Three-Dimensional Rigid-Body Collisions With Multiple Contact Points

1995 ◽  
Vol 62 (3) ◽  
pp. 725-732 ◽  
Author(s):  
D. B. Marghitu ◽  
Y. Hurmuzlu
Keyword(s):  
Special Class ◽  
External Surface ◽  
Three Dimensional ◽  
Kinematic Chain ◽  
Coefficient Of Restitution ◽  
Kinematic Chains ◽  
Contact Points ◽  
Differential Formulation ◽  
Impact Energies ◽  
The Impact

This article deals with three-dimensional collisions of rigid, kinematic chains with an external surface while in contact with other surfaces. We concentrate on a special class of kinematic chain problems where there are multiple contact points during the impact process. A differential formulation based algorithm is used to obtain solutions that utilize the kinematic, kinetic, and the energetic definitions of the coefficient of restitution. Planar and spatial collisions of a three-link chain with two contact points are numerically studied to compare the outcomes predicted by each approach. Particular emphasis is placed on the relation between the post and pre-impact energies, slippage and rebounds at the contact points, and differences among planar and nearly planar three-dimensional solutions.

Complementarity Relationships and Critical Configurations in Rigid-Body Collisions of Planar Kinematic Chains With Smooth External Contacts

2020 ◽  
Vol 87 (12) ◽  
Author(s):  
Yildirim Hurmuzlu
Keyword(s):  
Rigid Body ◽  
Special Class ◽  
Solution Method ◽  
External Surface ◽  
Kinematic Chain ◽  
Impulse Wave ◽  
Kinematic Chains ◽  
Complementarity Conditions ◽  
Critical Configurations

Abstract In this article, we consider a special class of collision problems that are frequently encountered in the field of robotics. Such problems can be described as a kinematic chain with one of its ends striking an external surface, while the remaining ends resting on other surfaces. This type of problem involves complementarity relationships between the normal velocities and impulses at the contacting ends. We present a solution method that takes into account the complementarity conditions at the contacting ends. In addition, we study the critical configurations of particle and rigid-body chains where the impulse wave generated by impact gets blocked before it reaches a contacting end.

The Effect of the Impactor Diameter and Boundary Conditions on Low Velocity Impact Composites Behaviour

2007 ◽  
Vol 7-8 ◽  
pp. 217-222 ◽  
Author(s):  
Ana M. Amaro ◽  
Paulo N.B. Reis ◽  
A.G. Magalhães ◽  
Marcelo F.S.F. de Moura
Keyword(s):  
Boundary Conditions ◽  
Damage Model ◽  
Testing Machine ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Low Velocity Impact ◽  
Low Velocity ◽  
Velocity Impact ◽  
Impact Energies ◽  
The Impact

The aim of present work is to study the influence of the impactor diameter and boundary conditions on low velocity impact on carbon-fibre-reinforced epoxy laminates. Experimental tests were performed on [04,904]s laminates, using a drop weight-testing machine. Circular plates were tested under low velocity impacts for two diameters of the hemispherical impactor, 12.7 mm and 20 mm, and considering similar impact energies, 2.6 J for the first impactor and 3 J for the second one. Rectangular and square plates were analysed under low velocity impacts with different boundary conditions. The impacted plates were inspected by X-radiography. Numerical simulations were also performed considering interface finite elements compatible with three-dimensional solid elements including a cohesive mixed-mode damage model, which allows to model delamination between layers. The impact tests showed that both the impactor’s diameter and boundary conditions have influence on the delaminated area. Good agreement between experimental and numerical analysis for shape, orientation and size of damage was obtained.

scholarly journals On the Influence of the Shoulder Kinematic Chain on Joint Kinematics and Musculotendon Lengths During Wheelchair Propulsion Estimated From Multibody Kinematics Optimization

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Pierre Puchaud ◽  
Samuel Hybois ◽  
Antoine Lombart ◽  
Joseph Bascou ◽  
Hélène Pillet ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Joint Kinematics ◽  
Open Loop ◽  
Regression Equations ◽  
Kinematic Chains ◽  
Marker Tracking ◽  
Good Trade ◽  
Shoulder Kinematics ◽  
The Impact

