scholarly journals Rigid Body Dynamic Simulation With Multiple Convex Contact Patches

2018 ◽  
Author(s):  
Jiayin Xie ◽  
Nilanjan Chakraborty
Keyword(s):  
Dynamic Simulation ◽  
Contact Point ◽  
Equations Of Motion ◽  
Point Contact ◽  
Rigid Bodies ◽  
The State ◽  
Contact Patch ◽  
Rigid Body Dynamic ◽  
Mixed Complementarity Problem ◽  
Intermittent Contact

We present a principled method for dynamic simulation of rigid bodies in intermittent contact with each other where the contact is assumed to be a non-convex contact patch that can be modeled as a union of convex patches. The prevalent assumption in simulating rigid bodies undergoing intermittent contact with each other is that the contact is a point contact. In recent work, we introduced an approach to simulate contacting rigid bodies with convex contact patches (line and surface contact). In this paper, for non-convex contact patches modeled as a union of convex patches, we formulate a discrete-time mixed complementarity problem where we solve the contact detection and integration of the equations of motion simultaneously. Thus, our method is a geometrically-implicit method and we prove that in our formulation, there is no artificial penetration between the contacting rigid bodies. We solve for the equivalent contact point (ECP) and contact impulse of each contact patch simultaneously along with the state, i.e., configuration and velocity of the objects. We provide empirical evidence to show that if the number of contact patches between two objects is less than or equal to three, the state evolution of the bodies is unique, although the contact impulses and ECP may not be unique. We also present simulation results showing that our method can seamlessly capture transition between different contact modes like non-convex patch to point (or line contact) and vice-versa during simulation.

scholarly journals Modeling and Prediction of Rigid Body Motion with Planar Non-Convex Contact

2021 ◽  
pp. 1-17
Author(s):  
Jiayin Xie ◽  
Nilanjan Chakraborty
Keyword(s):  
Rigid Body ◽  
Dynamic Simulation ◽  
Contact Region ◽  
Contact Point ◽  
Single Point ◽  
Point Contact ◽  
Rigid Bodies ◽  
Body Motion ◽  
Contact Patch ◽  
Connected Set

Abstract We present a principled method for motion prediction via dynamic simulation for rigid bodies in intermittent contact with each other where the contact region is a planar non-convex contact patch. Such methods are useful in planning and control for robotic manipulation. The planar non-convex contact patch can either be a topologically connected set or disconnected set. Most work in rigid body dynamic simulation assume that the contact between objects is a point contact, which may not be valid in many applications. In this paper, by using the convex hull of the contact patch, we build on our recent work on simulating rigid bodies with convex contact patches for simulating motion of objects with planar non-convex contact patches. We formulate a discrete-time mixed complementarity problem where we solve the contact detection and integration of the equations of motion simultaneously. We solve for the equivalent contact point (ECP) and contact impulse of each contact patch simultaneously along with the state, i.e., configuration and velocity of the objects. We prove that although we are representing a patch contact by an equivalent point, our model for enforcing non-penetration constraints ensure that there is no artificial penetration between the contacting rigid bodies. We provide empirical evidence to show that our method can seamlessly capture transition among different contact modes like patch contact, multiple or single point contact.

scholarly journals Towards Dynamic Simulation Guided Optimal Design of Tumbling Microrobots

2019 ◽  
Author(s):  
Jiayin Xie ◽  
Chenghao Bi ◽  
David J. Cappelleri ◽  
Nilanjan Chakraborty
Keyword(s):  
Optimal Design ◽  
Dynamic Simulation ◽  
Point Contact ◽  
Small Scale ◽  
Trial And Error ◽  
Rigid Body Dynamic ◽  
Simulation Tools ◽  
Different Shapes ◽  
Body Dynamic ◽  
Two Bodies

Abstract Design of robots at the small scale is a trial-and-error based process, which is costly and time-consuming. There are no good dynamic simulation tools to predict the motion or performance of a microrobot as it moves against a substrate. At smaller length scales, the influence of adhesion and friction, which scales with surface area, becomes more pronounced. Thus, rigid body dynamic simulators, which implicitly assume that contact between two bodies can be modeled as point contact are not suitable. In this paper, we present techniques for simulating the motion of microrobots where there can be intermittent and non-point contact between the robot and the substrate. We use this simulator to study the motion of microrobots of different shapes and select shapes that are most promising for performing a given task.

scholarly journals Dynamic Simulation-Guided Design of Tumbling Magnetic Microrobots

2021 ◽  
pp. 1-26
Author(s):  
Jiayin Xie ◽  
Chenghao Bi ◽  
David J. Cappelleri ◽  
Nilanjan Chakraborty
Keyword(s):  
Dynamic Simulation ◽  
Point Contact ◽  
Small Scale ◽  
Incline Angle ◽  
Performance Simulation ◽  
Rigid Body Dynamic ◽  
Simulation Tools ◽  
Different Shapes ◽  
Magnetic Microrobots ◽  
Body Dynamic

