scholarly journals Modeling of centrifugal deployment of three-section minisatellite boom

2021 ◽  
Vol 2021 (4) ◽  
pp. 56-65
Author(s):  
S.V. Khoroshylov ◽  
◽  
V.K. Shamakhanov ◽  
V.V. Vasyliev ◽  
◽  
...  
Keyword(s):  
Rigid Bodies ◽  
The Body ◽  
Lagrangian Formalism ◽  
Rotational Degree ◽  
Algebraic Equations ◽  
Flexible Beams ◽  
Earth Remote Sensing ◽  
Locking Mechanism ◽  
Body Reference ◽  
Servo Drives

The aim of the article is to model the processes of centrifugal deployment of a three-section boom and preliminary analyze the feasibility of this deployment method for an Earth remote sensing (ERS) minisatellite (MS). During the research, methods of theoretical mechanics, multibody dynamics, control theory, and computer modeling were used. Centrifugal deployment of multi-section booms have been successfully used on spin stabilized satellites, but not on ERS satellites, which have other features of operation and require additional studies. The main part of the MS is a platform to which a transformable antenna is attached by means of a transformable boom. Before deployment, the stowed boom and antenna are attached to the MS platform. The boom sections are connected by joints with one rotational degree of freedom and deployed sequentially due to centrifugal forces when the MS rotates in the required direction. Each of the boom joints has a locking mechanism that latches when a predetermined deploy angle is reached. To model the processes of the boom deployment, the MS is presented as a system of connected bodies, where the platform and the stowed antenna are absolutely rigid bodies, and the boom consists of three flexible beams of a tubular cross-section. The differential equations of the MS dynamics during the deployment are obtained using the Lagrangian formalism, which are supplemented by algebraic equations describing the constraints from the joints. The scenarios of the boom deployment with a constant control torque and a constant angular velocity of the MS are considered. These scenarios are simulated, and estimates of the control actions needed to ensure full deployment of the boom and the stabilization of the MS after latching of the joints are calculated. Dependences of variations of the loads on the boom structure during deployment are obtained. The simulation results allow us to conclude that it is feasible to implement the method of the boom centrifugal deployment for the MS, which can perform fast rotations about the three axes of the body reference frame. Implementation of this method allows designers to reduce mass of the MS because it does not require any servo drives in the boom deployment system.

scholarly journals B-Spline Impulse Response Functions of Rigid Bodies for Fluid-Structure Interaction Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
S. Zhou-Bowers ◽  
D. C. Rizos
Keyword(s):  
Impulse Response ◽  
Dynamic Models ◽  
Interaction Analysis ◽  
Fluid Structure Interaction ◽  
Rigid Bodies ◽  
The Body ◽  
Impulse Response Functions ◽  
Fluid Structure ◽  
B Spline ◽  
Structure Interaction

Reduced 3D dynamic fluid-structure interaction (FSI) models are proposed in this paper based on a direct time-domain B-spline boundary element method (BEM). These models are used to simulate the motion of rigid bodies in infinite or semi-infinite fluid media in real, or near real, time. B-spline impulse response function (BIRF) techniques are used within the BEM framework to compute the response of the hydrodynamic system to transient forces. Higher-order spatial and temporal discretization is used in developing the kinematic FSI model of rigid bodies and computing its BIRFs. Hydrodynamic effects on the massless rigid body generated by an arbitrary transient acceleration of the body are computed by a mere superposition of BIRFs. Finally, the dynamic models of rigid bodies including inertia effects are generated by introducing the kinematic interaction model to the governing equation of motion and solve for the response in a time-marching scheme. Verification examples are presented and demonstrate the stability, accuracy, and efficiency of the proposed technique.

scholarly journals Jumping in frogs: assessing the design of the skeletal system by anatomically realistic modeling and forward dynamic simulation

2002 ◽  
Vol 205 (12) ◽  
pp. 1683-1702 ◽  
Author(s):  
William J. Kargo ◽  
Frank Nelson ◽  
Lawrence C. Rome
Keyword(s):  
Degrees Of Freedom ◽  
The Body ◽  
Joint Torque ◽  
Rotational Degree ◽  
Skeletal System ◽  
Dynamic Simulations ◽  
Inverse Dynamic ◽  
Maximal Distance ◽  
Out Of Plane ◽  
Rotational Degrees Of Freedom

