An Efficient Method for Simulation of 3D Multi-Body Dynamic Problems Using Maple and Simulink Packages

2011 ◽  
Author(s):  
Kourosh H. Shirazi ◽  
Behrooz Attaran ◽  
Reza Zaeri
Keyword(s):  
Efficient Method ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
State Variables ◽  
Dynamic Problems ◽  
Algebraic Form ◽  
Graphical Environment ◽  
Time Accuracy ◽  
Multi Body ◽  
Body Dynamic

In this paper, an efficient method is proposed for modelling and simulation of multi-body dynamic problems. The method employs symbolic computational abilities of Maple as well as graphical environment of Matlab-Simulink to obtain and solve the equations of motion of a multi-body system accurately and rapidly. Considering a typical multi-body dynamical system the governing equations of system including second order equations of motion, first order nonholonomic and holonomic algebraic constraint equations are derived in Maple software. The state variables of the system are defined based on the systems degrees of freedom or generalized velocities. Converting the system’s equations to an algebraic form and combining them together by using a few Maple commands, the simplest form of the system’s equations of motion are obtained in the canonical standard state space form. This form is suitable when an explicit numerical method of integration is used. Then using a few toolboxes of Simulink, the equations are solved and can be studied. To procedural illustration of the method a lateral vehicle dynamic problem having thirty equations is considered. Beside the present method, Maple as well as Matlab is used to solve the problem. The results show the distinction of the method from the points of execution CPU time, accuracy and longer simulation. This method is suitable when investigation of long term behavior of multi-body dynamical systems is needed.

Development of a Robust Observer for Constrained Nonlinear Systems

2007 ◽  
Author(s):  
G. A. Kfoury ◽  
N. G. Chalhoub
Keyword(s):  
Combustion Engine ◽  
General Procedure ◽  
Equations Of Motion ◽  
The State ◽  
Nonlinear Observer ◽  
State Variables ◽  
Connecting Rod ◽  
Algebraic Form ◽  
Highly Nonlinear ◽  
Multi Body

The equations of motion for a constrained multi-body system are usually governed by a set of highly nonlinear differential-algebraic (D-A) equations. For nonlinear complex systems, the substitution method cannot be implemented to eliminate the superfluous coordinates. Thus, the differential-algebraic form of the equations of motion has to be retained. For control purposes, the state variables of the system should be available for the computation of the control signals. The current study presents a general procedure for developing a robust nonlinear observer capable of yielding accurate estimates of the state variables for a complex system whose dynamics are governed by a set of D-A equations. To assess the viability of the proposed approach, the multi-body dynamics of a piston/connecting-rod/crankshaft mechanism for a single cylinder internal combustion engine is considered in this study. The equations of motion account for both the rigid and flexible motions of the crank-slider mechanism. The simulation results demonstrate the capability of the proposed observer in accurately estimating all the state variables of the system including the superfluous ones. They illustrate the robustness of the observer to both structured and unstructured uncertainties. Moreover, they demonstrate that the nominal constraint equations are satisfied by the estimated state variables.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

Investigation of Dynamics and Vibration of a Three Unit PIG in Oil and Gas Pipelines

2008 ◽  
Author(s):  
Mohammad Durali ◽  
Amir Fazeli ◽  
Mohsen Azimi
Keyword(s):  
Oil And Gas ◽  
Equations Of Motion ◽  
Design Procedure ◽  
Pressure Waves ◽  
Gas Oil ◽  
Oil Pipeline ◽  
Under Construction ◽  
Multi Body ◽  
Dynamics And Vibration ◽  
Body Dynamic

In this paper, the transient motion of a three unit intelligent Pipe Inspection Gauge (PIG) while moving across anomalies and bends inside gas/oil pipeline has been investigated. The pipeline fluid has been considered as isothermal and compressible. In addition, the pipeline itself has also been considered to be flexible. The fluid continuity and momentum equations along with the 3D multi body dynamic equations of motion of the pig comprise a system of coupled dynamic differential equations which have been solved numerically. Pig’s position and velocity profiles as well as upstream and downstream fluid’s pressure waves are presented as simulation results which provide a better understanding of the complex behavior of pig motion through pipelines. This study has been conducted as a part of the design procedure for the Pig which is currently under construction.

A Unified Framework for Dynamics and Lyapunov Stability of Holonomically Constrained Rigid Bodies

2005 ◽  
Vol 9 (4) ◽  
pp. 387-394 ◽  
Author(s):  
Khoder Melhem ◽  
◽  
Zhaoheng Liu ◽  
Antonio Loría ◽  
◽  
...  
Keyword(s):  
System Dynamics ◽  
Lyapunov Stability ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Minimal Realization ◽  
State Variables ◽  
Unified Framework ◽  
Constrained System ◽  
And Control

A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a nonminimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between the elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantages coming with this model is that we can use it to demonstrate that Lyapunov stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot.

