On the Numerical Solution of Many-Body Contact Dynamics Problems Formulated as Complementarity Problems

2012 ◽  
Author(s):  
Toby Heyn ◽  
Dan Negrut ◽  
Mihai Anitescu ◽  
Alessandro Tasora ◽  
David Lamb
Keyword(s):  
Numerical Solution ◽  
Equations Of Motion ◽  
Contact Dynamics ◽  
Many Body ◽  
Computational Accuracy ◽  
Body Contact ◽  
Granular Dynamics ◽  
Minimum Residual ◽  
And Performance ◽  
Dynamics Problems

This contribution is concerned with the modeling and simulation of many-body dynamics problems. In such problems, the solution method has to routinely handle millions of unknowns when, for instance, investigating granular dynamics related phenomena. Given the size of these problems, the scope of tractable applications may be limited by computational efficiency and/or computational accuracy. This scenario has been found to be the case when the equations of motion embed a differential variational inequality (DVI) problem that captures frictional/contact interactions between rigid and/or flexible bodies. As the size of the system increases, the speed and quality of the numerical solution may decrease. This contribution describes an alternative numerical method, called the Gradient Projected Minimum Residual or GPMINRES method, which demonstrates better scalability and performance (in terms of solution speed and accuracy) than methods commonly used to solve problems posed in this manner.

scholarly journals Motion Planning and Control of an Omnidirectional Mobile Robot in Dynamic Environments

Robotics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 48
Author(s):  
Mahmood Reza Azizi ◽  
Alireza Rastegarpanah ◽  
Rustam Stolkin
Keyword(s):  
Mobile Robot ◽  
Collision Avoidance ◽  
Motion Control ◽  
Equations Of Motion ◽  
Dynamic Environments ◽  
Discrete State ◽  
Omnidirectional Mobile Robot ◽  
Planning And Control ◽  
Avoidance Strategy ◽  
And Performance

Motion control in dynamic environments is one of the most important problems in using mobile robots in collaboration with humans and other robots. In this paper, the motion control of a four-Mecanum-wheeled omnidirectional mobile robot (OMR) in dynamic environments is studied. The robot’s differential equations of motion are extracted using Kane’s method and converted to discrete state space form. A nonlinear model predictive control (NMPC) strategy is designed based on the derived mathematical model to stabilize the robot in desired positions and orientations. As a main contribution of this work, the velocity obstacles (VO) approach is reformulated to be introduced in the NMPC system to avoid the robot from collision with moving and fixed obstacles online. Considering the robot’s physical restrictions, the parameters and functions used in the designed control system and collision avoidance strategy are determined through stability and performance analysis and some criteria are established for calculating the best values of these parameters. The effectiveness of the proposed controller and collision avoidance strategy is evaluated through a series of computer simulations. The simulation results show that the proposed strategy is efficient in stabilizing the robot in the desired configuration and in avoiding collision with obstacles, even in narrow spaces and with complicated arrangements of obstacles.

scholarly journals Identical Limb Dynamics for Unilateral Impairments through Biomechanical Equivalence

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 705
Author(s):  
Fatemeh Rasouli ◽  
Kyle B. Reed
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
Dynamic Models ◽  
Assistive Devices ◽  
Assistive Device ◽  
Human Walking ◽  
Physical Parameters ◽  
Gait Rehabilitation ◽  
And Performance ◽  
Two Sides

Dynamic models, such as double pendulums, can generate similar dynamics as human limbs. They are versatile tools for simulating and analyzing the human walking cycle and performance under various conditions. They include multiple links, hinges, and masses that represent physical parameters of a limb or an assistive device. This study develops a mathematical model of dissimilar double pendulums that mimics human walking with unilateral gait impairment and establishes identical dynamics between asymmetric limbs. It introduces new coefficients that create biomechanical equivalence between two sides of an asymmetric gait. The numerical solution demonstrates that dissimilar double pendulums can have symmetric kinematic and kinetic outcomes. Parallel solutions with different physical parameters but similar biomechanical coefficients enable interchangeable designs that could be incorporated into gait rehabilitation treatments or alternative prosthetic and ambulatory assistive devices.

