scholarly journals A kinematics-based model for the settling of gravity-driven arbitrary-shaped particles on a surface

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0243716
Author(s):  
Mohsen Daghooghi ◽  
Iman Borazjani
Keyword(s):  
Equilibrium State ◽  
Contact Point ◽  
Center Of Mass ◽  
Stable State ◽  
Rigid Body Dynamics ◽  
Contact Points ◽  
Shaped Particle ◽  
Instantaneous Center ◽  
Point Line ◽  
Discrete Element Methods

A discrete model is proposed for settling of an arbitrary-shaped particle onto a flat surface under the gravitational field. In this method, the particle dynamics is calculated such that (a) the particle does not create an overlap with the wall and (b) reaches a realistic equilibrium state, which are not guaranteed in the conventional discrete element methods that add a repulsive force (torque) based on the amount of overlap between the particle and the wall. Instead, upon the detection of collision, the particle’s kinematics is modified depending on the type of contact, i.e., point, line, and surface types, by assuming the contact point/line as the instantaneous center/line of rotation for calculating the rigid body dynamics. Two different stability conditions are implemented by comparing the location of the projection of the center of mass on the wall along gravity direction against the contact points to identify the equilibrium (stable) state on the wall for particles with multiple contact points. A variety of simulations are presented, including smooth surface particles (ellipsoids), regular particles with sharp edges (cylinders and pyramids) and irregular-shaped particles, to show that the method can provide the analytically-known equilibrium state.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

scholarly journals Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations

2009 ◽  
Vol 465 (2107) ◽  
pp. 2267-2292 ◽  
Author(s):  
Zhen Zhao ◽  
Caishan Liu ◽  
Bernard Brogliato
Keyword(s):  
Qualitative Analysis ◽  
Rigid Body ◽  
Numerical Simulations ◽  
Contact Point ◽  
Impulsive Differential Equations ◽  
Companion Paper ◽  
Rigid Body Dynamics ◽  
Drift Motion ◽  
Contact Points ◽  
Static Coefficient Of Friction

The objective of this paper is to implement and test the theory presented in a companion paper for the non-smooth dynamics exhibited in a bouncing dimer. Our approach revolves around the use of rigid body dynamics theory combined with constraint equations from the Coulomb's frictional law and the complementarity condition to identify the contact status of each contacting point. A set of impulsive differential equations based on Darboux–Keller shock dynamics is established that can deal with the complex behaviours involved in multiple collisions, such as the frictional effects, the local dissipation of energy at each contact point, and the dispersion of energy among various contact points. The paper will revisit the experimental phenomena found in Dorbolo et al . ( Dorbolo et al . 2005 Phys. Rev. Lett. 95 , 044101), and then present a qualitative analysis based on the theory proposed in part I. The value of the static coefficient of friction between the plate and the dimer is successfully estimated, and found to be responsible for the formation of the drift motion of the bouncing dimer. Plenty of numerical simulations are carried out, and precise agreements are obtained by the comparisons with the experimental results.

scholarly journals Online Intelligent Perception of Pantograph and Catenary System Status Based on Parameter Adaptation

2021 ◽  
Vol 11 (4) ◽  
pp. 1948
Author(s):  
Yuan Shen ◽  
Xiao Pan ◽  
Luonan Chang
Keyword(s):  
Contact Point ◽  
Stable State ◽  
Stable Condition ◽  
Image Features ◽  
Parameter Adaptation ◽  
Contact State ◽  
Term Operation ◽  
Contact Points ◽  
Catenary System

