基于Laplace变换的线性系统碰撞过程分析方法

探讨了用Laplace变换原理分析线性系统碰撞接触过程的一般方法．首先,建立了线性系统的碰撞模型,并导出了分析的基本原理及计算公式,同时还给出了与之对应的时域卷积分形式;然后,给出了集中质量、弹性杆、梁等子系统的传递函数,并以这些子系统之间的相互碰撞为分析实例。验证了该方法的有效性．分析结果表明传统的碰撞恢复系数远不能揭示碰撞过程的动力学现象,系统的动态特性和碰撞前的运动状态都强烈地影响着碰撞过程和碰撞后果;该方法具有概念明晰、通用性强、数值计算高效等优点,且能得到较多的解析结果．     

基于恢复系数的碰撞过程模型分析

论述了恢复系数的含义及作用,并在此基础上介绍了几种碰撞过程模型.通过详细推导恢复系数与模型参数之间的关系,使得不同的碰撞过程模型可统一用恢复系数表示能量损失,并用接触刚度表示变形.这也阐明了碰撞过程模型与刚性模型之间的区别和联系,把动态接触理论和古典碰撞理论统一了起来.通过对一个单球碰撞系统进行数值仿真,不仅验证了关系推导的正确性,而且对各种模型从精度、效率、微观接触过程等方面进行了比较.     

基于物理的虚拟手交互碰撞力觉生成和反馈

提出一种考虑摩擦的虚拟手交互碰撞力觉生成和反馈方法，以让用户手指感受到逼真的冲击，增强虚拟操作的真实性和沉浸感．该方法首先运用冲量定理和弹性恢复系数，求得质点刚体在二维空间碰撞后的运动状态，然后结合库仑定理，生成质点刚体有摩擦的碰撞力，并拓展到三维空间的虚拟环境中，计算非质点的虚拟刚体碰撞的力矩，再通过虚拟手静力抓持力觉生成模型，将碰撞力和碰撞力矩作用到虚拟手上，求得每个虚拟手指受到的冲击力．当虚拟手抓持的物体与其它虚拟物体发生碰撞时，利用CyberGrasp力觉反馈数据手套，用户手指可感受到逼真的冲击力．实验结果表明运用所提出的方法，用户在虚拟装配时可感受到真实的碰撞力．     

土壤碰撞问题的刚-散耦合动力学分析

本文以探测器着陆行星土壤为背景,对土壤碰撞问题进行刚-散耦合动力学建模与仿真分析研究.结合离散元方法和多体动力学方法,对半球壳装置土壤跌落问题进行耦合动力学仿真.通过与实验结果及有限元仿真结果对比,验证所采用离散元方法的有效性.分析了颗粒场中颗粒尺寸、恢复系数、静摩擦系数等参数,对碰撞中物体和颗粒场的碰撞加速度、碰撞持续时间、振动波形等动力学响应的影响.本研究将拓展对刚-散耦合动力学问题的理论认识,为探测器着陆系统的设计提供技术支持.     

多体系统动力学仿真中的接触碰撞模型分析

为了明确多体系统动力学仿真时接触碰撞模型的选择依据,对恢复系数模型,IMPACT函数模型,迟滞阻尼模型三种模型进行了分析讨论,并指出了模型中各参数的物理意义.最后以小球与平面碰撞问题为例,通过理论推导与试验相结合的方法确定了模型的参数,在ADAMS软件中进行了仿真计算,得到了三种模型的计算结果.计算结果表明,恢复系数方法只能得到碰撞后的速度;IMPACT函数模型可以得到较好的仿真结果,但是参数确定困难;修正的迟滞阻尼模型可以解决恢复系数接近1的接触问题.     

基于高性能计算的离散介质冲击过程

基于高性能计算平台,数值模拟离散介质冲击过程,研究颗粒的恢复系数随冲击速度、颗粒尺度分布的变化规律。结果发现,给定冲击速度时,无论单分散还是多分散颗粒,随着链长度增加,颗粒的恢复系数逐渐达到稳定,只与冲击速度以及所冲击的颗粒的尺寸比相关,并且压缩阶段的冲量是一个不随链长度变化的定值。在此状态下,入射颗粒与链冲击后的恢复系数尽管随冲击速度增加而减小,却远大于与无限大半空间固体壁面冲击的恢复系数。对于多分散链恢复系数,其分布呈现典型的高斯分布的形式,并且该分布与颗粒的初始冲击速度以及颗粒的粒径比有关。     

柔性圆柱杆接触碰撞实验研究

对两柔性圆柱铝杆纵向接触碰撞进行实验研究．为了深入研究接触碰撞过程中物体的动力学响应,设计了柔性体之间接触碰撞的实验方案,利用铝的导电性精确地测量碰撞的接触时间,利用激光多普勒测振仪非接触地测量接触碰撞过程中柔性杆上各点的速度响应,同时通过动态应变技术测量出接触点附近的应变变化历程．实验结果揭示了碰撞过程中杆上各点速度响应形成弹性波的现象,说明碰撞过程中弹性波传播效应不能忽略．并验证了实验方案的可行性和合理性．     

