scholarly journals Rigid Body Motions and Local Compliance Response during Impact of Two Deformable Spheres

2017 ◽  
Vol 8 (1) ◽  
pp. 1 ◽  
Author(s):  
Akuro Big-Alabo
Keyword(s):  
Rigid Body ◽  
Dynamic Models ◽  
Numerical Solutions ◽  
Simple Procedure ◽  
Body Motion ◽  
Impact System ◽  
Rigid Body Motions ◽  
Local Compliance ◽  
Nonlinear Dynamic Models ◽  
The Impact

The impact of two hard deformable spheres is revisited with the aim of investigating the constituent rigid body motions and indentation response of each sphere during collision. The latter are determined theoretically and the theoretical solutions are validated by comparing with numerical solutions of the coupled nonlinear dynamic models for impact of two hard deformable spheres. For elastic impact events, normalized tabulated solutions are derived using the Force Indentation Linearisation Method (FILM) and the tabulated solutions can be used to generate actual rigid body motions and indentation histories for each of the colliding spheres without need for numerical or finite element solutions. The analysis shows that the rigid body motion and local compliance response of each sphere depend on: (a) ratio of mass of sphere to effective mass of impact system, and (b) ratio of initial velocity of sphere to initial relative velocity of impact system. Finally, the 2-D collision problem is discussed and a simple procedure to determine the unique solution of all four unknowns is presented.

On Higher Order Point-Line and the Associated Rigid Body Motions

2006 ◽  
Vol 129 (2) ◽  
pp. 166-172 ◽  
Author(s):  
Yi Zhang ◽  
Kwun-Lon Ting
Keyword(s):  
Rigid Body ◽  
Higher Order ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Dual Quaternion ◽  
Displacement Operator ◽  
Screw Motion ◽  
Rigid Body Motions ◽  
Point Line

This paper presents a study on the higher-order motion of point-lines embedded on rigid bodies. The mathematic treatment of the paper is based on dual quaternion algebra and differential geometry of line trajectories, which facilitate a concise and unified description of the material in this paper. Due to the unified treatment, the results are directly applicable to line motion as well. The transformation of a point-line between positions is expressed as a unit dual quaternion referred to as the point-line displacement operator depicting a pure translation along the point-line followed by a screw displacement about their common normal. The derivatives of the point-line displacement operator characterize the point-line motion to various orders with a set of characteristic numbers. A set of associated rigid body motions is obtained by applying an instantaneous rotation about the point-line. It shows that the ISA trihedrons of the associated rigid motions can be simply depicted with a set of ∞2 cylindroids. It also presents for a rigid body motion, the locus of lines and point-lines with common rotation or translation characteristics about the line axes. Lines embedded in a rigid body with uniform screw motion are presented. For a general rigid body motion, one may find lines generating up to the third order uniform screw motion about these lines.

Research on Dynamic Modelling and Simulation of Erection System of Mobile Equipment in Absolute Coordinates

2011 ◽  
Vol 66-68 ◽  
pp. 2034-2040
Author(s):  
Qin He Gao ◽  
Xiang Yang Li
Keyword(s):  
Rigid Body ◽  
Dynamic Models ◽  
Dynamic Modelling ◽  
Hydraulic Cylinder ◽  
Correction Method ◽  
Integration Time ◽  
Multi Stage ◽  
Rigid Body Model ◽  
Absolute Coordinates ◽  
The Impact

This paper employed the theories of multibody system dynamics to analyze the multi-rigid-body model of erection system and build the general dynamic models in absolute coordinates. The impact theory of contact mechanics and nonlinear spring-damper force function were used to model the impact problems between rods of multi-stage hydraulic cylinder of erection system and educe the dynamic models of multi-rigid-body erection system with impact. An automatic violation correction method according to the step of integration time was given to solve the violation which is an incident problem in numerical integration of dynamic models in absolute coordinates. Simulation results show that these dynamic models are effective.