Online autonomous perception of pantograph catenary system status is of great significance for railway autonomous operation and maintenance (RIOM). Image sensors combined with an image processing algorithm can realize the automatic acquisition of the pantograph catenary condition; however, it is difficult to meet the demand of long-term stable condition acquisition, which restricts the implementation of online contact state feedback and the realization of railway automation. This paper proposes an online intelligent perception of the pantograph and catenary system (PCS) status based on parameter adaptation to realize fast and stable state analysis when the train is in long-term operation outdoors. First, according to the feature of the contact point, we used histogram of gradient (HoG) features and one-dimensional signal combined with a KCF tracker as the baseline method. Then, a result discriminator located by L1 and hash similarity constraints was used to construct a closed-loop parameter adaptive localization framework, which retrieves and updates parameters when tracking failure occurs. After that, a pruned RefineDet method was used to detect pantograph horns and sparks, which, together with the contact points localization method, ensure the long-term stability of feature localization in PCS images. Then, based on the stereo cameras model, the three-dimensional trajectory of the whole pantograph body can be reconstructed by the image features, and we obtained pantograph catenary contact parameters including the pantograph slide posture, contact line offset, arc detection, separation detection, etc. Our method has been tested on more than 16,000 collected image pairs and the results show that the proposed method has a better positioning effect than the state-of-art method, and realizes the online acquisition of pantograph catenary contact state, representing a significant contribution to RIOM.

scholarly journals On a paradox in the impact dynamics of smooth rigid bodies

2018 ◽  
Vol 24 (3) ◽  
pp. 573-597 ◽  
Author(s):  
Peter Palffy-Muhoray ◽  
Epifanio G Virga ◽  
Mark Wilkinson ◽  
Xiaoyu Zheng
Keyword(s):  
Conservation Laws ◽  
Contact Point ◽  
Classical Mechanics ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Impact Dynamics ◽  
Contact Points ◽  
Impact Impulse ◽  
2D And 3D ◽  
The Impact

Paradoxes in the impact dynamics of rigid bodies are known to arise in the presence of friction. We show here that, on specific occasions, in the absence of friction, the conservation laws of classical mechanics are also incompatible with the collisions of smooth, strictly convex rigid bodies. Under the assumption that the impact impulse is along the normal direction to the surface at the contact point, two convex rigid bodies that are well separated can come into contact, and then interpenetrate each other. This paradox can be demonstrated in both 2D and 3D when the collisions are tangential, in which case no momentum or energy transfer between the two bodies is possible. The postcollisional interpenetration can be realized through the contact points or through neighboring points only. The penetration distance is shown to be [Formula: see text]. The conclusion is that rigid-body dynamics is not compatible with the conservation laws of classical mechanics.

A Contact Force Solution for Non-Colliding Contact Dynamics Simulation

2006 ◽  
Author(s):  
Inna Sharf ◽  
Yuning Zhang
Keyword(s):  
Rigid Body ◽  
Contact Force ◽  
Contact Point ◽  
Closed Form Solution ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Contact Dynamics ◽  
Dynamics Simulation ◽  
Friction Forces ◽  
Contact Points

Rigid-body impact modeling remains an intensive area of research spurred on by new applications in robotics, biomechanics, and more generally multibody systems. By contrast, the modeling of non-colliding contact dynamics has attracted significantly less attention. The existing approaches to solve non-colliding contact problems include compliant approaches in which the contact force between objects is defined explicitly as a function of local deformation, and complementarity formulations in which unilateral constraints are employed to compute contact interactions (impulses or forces) to enforce the impenetrability of the contacting objects. In this article, the authors develop a novel approach to solve the non-colliding contact problem for objects of arbitrary geometry in contact at multiple points. Similarly to the complementarity formulation, the solution is based on rigid-body dynamics and enforces contact kinematics constraints at the acceleration level. Differently, it leads to an explicit closed-form solution for the normal forces at the contact points. Integral to the proposed formulation is the treatment of tangential contact forces, in particular the static friction. These friction forces must be calculated as a function of microslip velocity or displacement at the contact point. Numerical results are presented for three test cases: 1) a thin rod sliding down a stationary wedge; 2) a cube rotating off the stationary wedge under application of an external moment and 3) the cube and the wedge both moving under application of a moment. To ascertain validity and correctness, the solutions to frictionless and frictional scenarios obtained with the proposed formulation are compared to those generated by using a commercial simulation tool MSC ADAMS.

scholarly journals Cavitation between cylinder-liner and piston-ring in a new designed optical IC engine