SUMMARY Comparative musculoskeletal modeling represents a tool to understand better how motor system parameters are fine-tuned for specific behaviors. Frog jumping is a behavior in which the physical properties of the body and musculotendon actuators may have evolved specifically to extend the limits of performance. Little is known about how the joints of the frog contribute to and limit jumping performance. To address these issues, we developed a skeletal model of the frog Rana pipiens that contained realistic bones, joints and body-segment properties. We performed forward dynamic simulations of jumping to determine the minimal number of joint degrees of freedom required to produce maximal-distance jumps and to produce jumps of varied take-off angles. The forward dynamics of the models was driven with joint torque patterns determined from inverse dynamic analysis of jumping in experimental frogs. When the joints were constrained to rotate in the extension—flexion plane, the simulations produced short jumps with a fixed angle of take-off. We found that, to produce maximal-distance jumping,the skeletal system of the frog must minimally include a gimbal joint at the hip (three rotational degrees of freedom), a universal Hooke's joint at the knee (two rotational degrees of freedom) and pin joints at the ankle,tarsometatarsal, metatarsophalangeal and iliosacral joints (one rotational degree of freedom). One of the knee degrees of freedom represented a unique kinematic mechanism (internal rotation about the long axis of the tibiofibula)and played a crucial role in bringing the feet under the body so that maximal jump distances could be attained. Finally, the out-of-plane degrees of freedom were found to be essential to enable the frog to alter the angle of take-off and thereby permit flexible neuromotor control. The results of this study form a foundation upon which additional model subsystems (e.g. musculotendon and neural) can be added to test the integrative action of the neuromusculoskeletal system during frog jumping.

A Semi-Discrete Approach for the Numerical Simulation of Freestanding Blocks

2016 ◽  
pp. 416-439
Author(s):  
Fernando Peña
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Numerical Modeling ◽  
Discrete Model ◽  
Mathematical Formulation ◽  
Equation Of Motion ◽  
Rigid Bodies ◽  
The Body ◽  
Discrete Approach ◽  
Rocking Motion

This chapter addresses the numerical modeling of freestanding rigid blocks by means of a semi-discrete approach. The pure rocking motion of single rigid bodies can be easily studied with the differential equation of motion, which can be solved by numerical integration or by linearization. However, when we deal with sliding and jumping motion of rigid bodies, the mathematical formulation becomes quite complex. In order to overcome this complexity, a Semi-Discrete Model (SMD) is proposed for the study of rocking motion of rigid bodies, in which the rigid body is considered as a mass element supported by springs and dashpots, in the spirit of deformable contacts between rigid blocks. The SMD can detect separation and sliding of the body; however, initial base contacts do not change, keeping a relative continuity between the body and its base. Extensive numerical simulations have been carried out in order to validate the proposed approach.

Hovering of a rigid pyramid in an oscillatory airflow

2010 ◽  
Vol 650 ◽  
pp. 415-425 ◽  
Author(s):  
ANNIE WEATHERS ◽  
BRENDAN FOLIE ◽  
BIN LIU ◽  
STEPHEN CHILDRESS ◽  
JUN ZHANG
Keyword(s):  
Body Mass ◽  
Rigid Bodies ◽  
The Body ◽  
The Asymmetry

We investigate the dynamics of rigid bodies (hollow ‘pyramids’) placed within a background airflow, oscillating with zero mean. The asymmetry of the body introduces a net upward force. We find that when the amplitude of the airflow is above a threshold, the net lift exceeds the weight and the object starts to hover. Our results show that the objects hover at far smaller air amplitudes than would be required by a quasi-steady theory, although this theory accounts qualitatively for the behaviour of the system as the body mass becomes small.

