces. Such an algorithm can be implemented using general-purpose (eventually open source) software packages or programming languages. Another remarkable advantage of this methodology stems from the fact that even when different (Classical or Analytical Mechanics) formalisms have been used in the modelling of subsystems, it is still possible to use the proposed algorithm. Well-known examples and a rederivation of the Whipple bicycle model are used to illustrate applications of this novel methodology.

Real-time MLton: A Standard ML runtime for real-time functional programs

2021 ◽  
Vol 31 ◽  
Author(s):  
BHARGAV SHIVKUMAR ◽  
JEFFREY MURPHY ◽  
LUKASZ ZIAREK
Keyword(s):  
Programming Languages ◽  
Real Time ◽  
Concurrency Control ◽  
General Purpose ◽  
Functional Languages ◽  
Control Mechanisms ◽  
Real Time Systems ◽  
Functional Programming Languages ◽  
Standard Ml ◽  
Time Systems

Abstract There is a growing interest in leveraging functional programming languages in real-time and embedded contexts. Functional languages are appealing as many are strictly typed, amenable to formal methods, have limited mutation, and have simple but powerful concurrency control mechanisms. Although there have been many recent proposals for specialized domain-specific languages for embedded and real-time systems, there has been relatively little progress on adapting more general purpose functional languages for programming embedded and real-time systems. In this paper, we present our current work on leveraging Standard ML (SML) in the embedded and real-time domains. Specifically, we detail our experiences in modifying MLton, a whole-program optimizing compiler for SML, for use in such contexts. We focus primarily on the language runtime, reworking the threading subsystem, object model, and garbage collector. We provide preliminary results over a radar-based aircraft collision detector ported to SML.

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.

On MBS Constraints and Projections

2021 ◽  
Author(s):  
Friedrich Pfeiffer
Keyword(s):  
Quadratic Form ◽  
Differential Equations ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Machine Process ◽  
Constraint Forces ◽  
Process Dynamics ◽  
Robot Tracking ◽  
Minimal Coordinates ◽  
Linear Differential

Abstract Constraints in multibody systems are usually treated by a Lagrange I - method resulting in equations of motion together with the constraint forces. Going from non-minimal coordinates to minimal ones opens the possibility to project the original equations directly to the minimal ones, thus eliminating the constraint forces. The necessary procedure is described, a general example of combined machine-process dynamics discussed and a specific example given. For a n-link robot tracking a path the equations of motion are projected onto this path resulting in quadratic form linear differential equations. They define the space of allowed motion, which is generated by a polygon-system.

MDA, Metamodeling and Transformation

2010 ◽  
pp. 34-47
Author(s):  
Liliana María Favre
Keyword(s):  
Programming Languages ◽  
General Purpose ◽  
Modeling Languages ◽  
Domain Specific Languages ◽  
Domain Specific ◽  
Underlying Principle

MDA requires the ability to understand different languages such as general purpose languages, domain specific languages, modeling languages or programming languages. An underlying principle of MDA for integrating semantically in a unified and interoperable way such languages is using metamodeling techniques.

scholarly journals Synthesis on the Acceleration Energies in the Advanced Mechanics of the Multibody Systems

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1077 ◽  
Author(s):  
Negrean ◽  
Crișan
Keyword(s):  
Multibody Systems ◽  
Driving Forces ◽  
Higher Order ◽  
Analytical Mechanics ◽  
Polynomial Functions ◽  
Control Functions ◽  
Generalized Variables ◽  
The Matrix ◽  
Matrix Exponentials ◽  
Fifth Order

The present paper’s objective is to highlight some new developments of the main author in the field of advanced dynamics of systems and higher order dynamic equations. These equations have been developed on the basis of the matrix exponentials which prove to have undeniable advantages in the matrix study of any complex mechanical system. The present paper proposes some new approaches, based on differential principles from analytical mechanics, by using some important dynamics notions, regarding the acceleration energies of the first, second and third order. This study extended the equations of the higher order, which provide the possibility of applying the initial motion conditions in the positions, velocities and accelerations of the first and second order. In order to determine the time variation laws for the generalized variables, the driving forces and acceleration energies of the higher order are applied by the time polynomial functions of the fifth order. According to inverse kinematics also named control kinematics of the robots, the applications of polynomial functions lead to the kinematic control functions of mechanical motions, especially the transitory motions. They influence the dynamic behavior of multibody systems, in which robot structures are included.

A Vector Bond Graph Method of Kineto-Static Analysis for Spatial Multibody Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1725-1729 ◽  
Author(s):  
Zhong Shuang Wang ◽  
Yang Yang Tao ◽  
Quan Yi Wen
Keyword(s):  
Static Analysis ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Graph Model ◽  
Bond Graph ◽  
Constraint Forces ◽  
Decoupling Method ◽  
Complete Form ◽  
Three Degrees Of Freedom

In order to increase the reliability and efficiency of the kineto-static analysis of complex multibody systems, the corresponding vector bond graph procedure is proposed. By the kinematic constraint condition, spatial multibody systems can be modeled by vector bond graph. For the algebraic difficulties brought by differential causality in system automatic kineto-static analysis, the effective decoupling method is proposed, thus the differential causalities in system vector bond graph model can be eliminated. In the case of considering EJS, the unified formulae of driving moment and constraint forces at joints are derived based on vector bond graph, which are easily derived on a computer in a complete form and very suitable for spatial multibody systems. As a result, the automatic kineto-static analysis of spatial multibody system on a computer is realized, its validity is illustrated by the spatial multibody system with three degrees of freedom.

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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