Rigid Body Collision Research Articles

Modeling the Interaction of Proximal Fragments for Destructive Atmospheric Entry Analysis

The destructive atmospheric entry process is distinguished by the formation of several fragments due to the severe aerothermal loads encountered during the descent. The proximity of debris leads to shock wave interactions and collisions between bodies, influencing the overall dynamics of the fragments and affecting the prediction of demise and ground impact location. To account for these effects, the use of computational fluid dynamics is introduced to resolve the shock interaction patterns by employing a quasi-steady approach, and the use of a simple rigid-body collision model is introduced to represent the dynamics of fragments in the cloud of debris. The quasi-steady approach is assessed and validated by comparative analysis with a few studies in the literature. One of these examples is the rebuilding of the VKI’s experiment of a free-flying ring crossing a shock wave generated by the presence of a stationary cylinder. The impact of explicitly modeling collision dynamics in the trajectory of fragments and ground spread distance is validated by considering a set of relevant test cases from the literature and tested them for destructive atmospheric reentry of the Attitude Vernier Upper Module, the launcher VEGA upper stage.

Impact crusher kinematics: The dynamics of an impact swing mechanism as an analytical-mathematical model

This study presents an analytical-mathematical model that elucidates the mechanics/kinematics of an impact crusher's impact swing mechanism. Essentially, this model comprises a series of mathematical descriptions and equations that are leveraged from established mechanical principles, such as rigid body kinematics, multibody dynamics, and collision laws, thus enabling comprehensive analytical exploration of the complex mechanical-kinematical system underlying the impact swing's mechanism, particularly focusing on the system-critical activation of this mechanism when triggered by an impacting non-fragile particle. The developments presented in this paper, supportively illustrated through detailed diagrams, provide relevant insights into the operational behaviour of modern impact crushers. This research therefore not only advances the theoretical understanding of system-critical crusher kinematics but also holds significant implications for the design and optimisation of future equipment. The resulting model's ability to analytically and mathematically delineate the complex mechanical-kinematical system of an impact swing mechanism not only facilitates efficient analyses but also circumvents the extensive and resource-intensive demands typically associated with numerical simulations of such systems. Consequently, this approach thereby forms substantial added value, particularly in the realm of engineering analysis.

Development of a virtual reality-based zygomatic implant surgery training system with global collision detection and optimized finite element method model

Background and objectiveZygomatic implant surgery is challenging due to the complex structure of the zygomatic bone, limited visual range during surgery, and lengthy implant path. Moreover, traditional training methods are costly, and experimental subjects are scarce. MethodsTo overcome these challenges, we propose a novel training system that integrates visual, haptic, and auditory feedback to create a more immersive surgical experience. The system uses dynamic bounding volume hierarchy (BVH) and Symplectic Euler to detect global collisions between surgical tools and models, while an optimized finite element method (FEM) model simulates soft tissue and detects collisions. Compared to previous works, our system achieves global rigid-body collisions between surgical tools and patient models, while also providing stable and realistic simulation and collisions of soft tissues. This advancement offers a more realistic simulation for zygomatic implant surgery. ResultsWe conducted three experiments and evaluations. The first experiment measured the axial force generated during the zygomatic implant simulation process and compared it with actual surgery, demonstrating the realistic force rendering feedback of our system. The second evaluation involved 15 novice surgeons who experienced the system and completed a questionnaire survey focusing on five aspects. The results showed satisfactory evaluations. The third experiment involved six surgeons who underwent in-depth training for two hours daily and were tested on the first, third, and fifth days. We collected data and combined it with the doctors' feedback to prove that our system can improve surgeons' proficiency in zygomatic implant surgery and provide a novel training solution for this procedure. ConclusionWe have innovatively integrated global collision detection and optimized soft tissue simulation into our system. Furthermore, we have conducted experimental validation to demonstrate the effectiveness of this implementation. We present a novel solution for zygomatic implant surgery training.

Inconsistencies in Modeling Impact with Friction by Algebraic Equations

This paper is concerned with inconsistent results that can be obtained when modeling rigid body collisions via algebraic equations. Newton’s approach is kinematic and fails in several cases. Poisson’s formulation has been shown lead to energetic inconsistencies, particularly in work done by the impulsive forces. This paper shows that the energetic formulation may lead to unexpected results in the magnitudes of the impulsive forces. These inconsistencies are due to the simplifying assumptions made to model collisions as occurring instantaneously. The inconsistencies increase as friction in the system becomes higher. We propose an optimization procedure for solving the algebraic equations of impact so that inconsistencies are minimized. Using experimental results, we present a discussion about the coefficients of restitution and friction.

