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Physically-based Real-Time 3-D Simulation of Hoses for Virtual Automation Systems
Abstract
Current simulation systems for virtual automation usually ignore the simulation of cables and hoses. Cable simulations are commonly very specialized systems i.e. for laying cables in cars. Our approach adds a new aspect to the simulation of virtual automation systems by additionally simulating one-dimensional flexible objects like hoses and cables. The approach is physically-based and fast enough to work even in large automation systems. We describe the theoretical concepts for our mass-spring approach and identify the necessary physical parameters. In a detailed evaluation we measured the physical parameters and compared the form and characteristics of a real hose with the simulation as well as with a pure mathematical approach. Besides analysing the behaviour we evaluated the run-time performance to ensure real-time performance of the overall system.
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In this paper, we present a system for simulating one dimensional flexible parts such as cables or hoses. The modeling of bending and torsion follows the Cosserat model. For this purpose we use a generalized spring-mass system and describe its configuration by a care- fully chosen set of coordinates. Gravity and contact forces as well as the forces responsible for length conservation are expressed in Cartesian coordinates. But bending and torsion effects can be dealt with more effectively by using quaternions to represent the orientation of the segments joining two neighboring mass points. This augmented system allows an easy formulation of all interactions with the best appropriate coordinate type and yields a strongly banded Hessian matrix. An energy minimizing process accounts for a solution exempt from the oscillations that are typical of spring-mass systems. The whole system is numerically stable and can be solved at interactive frame rates. It is integrated in a Virtual Reality Software for use in applications such as cable routing and assembly simulation.
In this paper, the modelling strategy of a Cosserat rod element (CRE) is addressed systematically for 3-dimensional dynamical analysis of slender structures. We employ the exact nonlinear kinematic relationships in the sense of Cosserat theory, and adopt the Bernoulli hypothesis. For the sake of simplicity, the Kirchoff constitutive relations are adopted to provide an adequate description of elastic properties in terms of a few elastic moduli. A deformed configuration of the rod is described by the displacement vector of the deformed centroid curves and an orthonormal moving frame, rigidly attached to the cross-section of the rod. The position of the moving frame relative to the inertial frame is specified by the rotation matrix, parametrized by a rotational vector. The approximate solutions of the nonlinear partial differential equations of motion in quasi-static sense are chosen as the shape functions with up to third order nonlinear terms of generic nodal displacements. Based on the Lagrangian constructed by the Cosserat kinetic energy and strain energy expressions, the principle of virtual work is employed to derive the ordinary differential equations of motion with third order nonlinear generic nodal displacements. A simple example is presented to illustrate the use of the formulation developed here to obtain the lower order nonlinear ordinary differential equations of motion of a given structure. The corresponding nonlinear dynamical responses of the structures have been presented through numerical simulations by Matlab software.