Fast Simulation of Mass-Spring Systems

We describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. This scheme provides a fast solution for classical linear (Hookean) springs. We express the widely used implicit Euler method as an energy minimization problem and introduce spring directions as auxiliary unknown variables. The system is globally linear in the node positions, and the non-linear terms involving the directions are strictly local. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. Our method converges to the same final result as would be obtained by solving the standard form of implicit Euler using Newton’s method. Although the asymptotic convergence of Newton’s method is faster than ours, the initial ratio of work to error reduction with our method is much faster than Newton’s. For real-time visual applications, where speed and stability are more important than precision, we obtain visually acceptable results at a total cost per timestep that is only a fraction of that required for a single Newton iteration. When higher accuracy is required, our algorithm can be used to compute a good starting point for subsequent Newton’s iteration

Inverse problems for Jacobi operators II: Mass perturbations of semi-infinite mass-spring systems

We consider an inverse spectral problem for infinite linear mass-spring systems with different configurations obtained by changing the first mass. We give results on the reconstruction of the system from the spectra of two configurations. Necessary and sufficient conditions for two real sequences to be the spectra of two modified systems are provided.Comment: 25 pages, 2 figures. Typos were corrected, two remarks were added, material added to Sec.

A flexible rotor on flexible supports: modeling & experiments

In this study, a flexible rotor with variable support stiffness has been analyzed. Simple support models consisting of mass, spring systems are extracted from modal analysis of the isolated support and by applying static loads to the finite element model of the supports. The derived equivalent models of the supports are then implemented in the finite element based structural model which predicts the dynamic behavior of the rotor. Finally experimental modal analysis of the rotor is performed with different support stiffnesses. The experimental and theoretical results have been compared and different support modeling approaches have been examined

Approximate analysis of two-mass–spring systems and buckling of a column

AbstractMax–Min Approach (MMA) is applied to obtain an approximate solution of three practical cases in terms of a nonlinear oscillation system. After finding maximal and minimal solution thresholds of a nonlinear problem, an approximate solution of the nonlinear equation can be easily achieved using He Chengtian’s interpolation. Numerical results indicate the effectiveness of the proposed method both in respect of the whole range of involved parameters as well as the excellent agreement with the approximate frequencies and periodic solutions with the exact ones. It is predicted that MMA can be found widely applicable in engineering

Efficient techniques for soft tissue modeling and simulation

Performing realistic deformation simulations in real time is a challenging problem in computer graphics. Among numerous proposed methods including Finite Element Modeling and ChainMail, we have implemented a mass spring system because of its acceptable accuracy and speed. Mass spring systems have, however, some drawbacks such as, the determination of simulation coefficients with their iterative nature. Given the correct parameters, mass spring systems can accurately simulate tissue deformations but choosing parameters that capture nonlinear deformation behavior is extremely difficult. Since most of the applications require a large number of elements i. e. points and springs in the modeling process it is extremely difficult to reach realtime performance with an iterative method. We have developed a new parameter identification method based on neural networks. The structure of the mass spring system is modified and neural networks are integrated into this structure. The input space consists of changes in spring lengths and velocities while a "teacher" signal is chosen as the total spring force, which is expressed in terms of positional changes and applied external forces. Neural networks are trained to learn nonlinear tissue characteristics represented by spring stiffness and damping in the mass spring algorithm. The learning algorithm is further enhanced by an adaptive learning rate, developed particularly for mass spring systems. In order to avoid the iterative approach in deformation simulations we have developed a new deformation algorithm. This algorithm defines the relationships between points and springs and specifies a set of rules on spring movements and deformations. These rules result in a deformation surface, which is called the search space. The deformation algorithm then finds the deformed points and springs in the search space with the help of the defined rules. The algorithm also sets rules on each element i. e. triangle or tetrahedron so that they do not pass through each other. The new algorithm is considerably faster than the original mass spring systems algorithm and provides an opportunity for various deformation applications. We have used mass spring systems and the developed method in the simulation of craniofacial surgery. For this purpose, a patient-specific head model was generated from MRI medical data by applying medical image processing tools such as, filtering, the segmentation and polygonal representation of such model is obtained using a surface generation algorithm. Prism volume elements are generated between the skin and bone surfaces so that different tissue layers are included to the head model. Both methods produce plausible results verified by surgeons

A closed-loop digitally controlled MEMS gyroscope with unconstrained Sigma-Delta force-feedback

In this paper, we describe the system architecture and prototype measurements of a MEMS gyroscope system with a resolution of 0.025 degrees/s/root Hz. The architecture makes extensive use of control loops, which are mostly in the digital domain. For the primary mode both the amplitude and the resonance frequency are tracked and controlled. The secondary mode readout is based on unconstrained Sigma Delta force-feedback, which does not require a compensation filter in the loop and thus allows more beneficial quantization noise shaping than prior designs of the same order. Due to the force-feedback, the gyroscope has ample dynamic range to correct the quadrature error in the digital domain. The largely digital setup also gives a lot of flexibility in characterization and testing, where system identification techniques have been used to characterize the sensors. This way, a parasitic direct electrical coupling between actuation and readout of the mass-spring systems was estimated and corrected in the digital domain. Special care is also given to the capacitive readout circuit, which operates in continuous time