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.

Dynamics of Pipes Containing Pulsative Flow

1997 ◽  
Author(s):  
Zsolt Szabó ◽  
S. C. Sinha ◽  
Gábor Stépán
Keyword(s):  
Equations Of Motion ◽  
Time Instant ◽  
Mean Flow ◽  
Cross Sectional ◽  
Lagrangian Equations ◽  
Mechanical Models ◽  
Complex Models ◽  
A Chain ◽  
The Stability ◽  
Time Periodic

Abstract Several mechanical models exist on elastic pipes containing fluid flow. In this paper those models are considered, where the fluid is incompressible, frictionless and its velocity relative to the pipe has the same but time-periodic magnitude along the pipe at a certain time instant. The pipe can be modelled either as a chain of articulated rigid pipes or as a continuum. The dynamic behaviour of the system strongly depends on the different kinds of boundary conditions and on the fact whether the pipe is considered to be inextensible, i.e. the cross-sectional area of the pipe is constant. The equations of motion are derived via Lagrangian equations and Hamilton’s principle. These systems are non-conservative, and the amount of energy carried in and out by the flow appears in the model. It is well-known, that intricate stability problems arise when the flow pulsates and the corresponding mathematical model, a system of ordinary or partial differential equations, becomes time-periodic. There are several standard techniques, like perturbation method, harmonic balance, finite difference, etc., to analyze these models. The method which constructs the state transition matrix used in Floquet theory in terms of the shifted Chebyshev polynomials of the first kind is especially effective for stability analysis of large systems. The implementation of this method using computer algebra enables us to obtain more accurate results and to investigate more complex models. The stability charts are created with respect to three important parameters: the forcing frequency ω, the perturbation amplitude υ and the mean flow velocity U.

A unified tensor approach to the analysis of mechanical systems

1997 ◽  
Vol 211 (4) ◽  
pp. 313-322 ◽  
Author(s):  
A A Fogarasy ◽  
M R Smith
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Equation Of Motion ◽  
Newtonian Mechanics ◽  
Kinematic Constraint ◽  
Lagrangian Equation ◽  
Generalized Coordinates ◽  
Lagrangian Equations

It is shown in this paper that all methods of dynamic analysis of mechanisms used in practice can be derived from an invariant formed from the Lagrangian equation of motion. For the dynamic analysis of mechanisms subjected to kinematic constraint conditions, the Lagrangian equations of motion are far more suitable than the Newtonian approach. Since the Lagrangian equations are tensor equations, they are valid irrespective of what kind of generalized coordinates are used. This is not so, however, when the Newtonian approach is used. It is demonstrated by a simple example that a careless use of Newtonian mechanics can lead to erroneous results.

Dynamic Analysis of Mechanisms Using Constrained Lagrangian Bond Graphs

1992 ◽  
Author(s):  
Y. A. Khulief
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Bond Graph ◽  
Rigid Bodies ◽  
Interconnected System ◽  
Lagrangian Equations ◽  
System Of Rigid Bodies ◽  
Reaction Forces ◽  
Bond Graph Modeling ◽  
Generalized Constraint

Abstract A method for dynamic analysis of mechanisms using the Lagrangian equations of motion for an interconnected system of rigid bodies is presented. The method stems from a recent extension to the bond graph modeling technique. Intrinsically, this approach allows the formulation of the final form of equations for holonomic systems without recourse to the Lagrangian function. Consequently, the burdens of deriving the expressions for kinetic and potential energies, and performing the necessary differentiations have been eliminated. This method calls only for constructing the Jacobian matrix of constraints, and then employing a bond graph that accounts for the generalized constraint reaction forces.

D’Alembert’s Principle and the Equations of Motion for Nonholonomic Systems

2006 ◽  
Author(s):  
B. F. Feeny
Keyword(s):  
Variational Methods ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Nonholonomic Systems ◽  
Rigid Bodies ◽  
Virtual Power ◽  
Lagrangian Equations ◽  
Conservative Systems ◽  
Principle Of Virtual Power ◽  
D'alembert's Principle

D'Alembert's principle is manipulated in the presence of nonholonomic constraints to derive the principle of virtual power in nonholonomic form, and Lagrange's equations for nonholonomic systems. The Lagrangian equations had been expressed previously for conservative systems, derived by variational methods. The D'Alembert derivation confirms the roles of constrained and unconstrained Lagrangians directly by the presence of constrained and unconstrained velocities in D'Alembert's principle. The constrained form of nonconservative generalized forces is also determined for both particles and rigid bodies. An example is a rolling disk.

