scholarly journals Determination of Reaction Forces of a Deck Crane in Wave Motion Using Screw Theory

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Andrej Cibicik ◽  
Geir O. Tysse ◽  
Olav Egeland
Keyword(s):  
Wave Motion ◽  
Screw Theory ◽  
Equations Of Motion ◽  
Wave Spectrum ◽  
Force Response ◽  
Plücker Coordinates ◽  
Angular Velocities ◽  
Reaction Forces ◽  
Response Amplitude Operators

In this paper, we present a method for calculating reaction forces for a crane mounted on a ship moving in waves. The method is used to calculate the reaction forces between the crane base and the vessel deck. This includes the case where the crane is mounted on the platform that keeps the base of the crane horizontal when the vessel is moving in roll and pitch. The wave motion of the ship is modeled with force response amplitude operators (RAOs) based on the JONSWAP wave spectrum. The combined equations of motion for a vessel and a crane are derived using Kane’s equations of motion, where velocities and angular velocities are formulated in terms of twists, and the associated partial velocities and partial angular velocities are given as lines in Plücker coordinates. The unknown reaction forces are represented as wrenches and are determined using screw transformations. The method is used to study the effect of the roll and pitch compensation platform in numerical simulations. The efficiency of the platform is evaluated in terms of the magnitude of reaction forces and crane payload sway angles.

scholarly journals Horizon radiation reaction forces

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Walter D. Goldberger ◽  
Ira Z. Rothstein
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Finite Size ◽  
Radiation Reaction ◽  
Effective Field ◽  
Compact Objects ◽  
Finite Size Effect ◽  
Binary Black Holes ◽  
Dissipative Effects ◽  
Reaction Forces

Abstract Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

scholarly journals IV. On the dynamical theory of incompressible viscous fluids and the determination of the criterion

1895 ◽  
Vol 186 ◽  
pp. 123-164 ◽  
Keyword(s):  
Singular Solution ◽  
Physical State ◽  
Theoretical Calculations ◽  
Equations Of Motion ◽  
Dynamical Theory ◽  
Viscous Fluids ◽  
Linear Functions ◽  
Incompressible Viscous Fluids ◽  
Theoretical Results

1. The equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier seems to have first introduced in 1822, and which were much studied by Cauchy and Poisson) were finally shown by St. Venant and Sir Gabriel Stokes, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a co-efficient depending on the physical state of the fluid. By obtaining a singular solution of these equations as applied to the case of pendulums in steady periodic motion, Sir G. Stokes was able to compare the theoretical results with the numerous experiments that had been recorded, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved. This was also the result of comparing the flow of water through uniform tubes with the flow calculated from a singular solution of the equations so long as the tubes were small and the velocities slow. On the other hand, these results, both theoretical and practical, were directly at variance with common experience as to the resistance encountered by larger bodies moving with higher velocities through water, or by water moving with greater velocities through larger tubes. This discrepancy Sir G. Stokes considered as probably resulting from eddies which rendered the actual motion other than that to which the singular solution referred and not as disproving the assumption.

Investigation of Train Dynamics in Passing Through Curves Using a Full Model

Joint Rail ◽  
2004 ◽  
Author(s):  
Mohammad Durali ◽  
Mohammad Mehdi Jalili Bahabadi
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Full Model ◽  
Bogie Frame ◽  
Nonlinear Characteristics ◽  
Train Derailment ◽  
Train Dynamics

In this article a train model is developed for studying train derailment in passing through bends. The model is three dimensional, nonlinear, and considers 43 degrees of freedom for each wagon. All nonlinear characteristics of suspension elements as well as flexibilities of wagon body and bogie frame, and the effect of coupler forces are included in the model. The equations of motion for the train are solved numerically for different train conditions. A neural network was constructed as an element in solution loop for determination of wheel-rail contact geometry. Derailment factor was calculated for each case. The results are presented and show the major role of coupler forces on possible train derailment.

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.