Multibody kinematic optimization is frequently used to assess shoulder kinematics during manual wheelchair (MWC) propulsion, but multiple kinematics chains are available. It is hypothesized that these different kinematic chains affect marker tracking, shoulder kinematics, and resulting musculotendon (MT) lengths. In this study, shoulder kinematics and MT lengths obtained from four shoulder kinematic chains (open-loop thorax-clavicle-scapula-humerus (M1), closed-loop with contact ellipsoid (M2), scapula rhythm from regression equations (M3), and a single ball-and- socket joint between the thorax and the humerus (M4) were compared. Right-side shoulder kinematics from seven subjects were obtained with 34 reflective markers and a scapula locator using an optoelectronic motion capture system while propelling on a MWC simulator. Data were processed based on the four models. The results showed the impact of shoulder kinematic chains on all studied variables. Marker reconstruction errors were found to be similar between M1 and M2 and lower than for M3 and M4. Few degrees-of-freedom (DoF) were noticeably different between M1 and M2, but all shoulder DoFs were significantly affected between M1 and M4. As a consequence of differences in joint kinematics, MT lengths were affected by the kinematic chain definition. The contact ellipsoid (M2) was found as a good trade-off between marker tracking and penetration avoidance of the scapula. The regression-based model (M3) was less efficient due to limited humerus elevation during MWC propulsion, as well as the ball-and-socket model (M4) which appeared not suitable for upper limbs activities, including MWC propulsion.

scholarly journals Construction of Three-Dimensional Road Surface and Application on Interaction between Vehicle and Road

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Lu Yongjie ◽  
Huai Wenqing ◽  
Zhang Junning
Keyword(s):  
Quantitative Description ◽  
Three Dimensional ◽  
Point Contact ◽  
Estimation Method ◽  
Road Surface ◽  
Surface Model ◽  
Dynamical Process ◽  
Contact Points ◽  
Box Counting Dimension ◽  
The Impact

The quantitative description is given to three-dimensional micro and macro self-similar characteristics of road surface from the perspective of fractal geometry using FBM stochastic midpoint displacement and diamond-square algorithm in conjunction with fractal characteristics and statistical characteristics of standard pavement determined by estimation method of box-counting dimension. The comparative analysis between reconstructed three-dimensional road surface spectrum and theoretical road surface spectrum and correlation coefficient demonstrate the high reconstruction accuracy of fractal reconstructed road spectrum. Furthermore, the bump zone is taken as an example to reconstruct a more arbitrary 3D road model through isomorphism of special road surface with stochastic road surface model. Measurement is taken to assume the tire footprint on road surface to be a rectangle, where the pressure distribution is expressed with mean stiffness, while the contact points in the contact area are replaced with a number of springs. Two-DOF vehicle is used as an example to analyze the difference between three-dimensional multipoint-and-plane contact and traditional point contact model. Three-dimensional road surface spectrum provides a more accurate description of the impact effect of tire on road surface, thereby laying a theoretical basis for studies on the dynamical process of interaction of vehicle-road surface and the road friendliness.

scholarly journals Kinematic Synthesis of Mechanism for System with a Technical Vision

2018 ◽  
Vol 237 ◽  
pp. 03009
Author(s):  
Baurzhan Tultayev ◽  
Gani Balbayev ◽  
Algazy Zhauyt ◽  
Aidos Sultan ◽  
Aigerim Mussina
Keyword(s):  
Design Process ◽  
Three Dimensional ◽  
Kinematic Chain ◽  
Kinematic Synthesis ◽  
New Approach ◽  
Kinematic Chains ◽  
Spatial Mechanisms ◽  
Input And Output ◽  
Technical Vision ◽  
Synthesis Of Mechanism