共线三球链问题的碰撞动力学研究

共线三球链的碰撞动力学问题能够展示多刚体系统碰撞问题的困难之一：非唯一解的问题.本文建立了三球链碰撞的Hertz接触模型,研究对其求解的数值算法,并用有限元模型（FEM）对其进行验证,研究表明：同线性模型比较,采用Hertz接触力模拟小球之间的接触力更接近有限元计算结果;在Hertz接触模型基础上,分析碰撞过程中接触力的变化过程;研究刚度比和质量比对于碰撞结束后各个小球运动状态的影响,并研究了两种刚体模型下碰撞次序假设成立的条件.     

凸多面体连续碰撞检测的运动轨迹分离轴算法

针对凸体间的连续碰撞检测,在距离算法(Gilbert-Johnson-Keerthi distance algorithm,GJK)基础上,提出一种采用运动轨迹分离轴计算的线性连续碰撞检测算法.该算法首先采用支撑点和投影技术,剔除必定不发生碰撞的物体,以加速碰撞检测的速度;然后,对可能发生碰撞的物体,计算2个凸体的Minkowski差集,所形成的凸包与运动路径执行GJK分离轴算法,实现在整个时间区间内一次性完成碰撞检测任务;最后,采用几何方法以及超平面与射线求解方式计算射线与凸体边界近交点,确定出第一次发生碰撞位置,并调整运动物体位置,完成碰撞响应过程.该算法不需要构造扫掠体,连续检测过程中不需要凸体间的求交计算.将文中算法应用于物体方向包围盒的连续碰撞检测,算法分析和实验结果表明,该算法对包围盒的连续碰撞检测具有较高检测精度和响应速度.     

一个计算凸多面体间碰撞点的快速算法

计算两个物体之间的碰撞点是碰撞响应的基础,也是一项系统开销很大的任务.因此,研究碰撞点快速求解算法对碰撞响应的实时性具有重要意义.该文提出了一个算法,当在虚拟环境中检测到碰撞时,应用此算法可以在碰撞响应之前快速计算出两个物体之间的准确碰撞时间,并能计算出此时两个物体之间的碰撞点.     

Impact dynamics of flexible-joint robots

In this paper the dynamic analysis of a flexible-joint robot colliding with its environments is presented. The system considered here is an n-rigidlink manipulator driven by n DC-motors through n revolute flexible-joints. The flexibility of each flexible joint is modelled as a linearly elastic torsional spring. 2n generalized coordinates are introduced to identify the configuration of the robot. The concept of impulse potential energy is introduced, and the generalized impulse-momentum equations along with the equation involving coefficient of restitution are used to establish the complete mathematic model for dealing with the case of a flexible-joint manipulator colliding with its environments (such as the ground, another manipulator, and so on). Solving for this mathematic model, one can obtain the jump discontinuities in system generalized velocities and the impulses at the impact points explicitly. To validate the algorithm presented in this paper, the dynamic simulation of a robot involving impact with its environments is given as an example.     

Influence of Reference Conditions on the Analysis of Impact-Induced Elastic Waves

Impact problems involving flexible bodies that undergo largerotations and translations were solved by using the floating frame ofreference approach. Analytically defined modes were selected to describedeformation. Different mode shapes can be used depending on the type ofattachment between the body frames of reference and the flexible bodies.Evaluating the kinematic coefficient of restitution during impactentails using the equivalent rigid body velocities of the flexiblebodies. In general, however, such velocities cannot be identified withreference velocities.When the colliding bodies can undergo large translations, freeattachments allow the use of mode shapes that possess zero totalmomentum. In this case, reference motion coincides with the equivalentrigid body motion of the flexible bodies and is not coupled to elasticmotion. When the colliding solids can rotate freely, the use of modeshapes with a zero angular momentum does not uncouple reference andelastic motion. However, if small deformation occurs during freerotation of the flexible body, the derivative of the reference angleremains roughly constant. Such a derivative can be interpreted as theequivalent angular velocity of the flexible body. When using a rigidattachment between the body frames of reference and the flexible bodies,reference motion does not coincide with the equivalent rigid bodyvelocity of the flexible bodies, which leads to non-constant referencevelocities when the bodies move freely. As a result, the equivalentrigid body velocities must be evaluated as linear combinations ofreference and elastic velocities.     

Analytic solution for planar indeterminate impact problems using an energy constraint

This work proposes an analytic method for resolving planar multi-point indeterminate impact problems for rigid-body systems. An event-based approach is used to detect impact events, and constraints consistent with the rigid-body assumption are used to resolve the indeterminacy associated with multi-point impact analysis. The work-energy relation is utilized to determine post-impact velocities based on an energetic coefficient of restitution to model energy dissipation, thereby yielding an energetically consistent set of post-impact velocities based on Stronge’s energetic coefficient of restitution for the treatment of rigid impacts. The effect of stick–slip transition is analyzed based on Coulomb friction. This paper also discusses the transition from impact to contact. This analysis is essential for considering the rocking block problem that is used as an example herein. The predictions of the model for the rocking block problem are compared to experimental results published in the literature. An example of a planar ball undergoing two-point impact is also presented.     

