Equimomental System and Its Applications

2006 ◽  
Author(s):  
Himanshu Chaudhary ◽  
Subir Kumar Saha
Keyword(s):  
Rigid Body ◽  
Euler Equations ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Performance Characteristics ◽  
Spatial Motion ◽  
Space System ◽  
Optimization Scheme ◽  
Equimomental System ◽  
Dynamic Performances

This paper presents a study of an equimomental system and its application. The equimomental system of point-masses for a rigid body moving in plane and space system is studied. Sets of three and seven equimomental point-masses are proposed for a planar and spatial motion, respectively. The set of equimomental point-masses is then applied for the optimization of dynamic performance characteristics of a mechanism, e.g, shaking forces and moments, driving torques, bearing reactions, etc. The Newton-Euler equations of motion of a link undergoing planar motion are formulated systematically in the parameters related to the point-masses, which leads to an optimization scheme for the mass distribution of the links to improve the dynamic performances. The effectiveness of the proposed methodology is shown by applying it to a multiloop mechanism of carpet scrapping machine. A significant improvement in all the dynamic performance characteristics is obtained compared to those of the original mechanism.

scholarly journals Equivalence of Euler equations and torque-angular momentum relation

2021 ◽  
Vol 18 (1) ◽  
pp. 136
Author(s):  
V. Tanriverdi
Keyword(s):  
Angular Momentum ◽  
Rigid Body ◽  
Reference Frame ◽  
Euler Equations ◽  
Equations Of Motion ◽  
The Body ◽  
Moments Of Inertia ◽  
Body Reference ◽  
Stationary Reference Frame ◽  
Momentum Relation

Euler derived equations for rigid body rotations in the body reference frame and in the stationary reference frame by considering an infinitesimal part of the rigid body.Another derivation is possible, and it is widely used: transforming torque-angular momentum relation to the body reference frame.However, their equivalence is not shown explicitly.In this work, for a rigid body with different moments of inertia, we calculated Euler equations explicitly in the body reference frame and in the stationary reference frame and torque-angular momentum relation.We also calculated equations of motion from Lagrangian.These calculations show that all four of them are equivalent.

Comparison on General Track Spectrum for Chinese Main Railway Lines and Track Spectrum of American Railway Lines

2011 ◽  
Vol 250-253 ◽  
pp. 3822-3826 ◽  
Author(s):  
Xian Mai Chen ◽  
Xia Xin Tao ◽  
Gao Hang Cui ◽  
Fu Tong Wang
Keyword(s):  
Dynamic Performance ◽  
Dynamic Responses ◽  
Wave Band ◽  
Wheel Load ◽  
Railway Line ◽  
Acceleration Rate ◽  
Time Histories ◽  
Railway System ◽  
Dynamic Performances ◽  
Track Irregularity

The general track spectrum of Chinese main railway lines (ChinaRLS) and the track spectrum of American railway lines (AmericaRLS) are compared in terms of character of frequency domain, statistical property of time domain samples and dynamic performance. That the wavelength range of the ChinaRLS, which is characterized by the three levels according to the class of railway line, is less than AmericaRLS at common wave band of 1~50m is calculated. Simultaneously, the mean square values of two kinds of track spectra are provided at the detrimental wave bands of 5~10m, 10~20m, and so on. The time-histories of ChinaRLS and AmericaRLS are simulated according to the trigonometric method, and the digital statistical nature of simulated time samples is analyzed. With inputting the two kinds of time-histories into the vehicle-railway system, the comparative analysis of the two kinds of dynamic performances for ChinaRLS and AmericaRLS is done in terms of car body acceleration, rate of wheel load reduction, wheel/rail force, and the dynamic responses of track structure. The result shows that ChinaRLS can characterize the feature of the Chinese track irregularity better than AmericaRLS, the track irregularity with the ChinaRLS of 200km/h is superior to the AmericaRLS, and the track irregularity with the ChinaRLS of 160km/h corresponds to with the sixth of AmericaRLS.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Effects of compressor frequency and heat exchanger geometry on dynamic performance characteristics of heat pump dryers

Energy ◽  
2021 ◽  
pp. 121391
Author(s):  
JunYoung Choi ◽  
DongChan Lee ◽  
Myeong Hyen Park ◽  
Yongju Lee ◽  
Yongchan Kim
Keyword(s):  
Heat Exchanger ◽  
Heat Pump ◽  
Dynamic Performance ◽  
Performance Characteristics

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.

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

Nonlinear Coupled Transverse and Axial Vibration of Variable Cross-Section Beam Flexures Interconnecting Rigid Body

2016 ◽  
Author(s):  
Hasan Malaeke ◽  
Hamid Moeenfard ◽  
Amir H. Ghasemi
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Cross Section ◽  
Multiple Scales ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Closed Form Solutions ◽  
Dynamic Performances

The objective of this paper is to analytically study the nonlinear behavior of variable cross-section beam flexures interconnecting an eccentric rigid body. Hamilton’s principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. Using a single mode approximation, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. The method of multiple scales are employed to obtain parametric closed-form solutions. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. These analytical expressions provide design insights for modeling and optimization of more complex flexure mechanisms for improved dynamic performances.

scholarly journals Effect of Dam Depth and Relief Track Depth on Steady-State and Dynamic Performance Parameters of 3-Lobe Pressure Dam Bearing

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ashutosh Kumar ◽  
S. K. Kakoty
Keyword(s):  
Steady State ◽  
Dynamic Performance ◽  
Performance Characteristics ◽  
Performance Parameters ◽  
Effect Of Pressure ◽  
And Performance

The present study analyzes the effect of pressure dam depth and relief track depth on the performance of three-lobe pressure dam bearing. Different values of dam depth and relief track depth are taken in nondimensional form in order to analyze their effect. Results are plotted for different parameters against eccentricity ratios and it is shown that the effect of pressure dam depth and relief track depth has great significance on stability and other performance parameters. Study of stability and performance characteristics is undertaken simultaneously.

MULTIBODY DYNAMIC MODELING AND FLUTTER ANALYSIS OF A FLEXIBLE SLENDER VEHICLE

2012 ◽  
Vol 12 (06) ◽  
pp. 1250049 ◽  
Author(s):  
A. RASTI ◽  
S. A. FAZELZADEH
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Equations Of Motion ◽  
The Body ◽  
Elastic Deformations ◽  
Strip Theory ◽  
Multibody Dynamic ◽  
Flutter Analysis ◽  
Rigid Body Motions

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

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