A solution to the problem of synthesizing an initial three-dimensional kinematic chain with spherical and rotary kinematic pairs is presented. It is shown that this chain can be used as a structural module for structural-kinematic synthesis of three-dimensional four-link motion generating lever mechanisms by the preset positions of the in-and output links. This paper affects the actual today’s problem of optimal synthesis of spatial link mechanisms. In this regard, the task of developing methods for the synthesis of complex spatial link mechanisms with the desired laws of motion of the input and output elements allowing automatizing the implementation of all design phases with the use of computer is quite relevant. The authors develop machine-oriented method of structural and kinematic synthesis of spatial link mechanisms based on the use of spatial initial kinematic chains (IKC) realizing prescribed motions. A new approach to the design of spatial mechanisms is suggested, according to which the design process is based on the kinematic synthesis of four-link initial kinematic chain (IKC) and associable kinematic chains (AKC).

scholarly journals Behaviour of reinforcement in drop tower beam tests

2020 ◽  
Vol 323 ◽  
pp. 01007
Author(s):  
Lena Leicht ◽  
Franz Bracklow ◽  
Marcus Hering ◽  
Manfred Curbach
Keyword(s):  
Three Dimensional ◽  
Drop Tower ◽  
Strain Gauges ◽  
Strain Rates ◽  
General Behaviour ◽  
Concrete Members ◽  
Concrete Damage ◽  
Impact Energies ◽  
The Impact ◽  
Semiconductor Strain

Drop tower tests help to gain understanding about the general behaviour of reinforced concrete members under impact loading and to analyse strains and strain rates occurring within their reinforcement. For this purpose, beam and slab specimens are usually employed. The main advantage of beams compared to slabs is that they are less complex due to the almost two-dimensional instead of three-dimensional wave propagation within them. To investigate the steel strains and strain rates, ten impact tests on beam specimens with various impact energies were performed. The impactor sizes and velocities were varied. The reinforcement bars of the beams were instrumented with semiconductor strain gauges. The measured data suggest that the occurring strains in beam tests are independent of the loading velocity. The same was found for the strain rates. The reason is that higher impact energies mostly influence the concrete damage due to spalling on the impact-facing side which happens after the maximum strains occurred. The strains in the reinforcement bars generally result from the overall deflection because of the impact, the spreading of longitudinal waves in the horizontal direction, and the localized cracking of the concrete due to the formation of a punching cone.

Defining the Coefficient of Restitution for the Impact Between Free and Constrained Bodies

1999 ◽  
Author(s):  
J. L. Escalona ◽  
J. M. Mayo ◽  
J. Domínguez
Keyword(s):  
Mechanical Energy ◽  
Coefficient Of Restitution ◽  
Rigid Bodies ◽  
Momentum Balance ◽  
Balance Equations ◽  
Flexible Bodies ◽  
Local Loss ◽  
Contact Points ◽  
Before And After ◽  
The Impact

Abstract This paper revisits the coefficient of restitution involved in the impulse-momentum balance equations for colliding rigid bodies and examines its extension to impacts between flexible bodies. The analytical solution to axial impact on a flexible rod is used to demonstrate that the coefficient of restitution is not inherent in the underlying physical process. In fact, the type of coefficient to be used in each case depends on the particular model employed by the analyst to describe flexibility in the bodies concerned. It is demonstrated that the coefficient of restitution used in the generalized impulse-momentum balance for flexible bodies does not represent a physical magnitude. In any case, as shown in this paper, the ratio between the relative velocities at the contact points or surfaces of the flexible bodies before and after impact is no measure of the local loss of mechanical energy during the process.

scholarly journals A Note on the Influence of Smectite Coating on the Coefficient of Restitution of Natural Sand Particles Impacting Granitic Blocks

Coatings ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 996
Author(s):  
Lina Luo ◽  
Jing Ren ◽  
Sathwik S. Kasyap ◽  
Kostas Senetakis
Keyword(s):  
Debris Flows ◽  
High Speed ◽  
Three Dimensional ◽  
Industrial Applications ◽  
Coefficient Of Restitution ◽  
Natural Sand ◽  
Perfectly Plastic ◽  
Solid Objects ◽  
Clay Coating ◽  
The Impact