On the Parametric Excitation of Pendulum-Type Vibration Absorber

1961 ◽  
Vol 28 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Energy Transfer ◽  
Numerical Solution ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Absorber ◽  
Single Cycle ◽  
Linearized System ◽  
Nonlinear Equations Of Motion ◽  
Beam Oscillation ◽  
Energy Interchange

The free motion of an undamped pendulum-type vibration absorber is studied on the basis of approximate nonlinear equations of motion. It is shown that this type of mechanical system exhibits the phenomenon of auto parametric excitation; a type of “instability” which cannot be accounted for on the basis of the linearized system. Complete energy transfer between modes is shown to occur when the beam frequency is twice the simple pendulum frequency. On the basis of a numerical solution, approximately 150 cycles of the beam oscillation take place during a single cycle of energy interchange.

Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed M. Khader
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Convergence Order ◽  
Variable Order ◽  
Numerical Treatment ◽  
Dynamical Models ◽  
Fractional Modeling ◽  
Dynamics Problems

AbstractThis paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

scholarly journals Simplified Method for Flow Analysis and Performance Calculation Through an Axial Compressor

1984 ◽  
Author(s):  
Hubert Miton ◽  
Youssef Doumandji ◽  
Jacques Chauvin
Keyword(s):  
Equations Of Motion ◽  
Computing Time ◽  
Flow Analysis ◽  
Axial Compressor ◽  
Computation Method ◽  
Duct Flow ◽  
Axial Compressors ◽  
Flow Through ◽  
And Performance ◽  
Performance Calculation

This paper describes a fast computation method of the flow through multistage axial compressors of the industrial type. The flow is assumed to be axisymmetric between the blade rows which are represented by actuator disks. Blade row losses and turning are calculated by means of correlations. The equations of motion are linearized with respect to the log of static pressure, whose variation along the radius is usually of limited extent for the type of machines for which the method has been developed. In each computing plane (i.e. between the blade rows) two flows are combined: a basic flow with constant pressure satisfying the mass flow requirements and a perturbation flow fulfilling the radial equilibrium condition. The results of a few sample calculations are given. They show a satisfactory agreement with a classical duct flow method although the computing time is reduced by a factor five. The method has also been coupled with a surge line prediction calculation.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

Propagation of Nonlinearities in the Inertia Matrix of Tracked Vehicles

1994 ◽  
Author(s):  
J. H. Choi ◽  
A. A. Shabana ◽  
Roger A. Wehage
Keyword(s):  
Numerical Solution ◽  
Vehicle Dynamics ◽  
Equations Of Motion ◽  
Coefficient Matrix ◽  
Influence Coefficient ◽  
Dynamic Force ◽  
Tracked Vehicles ◽  
Revolute Joints ◽  
Inertia Matrix ◽  
Force Coupling

Abstract In this investigation, a procedure is presented for the numerical solution of tracked vehicle dynamics equations of motion. Tracked vehicles can be represented as two kinematically decoupled subsystems. The first is the chassis subsystem which consists of chassis, rollers, idlers, and sprockets. The second is the track subsystem which consists of track links interconnected by revolute joints. While there is dynamic force coupling between these two subsystems, there is no inertia coupling since the kinematic equations of the two subsystems are not coupled. The objective of the procedure developed in this investigation is to take advantage of the fact that in many applications, the shape of the track does not significantly change even though the track links undergo significant configurations changes. In such cases the nonlinearities propagate along the diagonals of a velocity influence coefficient matrix. This matrix is the only source of nonlinearities in the generalized inertia matrix. A permutation matrix is introduced to minimize the number of generalized inertia matrix LU factor evaluations for the track.

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