A Perturbation Scheme for Spherical Arrangements with Application to Molecular Modeling

We describe a software package for computing and manipulating the subdivision of a sphere by a collection of (not necessarily great) circles and for computing the boundary surface of the union of spheres. We present problems that arise in the implementation of the software and the solutions that we have found for them. At the core of the paper is a novel perturbation scheme to overcome degeneracies and precision problems in computing spherical arrangements while using floating point arithmetic. The scheme is relatively simple, it balances between the efficiency of computation and the magnitude of the perturbation, and it performs well in practice. In one O(n) time pass through the data, it perturbs the inputs necessary to insure no potential degeneracies and then passes the perturbed inputs on to the geometric algorithm. We report and discuss experimental results. Our package is a major component in a larger package aimed to support geometric queries on molecular models; it is currently employed by chemists working in "rational drug design." The spherical subdivisions are used to construct a geometric model of a molecule where each sphere represents an atom. We also give an overview of the molecular modeling package and detail additional features and implementation issues.

Automatic Qualitative Modeling of Dynamic Physical Systems

This report describes MM, a computer program that can model a variety of mechanical and fluid systems. Given a system's structure and qualitative behavior, MM searches for models using an energy-based modeling framework. MM uses general facts about physical systems to relate behavioral and model properties. These facts enable a more focussed search for models than would be obtained by mere comparison of desired and predicted behaviors. When these facts do not apply, MM uses behavior-constrained qualitative simulation to verify candidate models efficiently. MM can also design experiments to distinguish among multiple candidate models.

Understanding and Modeling the Behavior of a Harmonic Drive Gear Transmission

In my research, I have performed an extensive experimental investigation of harmonic-drive properties such as stiffness, friction, and kinematic error. From my experimental results, I have found that these properties can be sharply non-linear and highly dependent on operating conditions. Due to the complex interaction of these poorly behaved transmission properties, dynamic response measurements showed surprisingly agitated behavior, especially around system resonance. Theoretical models developed to mimic the observed response illustrated that non-linear frictional effects cannot be ignored in any accurate harmonic-drive representation. Additionally, if behavior around system resonance must be replicated, kinematic error and transmission compliance as well as frictional dissipation from gear-tooth rubbing must all be incorporated into the model.