Generation of Motion Equations for a Tree-Like System of Granular Bodies

1993 ◽  
Author(s):  
Oleg Vinogradov
Keyword(s):  
Computer Simulation ◽  
Discrete System ◽  
Sparse Matrices ◽  
Equations Of Motion ◽  
Computer Time ◽  
Arbitrary System ◽  
Rigid Spheres ◽  
Motion Equations ◽  
Nonsteady Motion ◽  
Topological Tree

Abstract An arbitrary system of 3D-bodies made out of rigid spheres and arranged topologically in a tree is considered. For such a system explicit expressions for the equations of motion are derived based on the Lagrangian approach. The equations are given in terms of the path matrix characterizing the topological tree. The analytical method of generation of equations of motion makes the computer simulation of the nonsteady motion of the discrete system of bodies more efficient in term of both computer time and accuracy. It is achieved by avoiding operations with large sparse matrices (if the equations were generated numerically) and by cancelling out some terms in Lagrange’s equations analytically.

Computer Simulation of a Press Feed Mechanism and Experimental Confirmation

1994 ◽  
Vol 116 (1) ◽  
pp. 248-256 ◽  
Author(s):  
C. Chassapis ◽  
G. G. Lowen
Keyword(s):  
Computer Simulation ◽  
Data Acquisition System ◽  
Quantitative Agreement ◽  
Drive Shaft ◽  
Strain Gages ◽  
Motion Equations ◽  
Qualitative And Quantitative ◽  
Bending Strain ◽  
Out Of Plane ◽  
Set Up

An experimentally verified simulation of the elastic-dynamic behavior of a lever-type feed mechanism is presented. Based on a combination of experimental and analytical findings, simplified motion equations could be introduced. In the experimental set-up, the motion of the mechanism is monitored by three angular encoders, which are attached to the drive shaft, the rocker-link shaft, and the feed roller shaft, respectively. Their output, which is stored in a specially designed data acquisition system, allows the correlation of the instantaneous rotations of the feed roller and the rocker shafts to that of the drive shaft. Strain gages provide in and out-of-plane bending-strain histories of the bent coupler. Experiment and theory, for different loading conditions, are correlated by way of the coupler strain, the clutch windup angle and the total feed length. Good qualitative and quantitative agreement between computed and experimental results was found.

Efficient Dynamic Computer Simulation of Simple-Closed Spatial Linkages

1990 ◽  
Author(s):  
L. T. Wang
Keyword(s):  
Computer Simulation ◽  
Computational Algorithm ◽  
Equations Of Motion ◽  
Joint Space ◽  
Kinematic Chains ◽  
Spatial Linkages ◽  
Dynamic Computer Simulation ◽  
The Stability ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

Abstract A new method of formulating the generalized equations of motion for simple-closed (single loop) spatial linkages is presented in this paper. This method is based on the generalized principle of D’Alembert and the use of the transformation Jacobian matrices. The number of the differential equations of motion is minimized by performing the method of generalized coordinate partitioning in the joint space. Based on this formulation, a computational algorithm for computer simulation the dynamic motions of the linkage is developed, this algorithm is not only numerically stable but also fully exploits the efficient recursive computational schemes developed earlier for open kinematic chains. Two numerical examples are presented to demonstrate the stability and efficiency of the algorithm.

Differential-Geometric Methods in Multibody Dynamics and Control

2005 ◽  
Author(s):  
P. Maißer
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Multibody System ◽  
Equations Of Motion ◽  
Geometric Approach ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Dynamics And Control ◽  
Set Up ◽  
Lagrangian Motion

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

scholarly journals Treatment of Close Approaches in the Numerical Integration of the Gravitational Problem of N Bodies

1971 ◽  
Vol 10 ◽  
pp. 133-150 ◽  
Author(s):  
D. G. Bettis ◽  
V. Szebehely
Keyword(s):  
Numerical Integration ◽  
Body Problem ◽  
Considerable Increase ◽  
Equations Of Motion ◽  
Computer Time ◽  
Tidal Effects ◽  
Basic Ideas ◽  
Gravitational Problem ◽  
Considerable Detail ◽  
Numerical Approaches