A Computationally Efficient Planar Rigid Body Velocity Measure

2009 ◽  
Author(s):  
Luis E. Criales ◽  
Joseph M. Schimmels
Keyword(s):  
Rigid Body ◽  
Rigid Bodies ◽  
Body Motion ◽  
Computationally Efficient ◽  
Straight Line ◽  
Body Velocity ◽  
Velocity Measure ◽  
Rigid Body Motions ◽  
Line Path ◽  
Planar Motions

A planar rigid body velocity measure based on the instantaneous velocity of all particles that constitute a rigid body is developed. This measure compares the motion of each particle to an “ideal”, but usually unobtainable, motion. This ideal motion is one that would carry each particle from its current position to its desired position on a straight-line path. Although the ideal motion is not a valid rigid body motion, this does not preclude its use as a reference standard in evaluating valid rigid body motions. The optimal instantaneous planar motions for general rigid bodies in translation and rotation are characterized. Results for an example planar positioning problem are presented.

scholarly journals A Matrix Information-Geometric Method for Change-Point Detection of Rigid Body Motion

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 531
Author(s):  
Xiaomin Duan ◽  
Huafei Sun ◽  
Xinyu Zhao
Keyword(s):  
Rigid Body ◽  
Change Point ◽  
Order Approximation ◽  
Local Maximum ◽  
Change Point Detection ◽  
Body Motion ◽  
Geometric Method ◽  
Change Points ◽  
Gradient Descent Algorithm ◽  
Rigid Body Motions

A matrix information-geometric method was developed to detect the change-points of rigid body motions. Note that the set of all rigid body motions is the special Euclidean group S E ( 3 ) , so the Riemannian mean based on the Lie group structures of S E ( 3 ) reflects the characteristics of change-points. Once a change-point occurs, the distance between the current point and the Riemannian mean of its neighbor points should be a local maximum. A gradient descent algorithm is proposed to calculate the Riemannian mean. Using the Baker–Campbell–Hausdorff formula, the first-order approximation of the Riemannian mean is taken as the initial value of the iterative procedure. The performance of our method was evaluated by numerical examples and manipulator experiments.

Dynamic Response of Composite Pressure Vessels to Inertia Loads

1991 ◽  
Vol 113 (1) ◽  
pp. 86-91
Author(s):  
J. C. Prucz ◽  
J. D’Acquisto ◽  
J. E. Smith
Keyword(s):  
Rigid Body ◽  
Combustion Engine ◽  
Pressure Vessels ◽  
Body Motion ◽  
Connecting Rod ◽  
Filament Wound ◽  
Potential Benefits ◽  
Rigid Body Motions ◽  
Crank Mechanism ◽  
Selection Of

A new analytical model has been developed in order to investigate the potential benefits of using fiber-reinforced composites in pressure vessels that undergo rigid-body motions. The model consists of a quasi-static lamination analysis of a cylindrical, filament-wound, pressure vessel, combined with an elastodynamic analysis that accounts for the coupling effects between its rigid-body motion and its elastic deformations. The particular type of motion investigated in this paper is that of an oil-pressurized, tubular connecting rod in a slider-crank mechanism of an internal combustion engine. A comprehensive parametric study has been focused on the maximum wall stresses induced in such a rod by the combined effect of internal pressure and inertia loads associated with its motion. The numerical results illustrate potential ways to reduce these stresses by appropriate selection of material systems, lay-up configurations and geometric parameters.

scholarly journals An Approach for the Impact Dynamic Modeling and Simulation of Planar Constrained Metamorphic Mechanism

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Yanyan Song ◽  
Boyan Chang ◽  
Guoguang Jin ◽  
Zhan Wei ◽  
Bo Li
Keyword(s):  
Rigid Body ◽  
Modeling And Simulation ◽  
Dynamic Modeling ◽  
Dynamic Models ◽  
Dynamic Theory ◽  
Coefficient Of Restitution ◽  
Body System ◽  
Metamorphic Mechanism ◽  
The Impact ◽  
Impact Motion

This paper studied the impact dynamic modeling of the planar constrained metamorphic mechanism (PCMM) during configuration transformation. Based on the dynamic theory of the multi-rigid-body system and the coefficient of restitution equation, a new method for dynamic modeling of PCMM considering impact motions generated by configuration transformation is presented, which can be treated as a theoretical foundation for performance design and dynamic control. Firstly, the topology theory based on the impact motion can be classified as the stable impact motion and the mobile impact motion, which is the prerequisite for dynamic modeling and simulation. Secondly, the stable and mobile impact dynamic models for PCMM are established according to the dynamic theory of the multi-rigid-body system. Then, using these models, the corresponding impulse solving models are deduced combining with the coefficient of restitution equation. Finally, the examples of the stable impact motion and the mobile impact motion are respectively given, and the configuration-complete dynamic simulations are carried out. By comparing with the dynamic models without considering the impact motion, the dynamic characteristics of PCMM are analyzed. The theory and method proposed in this paper can be also applied in general planar robotic systems to deal with the problem of internal collision dynamics.