2021 ◽  
pp. 146808742110080
Author(s):  
Jamshid Malekmohammadi Nouri ◽  
Ioannis Vasilakos ◽  
Youyou Yan
Keyword(s):  
High Speed ◽  
Contact Point ◽  
Cylinder Liner ◽  
Optical Methods ◽  
Engine Management System ◽  
Great Success ◽  
Ic Engine ◽  
Contact Points ◽  
Lubricant Flow ◽  
Cavitation Intensity

A new engine block with optical access has been designed and manufactured capable of running up to 3000 r/min with the same specification as the unmodified engine. The optical window allowed access to the full length of the liner over a width of 25 mm to investigate the lubricant flow and cavitation at contact point between the rings and cylinder-liner. In addition, it allowed good access into the combustion chamber to allow charged flow, spray and combustion visualisation and measurements using different optical methods. New custom engine management system with build in LabView allowed for the precise full control of the engine. The design of the new optical engine was a great success in producing high quality images of lubricant flow, cavitation formation and development at contact point at different engine speeds ranging from 208 to 3000 r/min and lubricant temperatures (30°C–70°C) using a high-speed camera. The results under motorised operation confirmed that there was no cavitation at contact points during the intake/exhaust strokes due to low in-cylinder presure, while during compression/expansion strokes, with high in-cylinder pressure, considerable cavities were observed, in particular, during the compression stroke. Lubricant temperatures had the effect of promoting cavities both in their intensity and covered ring area up to 50°C as expected. Beyond that, although the cavitation intensity increases further with temperature, its area reduces due to possible collapse of the cavitating bubbles at higher temperature. The change of engine speed from 208 to 800 r/min increased cavitating area considerably by 52% of the ring area and was further increased by 19% at 1000 r/min. After that, the results showed very small increase in cavitation area (1.3% at 2000 r/min) with similar intensity and distribution across the ring.

scholarly journals The macroscopic shape of assemblies formed from microparticles based on host–guest interaction dependent on the guest content

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Takahiro Itami ◽  
Akihito Hashidzume ◽  
Yuri Kamon ◽  
Hiroyasu Yamaguchi ◽  
Akira Harada
Keyword(s):  
Molecular Recognition ◽  
Smart Materials ◽  
Self Assembly ◽  
Early Stage ◽  
Contact Point ◽  
Sodium Acrylate ◽  
Contact Points ◽  
Assembly Behavior ◽  
Small Clusters ◽  
Macroscopic Shape

AbstractBiological macroscopic assemblies have inspired researchers to utilize molecular recognition to develop smart materials in these decades. Recently, macroscopic self-assemblies based on molecular recognition have been realized using millimeter-scale hydrogel pieces possessing molecular recognition moieties. During the study on macroscopic self-assembly based on molecular recognition, we noticed that the shape of assemblies might be dependent on the host–guest pair. In this study, we were thus motivated to study the macroscopic shape of assemblies formed through host–guest interaction. We modified crosslinked poly(sodium acrylate) microparticles, i.e., superabsorbent polymer (SAP) microparticles, with β-cyclodextrin (βCD) and adamantyl (Ad) residues (βCD(x)-SAP and Ad(y)-SAP microparticles, respectively, where x and y denote the mol% contents of βCD and Ad residues). Then, we studied the self-assembly behavior of βCD(x)-SAP and Ad(y)-SAP microparticles through the complexation of βCD with Ad residues. There was a threshold of the βCD content in βCD(x)-SAP microparticles for assembly formation between x = 22.3 and 26.7. On the other hand, the shape of assemblies was dependent on the Ad content, y; More elongated assemblies were formed at a higher y. This may be because, at a higher y, small clusters formed in an early stage can stick together even upon collisions at a single contact point to form elongated aggregates, whereas, at a smaller y, small clusters stick together only upon collisions at multiple contact points to give rather circular assemblies. On the basis of these observations, the shape of assembly formed from microparticles can be controlled by varying y.