AbstractOne of the main difficulties encountered in the numerical integration of the gravitational n-body problem is associated with close approaches. The singularities of the differential equations of motion result in losses of accuracy and in considerable increase in computer time when any of the distances between the participating bodies decreases below a certain value. This value is larger than the distance when tidal effects become important, consequently, numerical problems are encountered before the physical picture is changed. Elimination of these singularities by transformations is known as the process of regularization. This paper discusses such transformations and describes in considerable detail the numerical approaches to more accurate and faster integration. The basic ideas of smoothing and regularization are explained and applications are given.

Automatic Generation of Equations of Motion of Mechanical Systems

2014 ◽  
Vol 611 ◽  
pp. 40-45
Author(s):  
Darina Hroncová ◽  
Jozef Filas
Keyword(s):  
Computer Simulation ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Automatic Generation ◽  
Lagrange Equations ◽  
Kinematic Chains ◽  
Transformation Matrices

The paper describes an algorithm for automatic compilation of equations of motion. Lagrange equations of the second kind and the transformation matrices of basic movements are used by this algorithm. This approach is useful for computer simulation of open kinematic chains with any number of degrees of freedom as well as any combination of bonds.

Application of Data Mining Technology Based on Apriori Algorithm

2014 ◽  
Vol 543-547 ◽  
pp. 2036-2039
Author(s):  
Jian Xing Chen
Keyword(s):  
Data Mining ◽  
Computer Simulation ◽  
Association Rule ◽  
Computer Time ◽  
Data Mining Algorithm ◽  
Apriori Algorithm ◽  
Mining Technology ◽  
Computer Data ◽  
Mining Algorithm ◽  
Step Distance

With the continuous expansion of computer simulation scale, the demand for data mining algorithm is also more and more big. The difficulties in computer data mining technology are focused on algorithm development. Apriori algorithm is a kind of computer data mining algorithm which can greatly improve the computational efficiency. The algorithm uses association rule, which can avoid repeated frequently by layer scanning, reducing the computer time. This paper uses Apriori algorithm to design the data mining parameter optimization model of computer 3D human biology simulation, and applies to improve the step three jump. Through the simulation we found step distance appropriate, it provides technical reference for the application of computer simulation technology in sports.

Motion Equations for the Ball and Beam and the Ball and Arc Systems

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Constance Lare ◽  
Warren N. White ◽  
Sanzida Hossain
Keyword(s):  
Dynamic Models ◽  
Controller Design ◽  
Equations Of Motion ◽  
Dimensionless Form ◽  
Dimensionless Numbers ◽  
Motion Equations ◽  
Systems Model ◽  
Consistent Manner ◽  
Simplifying Assumptions ◽  
The Impact

Abstract Presently, most derivations of the equations of motion for the ball and beam and ball and arc systems model the ball as a point mass. Other derivations apply assumptions related to the ball that lack physical justification. To understand fully the impact the ball has on the equations of motion and controller design, equations of motion are needed that stem from a derivation invoking few assumptions. At that point, simplifying assumptions applied in a consistent manner are possible. This paper derives the equations of motion for each mechanical system using fewer assumptions than what appears in the literature. The development then applies the assumptions needed to convert the derived dynamics to the well-used equations of motion seen in the literature. The presentation shows that some ball and beam models appearing in the literature do not stem from consistent assumptions or correct kinematics. Incorrect kinematics are also present in some of the ball and arc dynamic models. This paper also introduces dimensionless quantities to the dynamic equations of both systems rendering them in dimensionless form. Such formulations allow for comparisons between different systems through the size of the dimensionless quantities. The dimensionless systems are the means used to demonstrate that the equations of motion of each system are the same as the radius of the arc grows without bound. Finally, the paper shows that comparisons between different ball and beam models using these dimensionless numbers are now possible.

