Simulating Hard Rigid Bodies

Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in condensed matter. The next level of description is to consider particles as rigid objects of generic shape, which would enrich the possible phenomenology enormously. This kind of modeling will prove to be interesting in all those situations in which steric effects play a relevant role. These include biology, soft matter, granular materials and molecular systems. With a view to developing a general recipe for event-driven Molecular Dynamics simulations of hard rigid bodies, two algorithms for calculating the distance between two convex hard rigid bodies and the contact time of two colliding hard rigid bodies solving a non-linear set of equations will be described. Building on these two methods, an event-driven molecular dynamics algorithm for simulating systems of convex hard rigid bodies will be developed and illustrated in details. In order to optimize the collision detection between very elongated hard rigid bodies, a novel nearest-neighbor list method based on an oriented bounding box will be introduced and fully explained. Efficiency and performance of the new algorithm proposed will be extensively tested for uniaxial hard ellipsoids and superquadrics. Finally applications in various scientific fields will be reported and discussed.Comment: 36 pages, 17 figure

A Collision Detection Algorithm For Virtual Robot-Centered Flexible Manufacturing Cell

Collision detection is crucial in virtual manufacturing applications such as virtual prototyping, virtual assembly and virtual robot path planning. For accurate simulation of manufacturing systems and processes in virtual environment, physical interaction with the objects in the scene are triggered by collision detection. This thesis presents a collision detection algorithm for accurate simulation of a virtual flexible manufacturing cell. The technique utilizes the narrow phase approach in detecting collision detection of non-convex object by testing collision between basic primitive and polygon. This algorithm is implemented in a virtual flexible manufacturing cell for the loading and unloading process performed by the robot. The robot’s gripper is treated as non-convex object and the exact point of collision is represented with a virtual sphere and collision is tested between the virtual sphere and the polygon. To verify the collision detection algorithm, it is tested with different positions and heights of the storage system during simulation of the virtual flexible manufacturing cell. The results showed that the collision detection algorithm can be used to support the concept of hardware reconfigurablility of FMC which can be achieved by changing, removing, recombining or rearranging its manufacturing elements in order to meet new demands such as introduction of new product or change

PHYSICS-BASED SHAPE MORPHING AND PACKING FOR LAYOUT DESIGN

The packing problem, also named layout design, has found wide applications in the mechanical engineering field. In most cases, the shapes of the objects do not change during the packing process. However, in some applications such as vehicle layout design, shape morphing may be required for some specific components (such as water and fuel reservoirs). The challenge is to fit a component of sufficient size in the available space in a crowded environment (such as the vehicle under-hood) while optimizing the overall performance objectives of the vehicle and improving design efficiency. This work is focused on incorporating component shape design into the layout design process, i.e. finding the optimal locations and orientations of all the components within a specified volume, as well as the suitable shapes of selected ones. The first major research issue is to identify how to efficiently and accurately morph the shapes of components respecting the functional constraints. Morphing methods depend on the geometrical representation of the components. The traditional parametric representation may lend itself easily to modification, but it relies on assumption that the final approximate shape of the object is known, and therefore, the morphing freedom is very limited. To morph objects whose shape can be changed arbitrarily in layout design, a mesh based morphing method based on a mass-spring physical model is developed. For this method, there is no need to explicitly specify the deformations and the shape morphing freedom is not confined. The second research issue is how to incorporate component shape design into a layout design process. Handling the complete problem at once may be beyond our reach,therefore decomposition and multilevel approaches are used. At the system level, a genetic algorithm (GA) is applied to find the positions and orientations of the objects, while at the sub-system or component level, morphing is accomplished for select components. Although different packing applications may have different objectives and constraints, they all share some common issues. These include CAD model preprocessing for packing purpose, data format translation during the packing process if performance evaluation and morphing use different representation methods, efficiency of collision detection methods, etc. These common issues are all brought together under the framework of a general methodology for layout design with shape morphing. Finally, practical examples of vehicle under-hood/underbody layout design with the mass-spring physical model based shape morphing are demonstrated to illustrate the proposed approach before concluding and proposing continuing work

Articular human joint modelling

Copyright @ Cambridge University Press 2009.The work reported in this paper encapsulates the theories and algorithms developed to drive the core analysis modules of the software which has been developed to model a musculoskeletal structure of anatomic joints. Due to local bone surface and contact geometry based joint kinematics, newly developed algorithms make the proposed modeller different from currently available modellers. There are many modellers that are capable of modelling gross human body motion. Nevertheless, none of the available modellers offer complete elements of joint modelling. It appears that joint modelling is an extension of their core analysis capability, which, in every case, appears to be musculoskeletal motion dynamics. It is felt that an analysis framework that is focused on human joints would have significant benefit and potential to be used in many orthopaedic applications. The local mobility of joints has a significant influence in human motion analysis, in understanding of joint loading, tissue behaviour and contact forces. However, in order to develop a bone surface based joint modeller, there are a number of major problems, from tissue idealizations to surface geometry discretization and non-linear motion analysis. This paper presents the following: (a) The physical deformation of biological tissues as linear or non-linear viscoelastic deformation, based on spring-dashpot elements. (b) The linear dynamic multibody modelling, where the linear formulation is established for small motions and is particularly useful for calculating the equilibrium position of the joint. This model can also be used for finding small motion behaviour or loading under static conditions. It also has the potential of quantifying the joint laxity. (c) The non-linear dynamic multibody modelling, where a non-matrix and algorithmic formulation is presented. The approach allows handling complex material and geometrical nonlinearity easily. (d) Shortest path algorithms for calculating soft tissue line of action geometries. The developed algorithms are based on calculating minimum ‘surface mass’ and ‘surface covariance’. An improved version of the ‘surface covariance’ algorithm is described as ‘residual covariance’. The resulting path is used to establish the direction of forces and moments acting on joints. This information is needed for linear or non-linear treatment of the joint motion. (e) The final contribution of the paper is the treatment of the collision. In the virtual world, the difficulty in analysing bodies in motion arises due to body interpenetrations. The collision algorithm proposed in the paper involves finding the shortest projected ray from one body to the other. The projection of the body is determined by the resultant forces acting on it due to soft tissue connections under tension. This enables the calculation of collision condition of non-convex objects accurately. After the initial collision detection, the analysis involves attaching special springs (stiffness only normal to the surfaces) at the ‘potentially colliding points’ and motion of bodies is recalculated. The collision algorithm incorporates the rotation as well as translation. The algorithm continues until the joint equilibrium is achieved. Finally, the results obtained based on the software are compared with experimental results obtained using cadaveric joints

Efficient contact determination between geometric models

http://archive.org/details/efficientcontact00linmN