COGEM: Constrained Geometric Morphing of Product Families in Mechanical Design

本项目提出约束几何变形（COGEM）作为一种新的通用机械设计框架，允许通过形状变形（变形）程序对任意复杂的基线设计进行直观的几何修改，同时保留关键的规定几何参数。该项目的目标是为COGEM提供新的理论和计算基础，以实现对现有基线设计的直观和有效的几何修改，以满足新的功能需求。预期的方法将为复杂机械系统产品族的几何设计提供正式的基础，并将得到计算算法发展的支持。更广泛地说，每次参数更新都可以用一系列形状变形来表示，这意味着约束形状变形可以被认为是参数化设计的一种推广，并可能导致一门新学科的出现。提出的研究将使学生能够快速探索超出当前参数化实体建模技术能力的设计空间。同时，将几何推理和算法设计整合到工程课程中，将有助于培养新一代的工程师，他们将能够利用现代计算机辅助设计技术与传统机械工程专业知识相结合的潜力。

This project proposes Constrained Geometric Morphing (COGEM) as a novel generic mechanical design framework that will allow intuitive geometric modifications of arbitrarily complex baseline designs via shape morphing (deformation) procedures while preserving key prescribed geometric parameters. The goal of the project is to provide new theoretical and computational foundations for COGEM to enable intuitive and efficient geometric modifications of existing baseline designs to satisfy new functional requirements. The anticipated approach will lead to formal foundations for the geometric design of product families of complex mechanical systems, and will be supported by the development of computational algorithms. More broadly, the fact that every parametric update can be expressed in terms of a sequence of shape deformations implies that constrained shape deformation can be thought of as a generalization of parametric design, and could potentially lead to the emergence of a new discipline. The proposed research will enable students to quickly explore the design spaces above and beyond the current capabilities of parametric solid modeling technology. At the same time, the integration of geometric reasoning and algorithmic design into the engineering curriculum will help develop a new generation of engineers that will be able to exploit the potential of modern computer aided design technology in conjunction with traditional mechanical engineering expertise.