Computer Simulation of Dynamical Behavior of Self-Propelled Gurney

1993 ◽  
Author(s):  
Wieslaw M. Szydlowski ◽  
Srinivas Sastry
Keyword(s):  
Computer Simulation ◽  
Equations Of Motion ◽  
Dynamical Behavior ◽  
Design Parameters ◽  
Dynamical Response ◽  
Straight Path ◽  
Main Disadvantage ◽  
Oscillatory Response ◽  
New Type ◽  
Difficult Part

Abstract The conventional gurneys used in hospitals to move patients from room to room have one main disadvantage: they are difficult to control. A typical gurney has a form of an oblong table moving on four castor wheels. The vehicle is difficult to maneuver, especially on corridor turns, and usually requires two operators — each at one end. Dr. J. Bleicher from the St. Joseph’s Hospital in Omaha, Nebraska suggested a new type of a self-propelled gurney which would be a cross-breed of a motorized wheelchair and a gurney. A new type of a gurney would have two additional wheels in the center of the gurney, each connected to a separate DC motor. The torques developed by the motors would be controlled by one operator using a joystick. Applying opposite torques to the controlled wheels would rotate a stationary gurney in place, or would curve the path of a moving gurney. The position of two additional wheels can be changed, so that the gurney can move sideways, translate in chosen direction or move along a curvelinear path. The work presented in the paper contains an analysis of the dynamics of such a gurney. A mathematical model of the vehicle was developed to check how much effort is needed on the part of the operator in straight path motion and during negotiating a corner. The most difficult part of the modelling was a proper description of forces and torques exerted by the ground on the wheels. The differential equations of motion of the gurney have been numerically integrated, and the dynamical response of the vehicle studied. The results of the computer simulation show a transient oscillatory response of the castor wheels (shimmying) which can be controlled by a proper choice of design parameters of the vehicle.

Novel derivation of equations of motion for a body falling with resistance

2021 ◽  
Vol 57 (1) ◽  
pp. 015017
Author(s):  
Zhiwei Chong ◽  
Zhuoyi Wu ◽  
Yajun Wei
Keyword(s):  
Secondary School ◽  
Differential Equations ◽  
Equations Of Motion ◽  
School Mathematics ◽  
Motion Equations ◽  
Secondary School Mathematics ◽  
Mathematical Operations

Abstract The motion equations of a body under gravity and resistance linearly dependent on speed are usually analysed by solving differential equations. In this paper we report a derivation not explicitly involving differential equations but instead based on some elementary mathematical operations. The derivation uses only knowledge covered in a typical secondary school mathematics syllabus.

A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 1

1977 ◽  
Vol 99 (3) ◽  
pp. 773-779 ◽  
Author(s):  
N. Orlandea ◽  
M. A. Chace ◽  
D. A. Calahan
Keyword(s):  
Computer Simulation ◽  
Dynamic Analysis ◽  
Numerical Solutions ◽  
Sparse Matrix ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Front Suspension ◽  
Analysis And Design

The work described herein is an extension of sparse matrix and stiff integrated numerical algorithms used for the simulation of electrical circuits and three-dimensional mechanical dynamic systems. By applying these algorithms big sets of sparse linear equations can be solved efficiently, and the numerical instability associated with widely split eigenvalues can be avoided. The new numerical methods affect even the initial formulation for these problems. In this paper, the equations of motion and constraints (Part 1) and the force function of springs and dampers (Part 2) are set up, and the numerical solutions for static, transient, and linearized types of analysis as well as the modal optimization algorithms are implemented in the ADAMS (automatic dynamic analysis of mechanical systems) computer program for simulation of three-dimensional mechanical systems (Part 2). The paper concludes with two examples: computer simulation of the front suspension of a 1973 Chevrolet Malibu and computer simulation of the landing gear of a Boeing 747 airplane. The efficiency of simulation and comparison with experimental results are given in tabular form.

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