The study of the collision behavior of solid objects has received a significant amount of research in various fields such as industrial applications of powders and grains, impacts of proppants and between proppant and rocks during hydraulic fracturing, and the study of debris flows and avalanches and the interactions of landslide materials with protective barriers. This problem has predominantly been studied through the coefficient of restitution (COR), which is computed from the dropping and rebound paths of particles; its value corresponds to 1 for perfectly elastic impacts and 0 for perfectly plastic impacts (i.e., at the collision there is no rebound of the particle). Often, the colliding particles (or particle–block systems) are not perfectly clean, and there is debris (or dust) on their surfaces, forming a coating, which is a highly possible scenario in the debris flows of natural particles and fragments; however, the topic of the influence of natural coatings on the surfaces of particles on the collision behavior of particle–block systems has been largely overlooked. Thus, the present study attempts to provide preliminary results with respect to the influence of natural coating on the surfaces of sand grains in the COR values of grain–block systems using a stiff granitic block as an analogue wall. Montmorillonite powder, which belongs to the smectite clay group, was used and a sample preparation method was standardized to provide a specific amount of clay coating on the surfaces of the sand grains. The results from the study showed a significant influence of the smectite coating in the COR values of the grain–block systems, which was predominantly attributed to the dissipation of energy at the collision moment because of the compression of the soft coating of microparticles. Additionally, the method of analysis for calculating the COR values based on one and two high-speed cameras was explored, as the impacts of natural grains involve deviations from the vertical, which influences the rebound paths. Thus, a sensitivity analysis was performed investigating the differences in the COR values in two-dimensional and three-dimensional analysis of the impact tests.

Differential Formulation for the Coefficient of Restitution of a Rigid Link

2015 ◽  
Vol 762 ◽  
pp. 175-182 ◽  
Author(s):  
Dorian Cojocaru ◽  
Dan B. Marghitu
Keyword(s):  
Mobile Robots ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Coefficient Of Restitution ◽  
Numerical Techniques ◽  
Differential Impact ◽  
Differential Formulation ◽  
Nonlinear Contact ◽  
Nonlinear Equations Of Motion ◽  
The Impact

The differential impact equations of motion are developed using an nonlinear contact force. The nonlinear equations of motion are written using symbolical MATLAB and are solved using numerical techniques. The impact equations are based on the Kogut-Etsion model. The numerical results are obtained for different geometries of the link, different coefficients of friction, and different initial conditions. The coefficient of restitution (COR) is discussed for specific cases. The results can be used for the impact of mobile robots with different type of surfaces.

Scanning and Transmission Microscopy of Nematocyst Batteries in Epitheliomuscular Cells of Hydra

1971 ◽  
Vol 29 ◽  
pp. 410-411 ◽  
Author(s):  
Jane A. Westfall ◽  
S. Yamataka ◽  
Paul D. Enos
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Osmium Tetroxide ◽  
External Surface ◽  
Three Dimensional ◽  
Surface Structures ◽  
Transmission Microscopy ◽  
Transmission Electron ◽  
Freeze Dried ◽  
Scanning Electron

Scanning electron microscopy (SEM) provides three dimensional details of external surface structures and supplements ultrastructural information provided by transmission electron microscopy (TEM). Animals composed of watery jellylike tissues such as hydras and other coelenterates have not been considered suitable for SEM studies because of the difficulty in preserving such organisms in a normal state. This study demonstrates 1) the successful use of SEM on such tissue, and 2) the unique arrangement of batteries of nematocysts within large epitheliomuscular cells on tentacles of Hydra littoralis.Whole specimens of Hydra were prepared for SEM (Figs. 1 and 2) by the fix, freeze-dry, coat technique of Small and Màrszalek. The specimens were fixed in osmium tetroxide and mercuric chloride, freeze-dried in vacuo on a prechilled 1 Kg brass block, and coated with gold-palladium. Tissues for TEM (Figs. 3 and 4) were fixed in glutaraldehyde followed by osmium tetroxide. Scanning micrographs were taken on a Cambridge Stereoscan Mark II A microscope at 10 KV and transmission micrographs were taken on an RCA EMU 3G microscope (Fig. 3) or on a Hitachi HU 11B microscope (Fig. 4).

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