scholarly journals Modular Multibody Formulation for Simulating Off-Road Tracked Vehicles

2014 ◽  
Vol 1 (2) ◽  
pp. 77 ◽  
Author(s):  
Mohamed A Omar
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Dynamic Equations ◽  
Solution Stability ◽  
Simulation Code ◽  
Tracked Vehicles ◽  
Main System ◽  
6 Degrees Of Freedom

This paper presents a formulation and procedure for incorporating the multibody dynamics analysis capability of tracked vehicles in large-scale multibody system.  The proposed self-contained modular approach could be interfaced to any exiting multibody simulation code without need to alter the existing solver architecture.  Each track is modeled as a super-component that can be treated separate from the main system.  The super-component can be efficiently used in parallel processing environment to reduce the simulation time.  In the super-component, each track-link is modeled as separate body with full 6 degrees of freedom (DoF).  To improve the solution stability and efficiency, the joints between track links are modeled as complaint connection.  The spatial algebra operator is used to express the motion quantities and develop the link’s nonlinear kinematic and dynamic equations of motion.  The super-component interacts with the main system through contact forces between the track links and the driving sprocket, the support rollers and the idlers using self-contained force modules.  Also, the super-component models the interaction with the terrain through force module that is flexible to include different track-soil models, different terrain geometries, and different soil properties.  The interaction forces are expressed in the Cartesian system, applied to the link’s equation of motion and the corresponding bodies in the main system.  For sake of completeness, this paper presents dynamic equations of motion of the links as well as the main system formulated using joint coordinates approach.

Railway Truck Response to Random Rail Irregularities

1975 ◽  
Vol 97 (3) ◽  
pp. 957-964 ◽  
Author(s):  
Neil K. Cooperrider
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Tangential Force ◽  
Contact Forces ◽  
Guidance Force ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Rail Irregularities ◽  
Frequency Domain Techniques

This paper discusses the random response of a seven degree of freedom, passenger truck model to lateral rail irregularities. Power spectral densities and root mean square levels of component displacements and contact forces are reported. The truck model used in the study allows lateral and yaw degrees of freedom for each wheelset, and lateral, yaw and roll freedoms for the truck frame. Linear creep relations are utilized for the rail-wheel contact forces. The lateral rail irregularities enter the analysis through the creep expressions. The results described in the paper were obtained using frequency domain techniques to solve the equations of motion. The reported results demonstrate that the guidance force needed when traveling over irregular rail at high speed utilizes a significant portion of the total available tangential force between wheel and rail.

Analysis of Varying Natural Frequencies and Damping Ratios of a Sample Parallel Manipulator Throughout its Workspace Using Linearized Equations of Motion

2001 ◽  
Author(s):  
Kris Kozak ◽  
Imme Ebert-Uphoff ◽  
William Singhose
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Parallel Architecture ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Dynamic Equations ◽  
Extreme Variation

Abstract This article investigates the dynamic properties of robotic manipulators of parallel architecture. In particular, the dependency of the dynamic equations on the manipulator’s configuration within the workspace is analyzed. The proposed approach is to linearize the dynamic equations locally throughout the workspace and to plot the corresponding natural frequencies and damping ratios. While the results are only applicable for small velocities of the manipulator, they present a first step towards the classification of the nonlinear dynamics of parallel manipulators. The method is applied to a sample manipulator with two degrees-of-freedom. The corresponding numerical results demonstrate the extreme variation of its natural frequencies and damping ratios throughout the workspace.