Analysis and Testing of Rigid–Flexible Coupling Collision Harvesting Processes in Blueberry Plants

China possesses a vast territory, and the manual harvesting of blueberries is time-consuming and labor-intensive. Due to the planting agronomy differences in other countries, China needs to develop a domestic blueberry harvester to realize mechanical blueberry harvesting. In the harvesting process, “collision” is the core problem. Most of the literature has studied rigid body–rigid body collision, while few authors have studied rigid–flexible coupling collision mechanisms in the field of berry harvesting. In this paper, a rigid–flexible coupling collision model between the harvester and the blueberry plant was established based on the L-N nonlinear spring damping model (describing the collision force model between two colliding objects, consisting of the nonlinear spring and the damper) and improved the Coulomb model (the tangential collision force model), and the collision mechanism of blueberry harvesting was analyzed. The harvesting collision process was analyzed using both MATLAB and ADAMS software and the same conclusions were obtained: the collision force and fruit harvesting force were inversely proportional to the machine velocity but positively proportional to the rotational velocity of the hydraulic motor of the harvesting device. The following machine parameters were required to meet harvesting conditions: a harvesting device output rotational velocity of 120–150 r/min and a machine velocity of 40–50 m/min. A harvesting field test using a self-propelled blueberry harvester was conducted, which showed that the test results were consistent with the software simulation conclusions. When the machine velocity of the harvester and the output rotational velocity of the hydraulic motor were 45 m/min and 130 r/min, respectively, the machine provided optimum harvesting efficiency and fruit quality with the following optimum parameters: a harvesting efficiency of 5.1 kg/min, a raw fruit harvesting rate of 2.9%, and a damaged fruit harvesting rate of 3.6%. This research can lay the preliminary theoretical foundation for the analysis of a blueberry harvesting mechanism, and the research results can provide a theoretical reference for the harvesting of other similar berry shrubs.

Vibration-dependent cutting marks and redesign of crawler track of a multiblade saw

ABSTRACT High-speed wood sawing results in an uneven surface were evaluated. Machine structure was redesigned to reduce noise and unevenness of such sawing. A crawler track is driven by an auxiliary wheel. The roller seat on top of the board saw stabilises chain pieces. Investigations revealed some influencing mechanical factors, including static deformation, resonance excitation, and rigid body collision. A complete chain feed model was constructed to analyse related acoustic noise. Quantitative analysis enabled a successful redesign of chain feed elements. Chain feed simulation enabled the reduction of conflicting factors and revealed the optimal shape for chain links. The structural deformation of die casting indicated the possibility of variation in the chain shape. The flatness of the chain surface was reduced, and noise generated during the collision of links was minimised. Simplified modelling enabled identification of problems in the multi-blade system.

Bi-stability induced by motion limiting constraints on boring bar tuned mass dampers

This paper investigates the effect of displacement constraints on the attenuation performance of tuned mass dampers (TMDs) used in boring and turning applications. A simplified piecewise-smooth mechanical model is investigated through time domain simulations and hybrid periodic orbit continuation, first under harmonic excitation, then under regenerative cutting load. A quasi-frequency response function is derived for impacting TMDs through composition of different families of period-1 orbits, then an acceptability map for turning is formulated based on the appearance of cutting-edge contact-loss and fly-over events. The bi-stable domain boundaries are determined through two parameter continuation of contact-loss grazing events. It is shown that in both cases arising rigid body collisions can significantly hinder TMD damping performance and lead to resonance problems or machine tool chatter.

Dynamic modeling and beating phenomenon analysis of space robots with continuum manipulators

Space robotics has been used extensively in complex space missions. Rigid-manipulator space robots may suffer from rigid-body collisions with targets. This collision is likely to cause damage to the space robot and the target. To overcome such a problem, a novel Continuum-Manipulator Space Robot (CMSR) for performing on-orbit servicing missions is proposed in this paper. Compared with rigid-manipulator space robots, CMSRs are able to perform compliant operations and avoid rigid-body collisions with a target. The CMSR consists of two kinds of flexible components, including solar arrays and continuum manipulators. The elastic vibrations of these flexible components disturb the position and attitude of CMSRs. The beating phenomenon introduced by the energy transfer among these flexible components can cause damage to solar arrays. The complicated dynamic coupling poses enormous challenges in dynamic modeling and vibration analysis. The dynamic model for CMSRs is derived and the mechanism of the beating phenomenon is analyzed in this paper. Simulation results show that an obvious beating phenomenon occurs and the amplitude of the solar arrays increases significantly when the natural frequencies of two kinds of flexible components are close. A method is provided to avoid the beating phenomenon.