Spatial Kinematic Analysis of Threaded Fastener Assembly

2005 ◽  
Vol 128 (1) ◽  
pp. 116-127 ◽  
Author(s):  
Stephen Wiedmann ◽  
Bob Sturges
Keyword(s):  
Design Space ◽  
Compliant Mechanisms ◽  
Contact Point ◽  
Three Dimensional ◽  
Vertical Movement ◽  
Initial Contact ◽  
Geometric Problem ◽  
Intelligent Sensor ◽  
Contact State ◽  
Contact Points

Compliant mechanisms for rigid part mating exist for prismatic geometries. A few instances are known of mechanisms to assemble screw threads. A comprehensive solution to this essentially geometric problem comprises at least three parts: parametric equations for nut and bolt contact in the critical starting phase of assembly, the possible space of motions between these parts during this phase, and the design space of compliant devices which accomplish the desired motions in the presence of friction and positional uncertainty. This work concentrates on the second part in which the threaded pair is modeled numerically, and contact tests are automated through software. Tessellated solid models were used during three-dimensional collision analysis to enumerate the approximate location of the initial contact point. The advent of a second contact point presented a more constrained contact state. Thus, the bolt is rotated about a vector defined by the initial two contact points until a third contact location was found. By analyzing the depth of intersection of the bolt into the nut as well as the vertical movement of the origin of the bolt reference frame, we determined that there are three types of contacts states present: unstable two-point, quasi-stable two-point, stable three point. The space of possible motions is bounded by these end conditions which will differ in detail depending upon the starting orientations. We investigated all potential orientations which obtain from a discretization of the roll, pitch, and yaw uncertainties, each of which has its own set of contact points. From this exhaustive examination, a full contact state history was determined, which lays the foundation for the design space of either compliant mechanisms or intelligent sensor-rich controls.

Multi-Agent Form Closure Capture of a Generic 2D Polygonal Object Based on Projective Path Planning

2006 ◽  
Author(s):  
Pankaj Sharma ◽  
Anupam Saxena ◽  
Ashish Dutta
Keyword(s):  
Path Planning ◽  
Contact Point ◽  
Point Contact ◽  
Object Boundary ◽  
Actual Object ◽  
Contact Points ◽  
Correct Orientation ◽  
Novel Approach ◽  
Form Closure ◽  
Multi Agent

The study of multi-agent capture and manipulation of an object has been an area of active interest for many researchers. This paper presents a novel approach using Genetic Algorithm to determine the optimal contact points and the total number of agents (mobile robots) required to capture a stationary generic 2D polygonal object. After the goal points are determined the agents then reach their respective goals using a decentralized projective path planning algorithm. Form closure of the object is obtained using the concept of accessibility angle. The object boundary is first expanded and the robots reach the expanded object goal points and then converge on the actual object. This ensures that the agents reach the actual goal points at the same time and have the correct orientation. Frictionless point contact between the object and robots is assumed. The shape of the robot is considered a circle such that it can only apply force in outward radial direction from its center and along the normal to the object boundary at the contact point. Simulations results are presented that prove the effectiveness of the proposed method.

Unraveling Paradoxical Theories for Rigid Body Collisions

1991 ◽  
Vol 58 (4) ◽  
pp. 1049-1055 ◽  
Author(s):  
W. J. Stronge
Keyword(s):  
Frictional Force ◽  
Contact Point ◽  
Tangential Velocity ◽  
Velocity Slip ◽  
Rigid Bodies ◽  
Contact Points ◽  
Before And After ◽  
Limited Applicability ◽  
Work Done ◽  
Impulsive Reaction

A collision between two rigid bodies has a normal impulsive reaction at the contact point (CP). If the bodies are slightly rough and the contact points have a relative tangential velocity (slip), there is also a frictional force that opposes slip. Small initial slip can halt before contact terminates; when slip halts the frictional force changes and the collision process is separated into periods before and after halting. An energetically consistent theory for collisions with slip that halts is based on the work done by normal (nonfrictional) forces during restitution and compression phases. This theory clearly separates dissipation due to frictional forces from that due to internal irreversible deformation. With this theory, both normal and tangential components of the impulsive reaction always dissipate energy during collisions. In contrast, Newton’s impact law results in calculations of paradoxical increases in energy for collisions where slip reverses. This law relates normal components of relative velocity for the CP at separation and incidence by a constant (the coefficient of restitution e). Newton’s impact law is a kinematic definition for e that generally depends on the slip process and friction; consequently it has limited applicability.

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