Autonomous Underwater Vehicle Control in Presence of Waves

2008 ◽  
Author(s):  
L. Moreira ◽  
C. Guedes Soares
Keyword(s):  
Degrees Of Freedom ◽  
Autonomous Underwater Vehicle ◽  
Equations Of Motion ◽  
Wave Force ◽  
Underwater Vehicle ◽  
Principle Of Superposition ◽  
Wave Disturbances ◽  
Underwater Vehicle Control ◽  
Different Depths ◽  
6 Degrees Of Freedom

In this paper, the 6 degrees of freedom equations of motion of an autonomous underwater vehicle (AUV) are described as a linear model and divided into three non-interacting (or lightly interacting) subsystems for speed control, steering and diving. In addition to the model of the AUV dynamics, the first and the second order wave force disturbances, i.e. the Froude-Kriloff and diffraction forces are introduced. Based on the principle of superposition it is possible to represent the AUV dynamics as the sum of low and high frequency motions. An algorithm of non-linear regression for the rationalization of the sub-surface sea spectrum is provided. Two different control designs, based on H2 and H∞ methodologies, were applied to the diving and course control of the vehicle considering the presence of the wave disturbances. The work is based on the slender form of the Naval Postgraduate School AUV, considering that the subsystems can be controlled by means of two single-screw propellers, a rudder, port and starboard bow planes and a stern plane. The wave effect on the corresponding motions of the underwater vehicle is analyzed and evaluated considering the AUV operating at different depths and different sea states using both controllers. The model presented here can be a useful simulation tool to predict the underwater vehicles behavior in different mission scenarios.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

A Hybrid Track Model for Studying Dynamic Track/Sprocket Contact

1999 ◽  
Author(s):  
Zheng-Dong Ma ◽  
Noel C. Perkins
Keyword(s):  
Hybrid Model ◽  
Degrees Of Freedom ◽  
Contact Region ◽  
Continuous Model ◽  
Contact Forces ◽  
Tracked Vehicles ◽  
Multibody Model ◽  
Nonlinear Contact ◽  
Track Circuit ◽  
Mining Vehicles

Abstract Tracked vehicles are propelled by the engagement of track pitches and a drive sprocket. This sprocket, referred to as a tumbler for the large tracked mining vehicles considered herein, may wear quickly under the action of the considerable contact forces that develop with the track. This paper summarizes a model of the track/tumbler seating process and the contact forces that control abrasive wear. A vehicle model is developed that employs a hybrid model for the track. This hybrid model combines a multibody model of the track within the seating region of the tumbler with a continuous model of the track elsewhere in the track circuit. The hybrid model is then employed to simulate the track/tumbler interactions and the associated nonlinear contact phenomena. This new modeling approach promotes accuracy within the track/tumbler contact region with few degrees of freedom outside this region where spatial resolution is less important.

Rigid Body dynamics and decoupled control architecture for two strongly interacting manipulators

Robotica ◽  
1991 ◽  
Vol 9 (4) ◽  
pp. 421-430 ◽  
Author(s):  
M.A. Unseren
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Position Control ◽  
Equations Of Motion ◽  
Joint Space ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Control Architecture ◽  
Reduced Order ◽  
Closed Chain

SUMMARYA rigid body dynamical model and control architecture are developed for the closed chain motion of two structurally dissimilar manipulators holding a rigid object in a three-dimensional workspace. The model is first developed in the joint space and then transformed to obtain reduced order equations of motion and a separate set of equations describing the behavior of the generalized contact forces. The problem of solving the joint space and reduced order models for the unknown variables is discussed. A new control architecture consisting of the sum of the outputs of a primary and secondary controller is suggested which, according to the model, decouples the force and position-controlled degrees of freedom during motion of the system. The proposed composite controller enables the designer to develop independent, non-interacting control laws for the force and position control of the complex closed chain system.

Computer Simulation of the Response of a Railway Vehicle Carbody

2002 ◽  
Author(s):  
M. Senthil Kumar ◽  
P. M. Jawahar
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Railway Vehicle ◽  
Lateral Stiffness ◽  
Lateral Vibration ◽  
Kutta Method ◽  
Nonlinear Mathematical Model ◽  
Rail Vehicle ◽  
Runge Kutta Method

