scholarly journals New class of exact solutions for the equations of motion of a chain of n rigid bodies

2013 ◽  
Keyword(s):  
Exact Solutions ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
New Class ◽  
A Chain

THE DYNAMICS OF A SINGLE ALGEBRAIC SCREW PAIR

2011 ◽  
Vol 35 (4) ◽  
pp. 491-503 ◽  
Author(s):  
James D. Robinson ◽  
M. John D. Hayes
Keyword(s):  
Equations Of Motion ◽  
Kinematic Chain ◽  
The Self ◽  
Dynamics Model ◽  
Kinematic Constraint ◽  
New Class ◽  
Gravity Effects ◽  
Specific Configuration ◽  
A Chain ◽  
The Impact

The algebraic screw pair, or A-pair, represents a new class of kinematic constraint that exploits the self-motions inherent to a specific configuration of Griffis-Duffy platform. Using the A-pair as a joint in a hybrid parallel-serial kinematic chain results in a sinusoidal coupling of rotation and translation between adjacent links. The resulting linkage is termed an A-chain. This paper reveals the dynamic equations of motion of a single A-pair and examines the impact of the inertial properties of the legs of the A-pair on the dynamics. A numerical example illustrates the impact of the leg effects from different perspectives and shows that while the gravity effects of the legs are significant, it may be possible to neglect the leg kinetic energy from the dynamics model.

Closed and Expanded Form of Manipulator Dynamics Using Lagrangian Approach

1985 ◽  
Vol 107 (2) ◽  
pp. 223-225 ◽  
Author(s):  
T. Wang ◽  
D. Kohli
Keyword(s):  
Equations Of Motion ◽  
Equation Of Motion ◽  
Rigid Bodies ◽  
Lagrangian Approach ◽  
Alternative Derivation ◽  
Manipulator Dynamics ◽  
Lagrangian Equations ◽  
A Chain ◽  
Expanded Form ◽  
Simplified Form

An alternative derivation of the equations of motion of a chain of rigid bodies using Lagrangian equations of motion is presented. In an effort to reduce the complexity of the coefficients appearing in the equations of motion, a modified form of Lagrangian equations due to Silver [3] are utilized. This approach leads to a simplified form of coefficients of the equation of motion.

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

New class of exact solutions of the Dirac equation

1975 ◽  
Vol 16 (10) ◽  
pp. 2089-2092 ◽  
Author(s):  
Franklin S. Felber ◽  
John H. Marburger
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
New Class

scholarly journals A Simulation Model for Computing the Loads Generated at Landing Site During Helicopter Take-Off or Landing Operation

2019 ◽  
Vol 2019 (2) ◽  
pp. 59-75
Author(s):  
Jarosław Stanisławski
Keyword(s):  
Equations Of Motion ◽  
Landing Site ◽  
Simulation Method ◽  
Rigid Bodies ◽  
Landing Gear ◽  
Rotor Blades ◽  
Wind Gust ◽  
The Galerkin Method ◽  
Lumped Masses ◽  
And Control

Summary The paper presents simulation method and results of calculations determining behavior of helicopter and landing site loads which are generated during phase of the helicopter take-off and landing. For helicopter with whirling rotor standing on ground or touching it, the loads of landing gear depend on the parameters of helicopter movement, occurrence of wind gusts and control of pitch angle of the rotor blades. The considered model of helicopter consists of the fuselage and main transmission treated as rigid bodies connected with elastic elements. The fuselage is supported by landing gear modeled by units of spring and damping elements. The rotor blades are modeled as elastic axes with sets of lumped masses of blade segments distributed along them. The Runge-Kutta method was used to solve the equations of motion of the helicopter model. According to the Galerkin method, it was assumed that the parameters of the elastic blade motion can be treated as a combination of its bending and torsion eigen modes. For calculations, data of a hypothetical light helicopter were applied. Simulation results were presented for the cases of landing helicopter touching ground with different vertical speed and for phase of take-off including influence of rotor speed changes, wind gust and control of blade pitch. The simulation method may help to define the limits of helicopter safe operation on the landing surfaces.

A new class of exact solutions of the Vlasov equation

2001 ◽  
Vol 8 (12) ◽  
pp. 5081-5085 ◽  
Author(s):  
M. Y. Yu ◽  
Zhaoyang Chen ◽  
L. Stenflo
Keyword(s):  
Exact Solutions ◽  
Vlasov Equation ◽  
New Class

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies: Part I — Characterization and Prediction of the Kinematic Constraint Changes

1987 ◽  
Author(s):  
B. J. Gilmore ◽  
R. J. Cipra
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
State Variables ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Force Closure ◽  
Simulation Strategy ◽  
Reaction Forces ◽  
Discontinuous Equations

Abstract Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part I. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforeseen changes in topology. Part II presents the implementation of the characterizations into a simulation strategy and presents examples.

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