Three Approaches for Elastodynamic Contact in Multibody Systems

In machine dynamics impacts may occur by interaction of solid bodies. There is no doubt that the method of multibody systems is most efficient for the dynamical analysis of the overall motion. However, during impact energy is lost macromechanically measured by the coefficient of restitution. This coefficient has to be estimated from experiments and experience but cannot be computed within the multibody system approach. The impacts, on the other hand, are generating waves in the bodies which are propagating until they are vanishing due to material damping. These high frequency phenomena are analyzed using wave propagation, modal approach and finite elements. The results of the simulation on the fast time scale are used to compute the coefficient of restitution which is then fed back to the multibody system equations and the solution continues on the related slow time scale. The efficiency of the approach presented is shown for the impact of a steel sphere on four different shaped aluminum bodies of comparable mass. The simulation results are verified with experiments performed on different time scales, too. Using the impact of a double pendulum on a stop as example, the application of the multiscale approach to a multibody system is shown.     

Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincaré maps

The verge and foliot escapement mechanism of a mechanical clock is a classical example of a feedback regulator. In this paper we analyse the dynamics of this mechanism to understand its operation from a feedback perspective. Using impulsive differential equations and Poincaré maps to model the dynamics of this closed-loop system, we determine conditions under which the system possesses a limit cycle, and we analyse the period and amplitude of the oscillations in terms of the inertias of the colliding masses and their coefficient of restitution.     

Quadratic Contact Energy Model for Multi‐impact Simulation

Simultaneous multi‐impact simulation is a challenging problem that frequently arises in physically‐based modeling of rigid bodies. There are several physical criteria that should be satisfied for rigid body collision handling, but existing methods generally fail to meet one or more of them. In order to capture the inner process of potential energy variation, which is the physical foundation of collisions in a multi‐impact system, we present a novel quadratic contact energy model for rigid body simulation. By constructing quadratic energy functions with respect to the impulses, post‐impact reactions of rigid bodies can be computed efficiently. Our model can satisfy the physical criteria and can simulate various natural phenomena including the wave effect. Also, our model can be easily combined with Linear Complementary Problem (LCP) and can provide feasible results with any restitution coefficient. In practice, our model can solve the simultaneous multi‐impact problem efficiently and robustly, and we highlight its performance on different benchmarks.     

Impact controllability of an air hockey puck

In this paper, we investigate the controllability of an air hockey puck sliding on a frictionless table and subject to impacts from a mallet. This problem is a special case of the more general problem of impulsive manipulation. We first characterize the set of velocities reachable with arbitrary impulsive inputs. In reality, one cannot specify impulsive forces as inputs but rather only the velocity of a mallet impacting the puck. Therefore, we refine the characterization to the case that the impulsive forces arise through impacts with a mallet whose velocity can be arbitrarily controlled. The characterization of the reachable puck velocities then depends on the material properties of the impacting objects. We use the two-dimensional Routh impact model to determine these reachable velocities in terms of the coefficients of friction and restitution. We show that the system satisfies an accessibility-like property as long as the coefficient of friction is nonzero.     

Energetic consistency conditions for standard impacts

The paper studies the conditions under which Newtonian impacts lead to an energetically consistent post-impact state, and identifies the mechanisms responsible for a potential violation. Unilateral and bilateral geometric and kinematic constraints, as well as various Coulomb type friction elements are equipped with a kinematic restitution coefficient and are taken into account in the impact problem as normal cone inclusions. Based on the condition number of the Delassus operator, bounds on the impact coefficients are derived that ensure energetic consistency. As counter-examples, a slide-push mechanism is presented, and Kane??s example of a frictional impact at a double pendulum is analyzed.     

Velocity observers for linear mechanical systems subject to single non-smooth impacts

In this paper, we consider the problem of the velocity estimation from position measurement for linear mechanical systems (with multiple degrees of freedom) subject to single non-smooth impacts, both elastic and inelastic (i.e., with coefficient of restitution e=1 and e(0,1), respectively). Through a simple example, it is shown that a classical Luenberger observer is not able to reproduce instantaneously the jumps in the mass velocities, since it recovers the error induced by such jumps only asymptotically: an infinite sequence of impacts can prevent the estimation error to asymptotically go to zero. A new observer structure is proposed for linear mechanical systems subject to single unilateral constraints, that guarantees that the corresponding error dynamics are exponentially stable, also in presence of an infinite sequence of non-smooth impacts. The observer that we propose switches at the impact times, that can be recognized by position measurements only. To validate the proposed observer, both simulation and experimental tests have been carried out and are briefly reported, pointing out the drawbacks and advantages of the observer.