scholarly journals Pole-skipping and hydrodynamic analysis in Lifshitz, AdS2 and Rindler geometries

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Haiming Yuan ◽  
Xian-Hui Ge
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Green's Function ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Boundary Theory ◽  
Hydrodynamic Analysis ◽  
Dimensionless Variables ◽  
Pass Through ◽  
Special Points

Abstract The “pole-skipping” phenomenon reflects that the retarded Green’s function is not unique at a pole-skipping point in momentum space (ω, k). We explore the universality of pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a more straightforward way to derive a pole-skipping point. We use this method in Lifshitz, AdS2 and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $$ \frac{\omega }{2\pi T} $$ ω 2 πT and $$ \frac{\left|k\right|}{2\pi T} $$ k 2 πT pass through pole-skipping points $$ \left(\frac{\omega_n}{2\pi T},\frac{\left|{k}_n\right|}{2\pi T}\right) $$ ω n 2 πT k n 2 πT at small ω and k in the Lifshitz background. We verify that the position of the pole-skipping points does not depend on the standard quantization or alternative quantization of the boundary theory in AdS2× ℝd−1 geometry. In the Rindler geometry, we cannot find the corresponding Green’s function to calculate pole-skipping points because it is difficult to impose the boundary condition. However, we can still obtain “special points” near the horizon where bulk equations of motion have two incoming solutions. These “special points” correspond to the nonuniqueness of the Green’s function in physical meaning from the perspective of holography.

Investigation on a Flexible Tether Slackness Based on In- and Out-of Plane Libration Angles

2012 ◽  
Vol 225 ◽  
pp. 411-416 ◽  
Author(s):  
Aaron Aw Teik Hong ◽  
Renuganth Varatharajoo
Keyword(s):  
Equation Of Motion ◽  
Rigid Bodies ◽  
Attitude Dynamics ◽  
Orbit Transfer ◽  
Operation System ◽  
Satellite Systems ◽  
Out Of Plane ◽  
Tethered Satellite Systems ◽  
Libration Angle ◽  
Space Interferometry

Tethered Satellite Systems (TSS) have been used in various applications such as in performing space interferometry, orbit transfer and other relevant fields. As far as the operation system of a TSS is concerned, it is crucial to ensure that the tether will not go slack as its slackness would adversely affects the overall operation outcome due to an undesirable system dynamics. Therefore, it is important to investigate the types of conditions that will cause the tether slackness. Investigations on in-plane and out-of plane libration angles can be utilized to measure at what point that the tether will go slack. Based on previous research works, usually a rigid tether comprising of a uniformed mass is considered while the connecting two satellites are regarded as point masses in order to simplify the governing dynamics equation of motion. However, in order to develop a much more accurate modeling, a flexible tether is chosen by further incorporating the reeling mechanism, attitude dynamics of rigid bodies and tether deformations. Furthermore, a tether has a tendency to go slack if the in-plane and out-of plane libration angle exceeds 65° and 60° respectively regardless of the types of tether utilized whether it being a rigid or a flexible one. Thus, the tension of the tether will serves as a constraint and plotted against the in-plane and out-of plane libration motions that would be attained via the generalized forces. The results will then be analyzed to establish in-plane and out-of plane libration boundaries. Subsequently, the in-plane and out-of plane operation contrains are established for TSS corresponding to a reference mission.

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.

Dynamic Characteristics of a Hydrostatic Gas Bearing Driven by Oscillating Exhaust Pressure

1984 ◽  
Vol 106 (4) ◽  
pp. 477-483 ◽  
Author(s):  
C. B. Watkins ◽  
H. D. Branch ◽  
I. E. Eronini
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Source Model ◽  
Regular Perturbation ◽  
Response Characteristics ◽  
Finite Difference Approximations ◽  
Bode Plots ◽  
Gas Bearing

Vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating exhaust pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and sleeve is solved together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The numerical solutions of the perturbation equations are obtained by discretizing the pressure field using finite-difference approximations with a discrete, nonuniform line-source model which excludes effects due to feeding hole volume. An iterative scheme is used to simultaneously satisfy the equations of motion for the journal. The results presented include Bode plots of bearing-oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency.

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