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

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.

Mitigating Peak Impact Forces by Customizing the Passive Foot Dynamics of Legged Robots

Abstract Impact forces are a destructive, yet common occurrence in legged locomotion. Every step produces a collision when the leg’s inertia stops as a result of ground contact. This results in peak forces and high-frequency vibrations that resonate through the system, damage components, and complicate control algorithms. Prior research considers how damping material, such as rubber, mitigates these effects. However, this paper shows the benefits of spring protection where both stiffness and maximum compression are customized to the leg. The spring mitigates the impact force peak by gradually bringing the leg’s inertia to rest. The maximum compression point (i.e., a hard stop) then provides a rigid surface that is ideal for stance. We provide a foot design methodology, validated through simulation and physical testing, that first considers springs in isolation, then in tandem with damping. We show that the coupling of springs and dampers reduces rigid body collisions and foot vibrations in a way that traditional methods—reliant on damping—have yet to achieve.

Local Optimization for Robust Signed Distance Field Collision

Signed distance fields (SDFs) are a popular shape representation for collision detection. This is due to their query efficiency, and the ability to provide robust inside/outside information. Although it is straightforward to test points for interpenetration with an SDF, it is not clear how to extend this to continuous surfaces, such as triangle meshes. In this paper, we propose a per-element local optimization to find the closest points between the SDF isosurface and mesh elements. This allows us to generate accurate contact points between sharp point-face pairs, and handle smoothly varying edge-edge contact. We compare three numerical methods for solving the local optimization problem: projected gradient descent, Frank-Wolfe, and golden-section search. Finally, we demonstrate the applicability of our method to a wide range of scenarios including collision of simulated cloth, rigid bodies, and deformable solids.

Verifying the tangential and normal restitution coefficients for double-sphere particles

The collision between a single-sphere and a double-sphere is measured in this study by a high speed camera to verify the fundamental issue of tangential and normal restitution coefficients for a particular shape of double-sphere. In this experiment, a single-sphere moves and collides on a stationary double-sphere, and a high speed camera is used to capture the collision of them. Numerous tests were performed by varying the pre-collisional inclinations and pre-collisional velocities of the single-sphere. Two different definitions of the kinematic coefficient of restitutions, both normal and tangential, have been scrutinized by the experimental data to see which one is realistically true or reasonable. After comparison, the contact-point (surface) based definition is the right one which has almost case-independent value for the restitution coefficient, either in the normal or tangential direction. This verifies a key point which would be very useful for modeling the rigid body collisions, either spherical or non-spherical.

Verification and Complement of EDR Speed Data through the Analysis of Real World Vehicle Collision Accidents

In this paper, two methods for practical verification and complementation of speed data stored in EDR are presented. Both methods are based on analyses of actual collision accidents and can be performed in parallel with conventional accident analysis procedure. One of the two methods uses video footage stored in vehicle-mounted camera (black box) to estimate the speed of vehicles. The other method is for performing optimal analysis based on vehicle collision model built in the range of rigid body dynamics. Through analyses of black box footage from actual collision accidents, it was confirmed that the estimated speed matched the data stored in EDR with high accuracy. Additionally, by using actual collision cases, the practicality of vehicle collision model-based speed estimation method was validated. In cases where video footage is not available, optimization method based on rigid body collision model can be used together with EDR data.

분석적으로 미분 가능한 시스템 동역학을 이용한 온라인 동작 합성 기법

In physics-based character animation, trajectory optimization has been widely adopted for automatic motion synthesis, through the prediction of an optimal sequence of future states of the character based on its system dynamics model. In general, the system dynamics model is neither in a closed form nor differentiable when it handles the contact dynamics between a character and the environment with rigid body collisions. Employing smoothed contact dynamics, researchers have suggested efficient trajectory optimization techniques based on numerical differentiation of the resulting system dynamics. However, the numerical derivative of the system dynamics model could be inaccurate unlike its analytical counterpart, which may affect the stability of trajectory optimization. In this paper, we propose a novel method to derive the closed-form derivative for the system dynamics by properly approximating the contact model. Based on the resulting derivatives of the system dynamics model, we also present a model predictive control (MPC)-based motion synthesis framework to robustly control the motion of a biped character according to on-line user input without any example motion data.