scholarly journals Kinematics of Serial Manipulators

2020 ◽  
Author(s):  
Ivan Virgala ◽  
Michal Kelemen ◽  
Erik Prada
Keyword(s):  
Rigid Body ◽  
Numerical Solutions ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Body Motion ◽  
Robot Kinematics ◽  
Kinematic Modeling ◽  
Open Chain ◽  
Serial Manipulators ◽  
Serial Robot

This book chapter deals with kinematic modeling of serial robot manipulators (open-chain multibody systems) with focus on forward as well as inverse kinematic model. At first, the chapter describes basic important definitions in the area of manipulators kinematics. Subsequently, the rigid body motion is presented and basic mathematical apparatus is introduced. Based on rigid body conventions, the forward kinematic model is established including one of the most used approaches in robot kinematics, namely the Denavit-Hartenberg convention. The last section of the chapter analyzes inverse kinematic modeling including analytical, geometrical, and numerical solutions. The chapter offers several examples of serial manipulators with its mathematical solution.

scholarly journals Rigid-body motion is the main source of diffuse scattering in protein crystallography

IUCrJ ◽  
2019 ◽  
Vol 6 (2) ◽  
pp. 277-289 ◽  
Author(s):  
T. de Klijn ◽  
A. M. M. Schreurs ◽  
L. M. J. Kroon-Batenburg
Keyword(s):  
Rigid Body ◽  
Diffuse Scattering ◽  
Body Motion ◽  
Maximum Information ◽  
Biologically Relevant ◽  
Internal Motions ◽  
X Ray Scattering ◽  
The Subject ◽  
Rigid Body Motions ◽  
A Minor

The origin of diffuse X-ray scattering from protein crystals has been the subject of debate over the past three decades regarding whether it arises from correlated atomic motions within the molecule or from rigid-body disorder. Here, a supercell approach to modelling diffuse scattering is presented that uses ensembles of molecular models representing rigid-body motions as well as internal motions as obtained from ensemble refinement. This approach allows oversampling of Miller indices and comparison with equally oversampled diffuse data, thus allowing the maximum information to be extracted from experiments. It is found that most of the diffuse scattering comes from correlated motions within the unit cell, with only a minor contribution from longer-range correlated displacements. Rigid-body motions, and in particular rigid-body translations, make by far the most dominant contribution to the diffuse scattering, and internal motions give only a modest addition. This suggests that modelling biologically relevant protein dynamics from diffuse scattering may present an even larger challenge than was thought.

scholarly journals Verified Solution Method for Population Epidemiology Models with Uncertainty

2009 ◽  
Vol 19 (3) ◽  
pp. 501-512 ◽  
Author(s):  
Joshua Enszer ◽  
Mark Stadtherr
Keyword(s):  
Solution Method ◽  
Dynamic Models ◽  
Initial Conditions ◽  
Time Dependent ◽  
Uncertain Parameters ◽  
Epidemiological Models ◽  
Taylor Models ◽  
Sirs Model ◽  
Nonlinear Dynamic Models ◽  
The Impact

Verified Solution Method for Population Epidemiology Models with UncertaintyEpidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.

Nonlinear Analysis of the Motion Structures

2013 ◽  
Vol 373-375 ◽  
pp. 90-94 ◽  
Author(s):  
Ren Zuo Wang ◽  
Shih Hung Chen ◽  
Bing Chang Lin ◽  
Chao Hsun Huang ◽  
Chung Yue Wang
Keyword(s):  
Rigid Body ◽  
Nonlinear Analysis ◽  
Dynamic Responses ◽  
Body Motion ◽  
Flexible Structure ◽  
Vector Form ◽  
Frame Element ◽  
Computation Process ◽  
Plane Frame ◽  
Rigid Body Motions

In this paper, the nonlinear analysis of the motion structures is studied by using the vector form intrinsic finite element (VFIFE, V-5) method. The main object of this research is to develop an internal hinge of two ends of the plane frame element. In this study, the hinge function of frame element is used to compute the nonlinear dynamic responses of the motion structures. A fictitious reversed rigid body motion can be used to separate the rigid body motions and the pure deformations of the frame element. It is not requires any iteration or any parameters for the VFIFE method during computation process. Four examples illustrate the accuracy of the proposed procedures in computing large motions of a flying flexible structure.

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