Die Pauli-Gleichung mit Differentialoperatoren für den Spin/ The Pauli Equation with Differential Operators for the Spin

1978 ◽  
Vol 33 (10) ◽  
pp. 1133-1150
Author(s):  
Eberhard Kern
Keyword(s):  
Angular Momentum ◽  
Rigid Body ◽  
Differential Operators ◽  
Spin Operator ◽  
Rigid Bodies ◽  
The Body ◽  
Wave Functions ◽  
Pauli Equation ◽  
Spin Eigenfunctions ◽  
Cartesian Coordinate

The spin operator s = (ħ/2) σ in the Pauli equation fulfills the commutation relation of the angular momentum and leads to half-integer eigenvalues of the eigenfunctions for s. If one tries to express s by canonically conjugated operators Φ and π = (ħ/i) ∂/∂Φ the formal angular momentum term s = Φ X π fails because it leads only to whole-integer eigenvalues. However, the modification of this term in the form s = 1/2 {π + Φ(Φ π) + Φ X π} leads to the required result.The eigenfunction system belonging to this differential operator s(Φ π) consists of (2s + 1) spin eigenfunctions ξm (Φ) which are given explicitly. They form a basis for the wave functions of a particle of spin s. Applying this formalism to particles with s = 1/2, agreement is reached with Pauli’s spin theory.The function s(Φ π) follows from the theory of rotating rigid bodies. The continuous spinvariable Φ = ((Φx , Φy, Φz) can be interpreted classically as a “turning vector” which defines the orientation in space of a rigid body. Φ is the positioning coordinate of the rigid body or the spin coordinate of the particle in analogy to the cartesian coordinate x. The spin s is a vector fixed to the body.

A Multibody System Model for Meshing Gears

2010 ◽  
Vol 44-47 ◽  
pp. 1273-1278 ◽  
Author(s):  
Liu Lei
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Gear Wheel ◽  
Numerical Approach ◽  
Computational Effort ◽  
Rigid Bodies ◽  
The Body ◽  
System Model ◽  
New Approach ◽  
Elastic Elements

As a type of numerical approach to dynamics of gears, multibody dynamics method can handle realistic cases of contact modeling with acceptable accuracy and considerably less computational effort. The ability to simulate contact between teeth has become an essential topic in multibody dynamics. Fully rigid method is not suited for a high quality of the analysis to take into account some elasticity in the model of meshing gear wheels. In our new approach the circumferentially rotatable rigid teeth and elastic elements composed of rotational spring-damper combinations are hereby put forward. The teeth and the body of each gear wheel are still regarded as rigid bodies, but they are connected with each other by elastic elements. Besides, Lankarani & Nikravesh Contact Model is utilized, which counts energy dissipation by means of viscous damping. Both large motions with revolutions and important elasticity are considered in this teeth-wheel multibody system model. Two examples are provided in which the simulation results of completely rigid method, the approach in [10], our new approach and finite element methods are compared. Comparisons indicate that our newly developed approach is more suitable for modeling multibody geared systems.

ENVELOPING SURFACES AND ADMISSIBLE VELOCITIES OF HEAVY RIGID BODIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2525-2553 ◽  
Author(s):  
IGOR N. GASHENENKO ◽  
PETER H. RICHTER
Keyword(s):  
Three Dimensional ◽  
Rigid Bodies ◽  
First Integrals ◽  
The Body ◽  
Heegaard Splitting ◽  
Body Motion ◽  
Invariant Sets ◽  
Poisson Problem ◽  
Integral Manifolds ◽  
Angular Velocities

The general Euler-Poisson problem of rigid body motion is investigated. We study the three-dimensional algebraic level surfaces of the first integrals, and their topological bifurcations. The main result of this article is an analytical and qualitatively complete description of the projections of these integral manifolds to the body-fixed space of angular velocities. We classify the possible types of these invariant sets and analyze the dependence of their topology on the parameters of the body and the constants of the first integrals. Particular emphasis is given to the enveloping surfaces of the sets of admissible angular velocities. Their pre-images in the reduced phase space induce a Heegaard splitting which lends itself for a general choice of complete Poincaré surfaces of section, irrespective of whether or not the system is integrable.