Particle-scale computational approaches to model dry and saturated granular flows of non-Brownian, non-cohesive, and non-spherical rigid bodies

We discuss methods to compute the flow of non-Brownian, non-cohesive, and non-spherical rigid bodies immersed in a single homogeneous fluid. We address both the case of negligible effect of the surrounding fluid corresponding to dry granular flows in which the dynamics of rigid bodies is controlled by gravity and collisions only, and the case of non-negligible effect of the surrounding fluid in which rigid bodies not only exchange momentum by collisions but also by two-way coupling with the surrounding fluid flow. We review the common computational methods to compute rigid body collisions and the two-way interaction of rigid bodies with the surrounding fluid flow. We specifically discuss the extension or applicability of these methods to non-spherical rigid bodies.

Three-dimensional Simulation on Collision Response of Ships

In order to enhance the realism and fidelity of the navigation simulator in ship collision response simulation, a technical solution for adding the Bullet physics engine to the three-dimensional visual simulation of the navigation simulator is proposed. Using rigid body dynamics theory, collision dynamics and energy conservation law to establish a three-dimensional collision mechanics model of ships. In the collision response phase, the Gauss-Seidel iterative algorithm is used to solve the real-time six-degree-of-freedom position and attitude parameters of the ship during the collision process, and the rendering update is synchronized in the 3D view. Experiments show that the scheme is feasible, and it can render ship collision scenes in real time and stably, and the collision process conforms to objective physical laws, which effectively improves the realism and fidelity of ship collision simulation in navigation simulator.

Thermophoretic force on nonspherical particles in the free-molecule regime.

The present paper is devoted to studying the thermophoresis of a nonspherical convex particle suspended in a gas with nonuniform temperature distribution in the free-molecule regime. Based on the gas kinetic theory and the assumption of a rigid-body collision for the gas-particle interaction, analytical expressions for the thermophoretic forces are obtained for several typical nonspherical bodies, including cylinders, spheroids, needles, disks, and cuboids. The orientation dependences of the thermophoretic forces and thermophoretic velocities are evaluated based on these expressions. It is found that the influence of the pitching effect of the nonspheres can be significant. The expressions for the orientation-averaged thermophoretic forces are also obtained under the assumption of a uniform particle orientation distribution.

Shear lift forces on nanocylinders in the free molecule regime

In the present paper, analytical formulae for the shear lift forces on nanocylinders moving in linear shear flows in the free molecule regime are derived on the basis of the gas kinetic theory. The model takes into account the intermolecular interactions between the nanocylinders and gas molecules, i.e., the non-rigid-body effect. It is shown that the resulting formulae are consistent with the previous theory in the limit of rigid-body collisions. The lift forces acting on carbon nanotubes and long-chain$n$-alkanes are evaluated as examples. It is found that the non-rigid-body effect is of great importance for small nanocylinders at low temperatures.

Wave-induced collisions of thin floating disks

Collisions between two thin floating disks forced by regular water waves are studied for a range of wave amplitudes and lengths, using laboratory wave basin experiments and a mathematical model. Three collision regimes are identified from the experiments in terms of collision frequency and strength, and the collisions are shown to be caused by drift for short incident wavelengths and relative surge motion between the disks for longer incident waves. The model is based on slope-sliding theory for the wave-induced disk motions and rigid-body collisions. It is shown to predict collision frequencies and velocities accurately for intermediate–long incident wavelengths. Incorporating drift and wave scattering forces into the model is shown to capture the collision behaviours for short incident wavelengths.

Thermophoretic force on nanocylinders in the free molecule regime.

We theoretically investigate the thermophoresis of nanocylinders in the free molecule regime, wherein the nonrigid-body effect is taken into account. The analytical formulas of the thermophoretic forces on cylinders suspended in both simple gases and binary gas mixtures are derived for the two limiting collision models, i.e., specular and diffuse scatterings, based on the gas kinetic theory. In the limit of the rigid-body collision, the expressions can be reduced to the theoretical results of Garcia-Ybarra and Rosner [AIChE J. 35, 139 (1989)10.1002/aic.690350115]. The thermophoretic velocities of the nanocylinders (including carbon nanotubes and long-chain n-alkanes) have been evaluated and it is found that the influence of the nonrigid-body effect on thermophoresis is significant for the case of small cylinder radius and low temperatures.