This project focuses on research into the solution of ultra-high degree polynomial systems that arise in the design of configuration manifolds for serial chains to support the conceptual design of new, complex mechanical systems. The set of design problems that compute these manifolds can be viewed as equivalent to the irreducible problems used in geometric constraint solvers found in modern computer-aided design systems. Rather than relate clusters of points and lines in the plane or space, these polynomial systems define configuration manifolds that constrain geometry in the six-dimensional configuration space of a rigid body. The research proposed here will yield an efficient system for specifying and computing these configuration manifolds that will make a fundamental contribution to the development of future computer-aided design systems. Research tasks focus on creating the methodology to support the integration of modern polynomial solution techniques into a mechanical system design environment. It is expected that the determination of all of the roots of high degree polynomial systems will yield thousands of design options for complex design tasks. The resulting rapid computation would allow the designer/inventor to vary the task requirements and immediately observe changes in the spectrum of design solutions, providing a powerful interactive design tool.
The broader impact resulting from this proposed activity include an expanded ability to invent products that provide controlled spatial movement. Future computer-aided design systems will provide the ability for designers to create mechanical movement as easily as they currently generate spatial shapes. This requires the ability to apply geometric constraint solvers to the six-dimensional configuration space of spatial movement. This new capability depends on the efficient computation of the configuration manifolds for serial chains. Leveraging the potential of this research with the efforts of others through an "open source" software coalition that is designed to integrate software solutions for various aspects of mechanical design will also be coordinated.