Contact Force Analysis in Static Two-Fingered Robot Grasping

2013 ◽  
Author(s):  
I Cheng ◽  
C. H. Liu ◽  
Yin-Tien Wang
Keyword(s):  
Rigid Bodies ◽  
The Body ◽  
Contact Forces ◽  
Contact Theory ◽  
Force Analysis ◽  
Equilibrium Solutions ◽  
Spherical Object ◽  
Closed Form Solutions ◽  
Robot Grasping ◽  
Force Displacement

Static grasping of a spherical object by two robot fingers is studied in this paper. The fingers may be rigid bodies or elastic beams, they may grasp the body with various orientation angles, and the tightening displacements may be linear or angular. Closed-form solutions for normal and tangential contact forces due to tightening displacements are obtained by solving compatibility equations, force-displacement relations based on Hertz contact theory, and equations of equilibrium. Solutions show that relations between contact forces and tightening displacements depend upon the orientation of the fingers, the elastic constants of the materials, and area moments of inertia of the beams.

Lattice Boltzmann Analysis of Fluid-Structure Interaction with Moving Boundaries

2013 ◽  
Vol 13 (3) ◽  
pp. 823-834 ◽  
Author(s):  
Alessandro De Rosis ◽  
Giacomo Falcucci ◽  
Stefano Ubertini ◽  
Francesco Ubertini ◽  
Sauro Succi
Keyword(s):  
Fluid Flow ◽  
Lattice Boltzmann ◽  
Time Discretization ◽  
Rigid Bodies ◽  
The Body ◽  
Moving Boundaries ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Body Dynamics ◽  
Boltzmann Method

AbstractThis work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies. The fluid flow is modelled by Lattice-Boltzmann Method, coupled to a set of ordinary differential equations describing the dynamics of the solid body in terms its elastic and damping properties. The time discretization of the body dynamics is performed via the Time Discontinuous Galerkin Method. Several numerical examples are presented and highlight the robustness and efficiency of the proposed methodology, by means of comparisons with previously published results. The examples show that the present fluid-structure method is able to capture vortex- induced oscillations of flexibly-supported rigid body.

scholarly journals Revealing the effect of rounded noise protection screens with finite sound insulation on an acoustic field around linear sound sources

2021 ◽  
Vol 1 (5 (109)) ◽  
pp. 16-22
Author(s):  
Vitalii Didkovskyi ◽  
Vitaly Zaets ◽  
Svetlana Kotenko
Keyword(s):  
Acoustic Field ◽  
Traffic Noise ◽  
The Body ◽  
Sound Insulation ◽  
Physical Parameters ◽  
Algebraic Equations ◽  
Sound Sources ◽  
Study Results ◽  
Almost All ◽  
Screen Model

This paper reports studying the reduction of traffic noise by rounded noise protection screens with finite sound insulation, that is, those that can pass sound. Almost all models of acoustic screens, which are examined by analytical methods, are either direct or such that disregard the passage of sound through the screen, that is, it is assumed that the screen sound insulation is non-finite. This approach made it possible to solve the problem for a simplified model analytically but made it impossible to analyze the required sound insulation of noise protection screens. In the current paper, the problem of investigating an acoustic field around the screen whose sound insulation is finite has been stated, that is, it was taken into consideration that a sound wave propagates through the body of the screen. In addition, a given problem considers a rounded screen, rather than vertical, which is also used in different countries. Such a problem was solved by the method of partial domains. This method has made it possible to strictly analytically build a solution to the problem by simplifying it to solving an infinite system of algebraic equations, which was solved by the method of reduction. The screen model was set by the values of the density and speed of sound in the screen material. This approach has made it possible to change the acoustic impedance of the screen material and thereby change the sound insulation of the screen. That has made it possible to quantify the effect of screen sound insulation on its effectiveness. It has been shown that the efficiency of noise protection screens with finite sound insulation is approaching the efficiency of acoustically rigid screens, provided that the screen's natural sound insulation is 13–15 dB greater than the estimated efficiency of the rigid screen. The study results could make it possible to more accurately assess the effectiveness of noise protection screens. Determining the screen acoustic efficiency would make it possible to set requirements for its sound insulation characteristics. That could make it possible to select the designs of noise protection screens with minimal physical parameters, such as thickness, weight, etc.

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