Modeling and Simulation of Motorcycle Ride Comfort Based on Bump Road

2010 ◽  
Vol 139-141 ◽  
pp. 2643-2647 ◽  
Author(s):  
Dong Mei Yuan ◽  
Xiao Mei Zheng ◽  
Ying Yang
Keyword(s):  
Degrees Of Freedom ◽  
Ride Comfort ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Vertical Displacement ◽  
Dynamics Model ◽  
Body Dynamics ◽  
Space Formulation ◽  
Simulation Results ◽  
Multi Body

Through analyzing the motion when motorcycle runs on the bump road, the 5-DOF multi-body dynamics model of motorcycle is developed, the degrees of freedom include vertical displacement of sprung mass, rotation of sprung mass, vertical displacement of driver, and vertical displacement of front and rear suspension under sprung mass. According to Lagrange Equation, the differential equations of motion and state-space formulation are derived. Then bump road is simulated by triangle bump, and input displacement is programmed by MATLAB. With the input of bump road, motorcycle ride comfort is simulated, and the simulation results are verified by experiment results combined with two channels tire-coupling road simulator. It indicates that the simulation results and experiment results match well; the 5-DOF model has guidance for development of motorcycle ride comfort.

Study on Lateral Stability of Vehicle-Trailer System Based on Multi-Body Dynamic Simulation

2013 ◽  
Vol 765-767 ◽  
pp. 345-350
Author(s):  
Ai Jun Ren ◽  
Zhi Cheng Wu ◽  
Jie Bao
Keyword(s):  
Dynamic Model ◽  
Critical Velocity ◽  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Damping Ratio ◽  
Dynamic Responses ◽  
Lateral Stability ◽  
Linear Dynamic ◽  
Multi Body ◽  
Body Dynamic

With a classical 4 degrees of freedom linear dynamic model of vehicle-trailer system in the yaw plane, preliminary study on lateral stability is carried out by means of analyzing systems damping ratio. The results show that structural parameters have important influence on lateral stability of vehicle-trailer system. Based on that study, a concept of critical velocity with zero damping ratio as an index is present. With the help of MSC.ADAMS, a multi-body dynamic model of a real vehicle-trailer system is built subsequently and the dynamic responses of vehicle-trailer system running on flat road and rough road is simulated respectively. The simulation results indicated that the characteristics of lateral stability of both of the linear dynamic model and the multi-body dynamic model running on flat road are similar. The critical velocity of multi-body dynamic model running on rough road decreases due to the disturbance from road. Since effects of road, nonlinear wheels, suspension structure and load transfer are taken into consideration, multi-body dynamic model of vehicle-trailer system running on the rough road could be more perfectly characterizing the lateral stability of vehicle-trailer system.

scholarly journals Design and Analysis of a Multi-Legged Robot with Pitch Adjustive Units

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Qiang Ruan ◽  
Jianxu Wu ◽  
Yan-an Yao
Keyword(s):  
Complex Terrain ◽  
Degrees Of Freedom ◽  
Virtual Model ◽  
Legged Robot ◽  
Dynamic Simulations ◽  
Compact Structure ◽  
Multi Body ◽  
6 Degrees Of Freedom ◽  
Body Dynamic ◽  
Pitch Adjustment

AbstractThe paper proposes a novel multi-legged robot with pitch adjustive units aiming at obstacle surmounting. With only 6 degrees of freedom, the robot with 16 mechanical legs walks steadily and surmounts the obstacles on the complex terrain. The leg unit with adjustive pitch provides a large workspace and empowers the legs to climb up obstacles in large sizes, which enhances the obstacle surmounting capability. The pitch adjustment in leg unit requires as few independent adjusting actuators as possible. Based on the kinematic analysis of the mechanical leg, the biped and quadruped leg units with adjustive pitch are analyzed and compared. The configuration of the robot is designed to obtain a compact structure and pragmatic performance. The uncertainty of the obstacle size and position in the surmounting process is taken into consideration and the parameters of the adjustments and the feasible strategies for obstacle surmounting are presented. Then the 3D virtual model and the robot prototype are built and the multi-body dynamic simulations and prototype experiments are carried out. The results from the simulations and the experiments show that the robot possesses good obstacle surmounting capabilities.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

Continuous multi-body dynamic analysis of float-over deck installation with rapid load transfer technique in open waters

2021 ◽  
Vol 224 ◽  
pp. 108729
Author(s):  
Shujie Zhao ◽  
Xun Meng ◽  
Huajun Li ◽  
Dejiang Li ◽  
Qiang Fu
Keyword(s):  
Dynamic Analysis ◽  
Load Transfer ◽  
Multi Body ◽  
Body Dynamic
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