Determination of Instability Boundaries for a Highly Flexible Prismatic-Jointed Robot Performing Repetitive Maneuvers

1991 ◽  
Author(s):  
Keith W. Buffinton
Keyword(s):  
Floquet Theory ◽  
Equations Of Motion ◽  
Perturbation Techniques ◽  
Axial Motion ◽  
The Third ◽  
Straightforward Application ◽  
Method Yield ◽  
Robotic Devices ◽  
Axially Moving

Abstract Presented in this work are the equations of motion governing the behavior of a simple, highly flexible, prismatic-jointed robotic manipulator performing repetitive maneuvers. The robot is modeled as a uniform cantilever beam that is subject to harmonic axial motions over a single bilateral support. To conveniently and accurately predict motions that lead to unstable behavior, three methods are investigated for determining the boundaries of unstable regions in the parameter space defined by the amplitude and frequency of axial motion. The first method is based on a straightforward application of Floquet theory; the second makes use of the results of a perturbation analysis; and the third employs Bolotin’s infinite determinate method. Results indicate that both perturbation techniques and Bolotin’s method yield acceptably accurate results for only very small amplitudes of axial motion and that a direct application of Floquet theory, while computational expensive, is the most reliable way to ensure that all instability boundaries are correctly represented. These results are particularly relevant to the study of prismatic-jointed robotic devices that experience amplitudes of periodic motion that are a significant percentage of the length of the axially moving member.

The Effect of Pitch Gyradius on Added Resistance of Yacht Hulls

1991 ◽  
Author(s):  
James F. Moran
Keyword(s):  
Water Resistance ◽  
Wave Spectrum ◽  
Response Amplitude ◽  
Added Resistance ◽  
Regular Waves ◽  
Low Frequencies ◽  
Irregular Wave ◽  
Wave Data ◽  
The Difference ◽  
Response Amplitude Operators

The purpose of this investigation was to determine the effect of pitch gyradius on added resistance of yacht hulls. Tank testing of a model yacht in head seas was performed in the Webb Robinson Model Basin. The model was tested in regular waves at two speeds and five variations of gyradius. The model was also evaluated in irregular seas of the Pierson-Moskowitz spectrum at various speeds with two gyradii. Response Amplitude Operators were developed from the regular wave data and comparisons made. The irregular wave data were analyzed for the effect of speed on the difference in added resistance between the maximum and minimum gyradius settings. Several conclusions were arrived at after analyzing the data. The Response Amplitude Operaters shift as the gyradius changes. In regular waves, at low frequencies of encounter, a lower, gyradius resulted in less added frequencies of encounter in regular waves, this trend reverses itself and the higher gyradii result in reduced added resistance. However, at higher frequencies of encounter in regular waves, this trend reverses, reverses itself in reduced added resistance. The peaks of the RAO curves shift to higher frequencies at higher gyradii. It was also concluded that at the higher speed, Froude Number of 0.3, the added resistance was lower relative to the still-water resistance for each gyradius tested. The irregular wave testing revealed the effect of the lower frequencies dominating the irregular wave spectrum. The minimum gyradius, in irregular seas showed less added resistance than the maximum gyradius. In addition, the irregular wave testing verified, the reduction of added resistance, relative to still-water resistance, at increasing speeds for both the minimum and maximum gyradii.

A Project in the Determination of the Moment of Inertia

2005 ◽  
Vol 33 (4) ◽  
pp. 319-338
Author(s):  
Ron P. Podhorodeski ◽  
Paul Sobejko
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Moment Of Inertia ◽  
Educational Goal ◽  
Centre Of Mass ◽  
Comparison Of Results ◽  
Physical Testing ◽  
The Moment

Analysis of the forces involved in mechanical systems requires an understanding of the dynamic properties of the system's components. In this work, a project on the determination of both the location of the centre of mass and inertial properties is described. The project involves physical testing, the proposal of approximate models, and the comparison of results. The educational goal of the project is to give students and appreciation of second mass moments and the validity of assumptions that are often applied in component modelling. This work reviews relevant equations of motion and discusses techniques to determine or estimate the centre of mass and second moment of inertia. An example project problem and solutions are presented. The value of such project problems within a first course on the theory of mechanisms is discussed.

Determination of Stability Derivatives by Impulse-Response Techniques

1977 ◽  
Vol 14 (02) ◽  
pp. 265-275
Author(s):  
Carl A. Scragg
Keyword(s):  
Memory Effect ◽  
Impulse Response ◽  
Traditional Method ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Regular Motion ◽  
Stability Derivatives ◽  
The Stability ◽  
Derivatives Of

This paper presents a new method of experimentally determining the stability derivatives of a ship. Using a linearized set of the equations of motion which allows for the presence of a memory effect, the response of the ship to impulsive motions is examined. This new technique is compared with the traditional method of regular-motion tests and experimental results are presented for both methods.

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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