In this paper, a nonlinear mathematical model has been constructed by deriving the equations of motion of a Rail Vehicle carbody using Newton’s law. The nonlinear formula is used to evaluate the wheel rail contact forces. The nonlinear profile of wheel and rail are taken into account. Also the lateral stiffness of the track is taken into consideration. The equations of motion are derived for (a) Carbody with conventional wheelset (b) Carbody with unconventional wheelset (independently rotating wheels). For lateral vibration, 17 degrees of freedom are considered. The degrees of freedom represent lateral and yaw movements of 4 wheelsets and lateral, yaw and roll movements of the bogie and carbody. These equations of motion are transformed into a form suitable for numerical differential equation by Runge Kutta method. In the interest of computing economy, certain approximations have been introduced for calculating the creep forces. Sample results are given for a model of a typical railway vehicle used by the Indian Railways. The lateral dynamic response of the railway vehicle carbody for both conventional and unconventional wheelset has been analysed.

Designing Efficient Trajectories for Underwater Vehicles Using Geometric Control Theory

2005 ◽  
Author(s):  
M. Chyba ◽  
T. Haberkorn
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Underwater Vehicles ◽  
Lagrangian Mechanics ◽  
The Maximum Principle ◽  
Marine Vehicles ◽  
Time Problem ◽  
Time Optimal ◽  
6 Degrees Of Freedom ◽  
Minimum Time Problem

In this paper, we consider the minimum time problem for underwater vehicles. Using Lagrangian mechanics, we write the equations of motion for marine vehicles with 6 degrees of freedom as a controlled mechanical system. We then apply the necessary conditions from the maximum principle for a trajectory to be time optimal. Using techniques from differential geometry we analyze the resuls. Finally we supplement the theoretical study with numerical simulations.

Non-Ideal System With Quadratic Nonlinearities Containing a Two-to-One Internal Resonance

2016 ◽  
Author(s):  
Rodrigo T. Rocha ◽  
Jose M. Balthazar ◽  
D. Dane Quinn ◽  
Angelo M. Tusset ◽  
Jorge L. P. Felix
Keyword(s):  
Internal Resonance ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Coupled System ◽  
Dynamical Behaviour ◽  
Main System ◽  
Weakly Coupled System ◽  
Ideal System ◽  
Quadratic Nonlinearities

The dynamical behaviour of a non-ideal three-degrees-of-freedom weakly coupled system associated with the quadratic nonlinearities in the equations of motion is investigated. The main system consists of two nonlinear mechanical oscillators coupling with quadratic nonlinearities and in which possess a 2:1 internal resonance between their translational movements. Under these conditions, we analyzed the response when a DC unbalanced motor with limited power supply (non-ideal system) excites the main system. When the excitation frequency is near to second natural frequency of the main system, saturation and jump phenomena are presented. Then, this work will analyze some torques of the motor, which causes the phenomena, and due to high amplitudes of motion will be possible to look for a way to harvest energy in a future work.

A Compliant Double Pin Track Link Model for Multibody Tracked Vehicles

1999 ◽  
Author(s):  
J. H. Choi ◽  
D. S. Bae ◽  
H. S. Ryu
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
High Mobility ◽  
Contact Forces ◽  
Integration Step ◽  
Step Size ◽  
Tracked Vehicles ◽  
Accelerated Motion ◽  
Pin Track

Abstract It is the objective of this investigation to develop compliant double pin track link models and investigate the use of these models in the dynamic analysis of high mobility tracked vehicles. There are two major difficulties encountered in developing the compliant track models discussed in this paper. The first is due to the fact that the integration step size must be kept small in order to maintain the numerical stability of the solution. This solution includes high oscillatory signals resulting from the impulsive contact forces and the use of stiff compliant elements to represent the joints between the track links. The characteristics of the compliant, elements used in this investigation to describe the track joints are measured experimentally. The second difficulty encountered in this investigation is due to the large number of the system equations of motion of the three dimensional multibody tracked vehicle model. The dimensionality problem is solved by decoupling the equations of motion of the chassis subsystem and the track subsystems. Recursive methods are used to obtain a minimum set of equations for the chassis subsystem. Several simulation scenarios including an accelerated motion, high speed motion, braking, and turning motion of the high mobility vehicle are tested in order to demonstrate the effectiveness and validity of the methods proposed in this investigation.

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