Abstract Design of robots at the small scale is a trial-and-error based process, which is costly and time-consuming. There are few dynamic simulation tools available to accurately predict the motion or performance of untethered microrobots as they move over a substrate. At smaller length scales, the influence of adhesion and friction, which scales with surface area, becomes more pronounced. Thus, rigid body dynamic simulators, which implicitly assume that contact between two bodies can be modeled as point contact are not suitable. In this paper, we present techniques for simulating the motion of microrobots where there can be intermittent and non-point contact between the robot and the substrate. We use these techniques to study the motion of tumbling microrobots of different shapes and select shapes that are optimal for improving locomotion performance. Simulation results are verified using experimental data on linear velocity, maximum climbable incline angle, and microrobot trajectory. Microrobots with improved geometry were fabricated, but limitations in the fabrication process resulted in unexpected manufacturing errors and material/size scale adjustments. The developed simulation model is able to incorporate these limitations and emulate their effect on the microrobot's motion, reproducing the experimental behavior of the tumbling microrobots, further showcasing the effectiveness of having such a dynamic model.

Wheel-Rail Multi-Point Contact Method for Railway Turnouts

2011 ◽  
Vol 97-98 ◽  
pp. 378-381
Author(s):  
Zhi Wei Chen ◽  
Linan Li ◽  
Shi Gang Sun ◽  
Jun Long Zhou
Keyword(s):  
Calculation Method ◽  
Normal Force ◽  
Contact Point ◽  
Point Contact ◽  
Contact Model ◽  
Contact Method ◽  
Elastic Contact ◽  
Simulation Calculation ◽  
Acute Change

A calculation method of wheel-rail multi-point contact based on the elastic contact model is introduced. Moreover, the simulation calculation of vehicles passing through branch lines of No.18 turnouts is carried out. The result showed that the acute change of wheel-rail normal force caused by the transfers of wheel-rail contact point between two rails can be avoid by wheel-rail multi-point contact method, and the transfers of wheel-rail normal force between two rails is smoother. The validity of wheel-rail multi-point contact method is verified.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

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.

STUDYING THE CONTACT POINT AND INTERFACE MOVING IN A SINUSOIDAL TUBE WITH LATTICE BOLTZMANN METHOD

2001 ◽  
Vol 15 (09) ◽  
pp. 1287-1303 ◽  
Author(s):  
HAI-PING FANG ◽  
LE-WEN FAN ◽  
ZUO-WEI WANG ◽  
ZHI-FANG LIN ◽  
YUE-HONG QIAN
Keyword(s):  
Boundary Conditions ◽  
Contact Line ◽  
Lattice Boltzmann ◽  
Complex Geometry ◽  
Contact Point ◽  
Point Contact ◽  
Immiscible Fluids ◽  
Lattice Boltzmann Model ◽  
Stick Slip ◽  
Bounce Back

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimension) is studied. Due to the roughness of the boundary, the contact point shows "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are non-wetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple menisci. The velocity is found to vary considerably between the neighbor nodes close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found different for different boundary conditions. The simple bounce-back rule makes the contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in comparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.

scholarly journals Novel analysis methods of dynamic properties for vehicle pantographs

2018 ◽  
Vol 180 ◽  
pp. 01005 ◽  
Author(s):  
Andrzej Wilk
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Simulation ◽  
High Speed ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Computer Software ◽  
Fem Analysis ◽  
Electrical Energy ◽  
Modern Approach ◽  
Static And Dynamic Analysis

Transmission of electrical energy from a catenary system to traction units must be safe and reliable especially for high speed trains. Modern pantographs have to meet these requirements. Pantographs are subjected to several forces acting on their structural elements. These forces come from pantograph drive, inertia forces, aerodynamic effects, vibration of traction units etc. Modern approach to static and dynamic analysis should take into account: mass distribution of particular parts, physical properties of used materials, kinematic joints character at mechanical nodes, nonlinear parameters of kinematic joints, defining different parametric waveforms of forces and torques, and numerical dynamic simulation coupled with FEM calculations. In this work methods for the formulation of the governing equations of motion are presented. Some of these methods are more suitable for automated computer implementation. The novel computer methods recommended for static and dynamic analysis of pantographs are presented. Possibilities of dynamic analysis using CAD and CAE computer software are described. Original results are also presented. Conclusions related to dynamic properties of pantographs are included. Chapter 2 presents the methods used for formulation of the equation of pantograph motion. Chapter 3 is devoted to modelling of forces in multibody systems. In chapter 4 the selected computer tools for dynamic analysis are described. Chapter 5 shows the possibility of FEM analysis coupled with dynamic simulation. In chapter 6 the summary of this work is presented.

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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