Collaborative Research: Variational Kinematic Geometry and Task Driven Mechanism Design in VR Environment

该奖项的研究目标是在虚拟环境中开发一种新的基于约束的任务驱动机制设计范式。 基于约束的几何建模变分几何的概念将从几何域扩展到运动域，用于表示和解决定义给定运动的运动约束。这有利于基于约束的分析，分类，并通过应用和调整现有的方法在计算形状分析领域的刚体运动的合成。可供选择的产品包括：（1）用于指定运动任务的B样条运动生成工具;（2）用于将指定的平面或球面运动转换成一组几何图元的新颖的运动轨迹分析工具;（3）基本平面或球面机构构造的数据库，该数据库根据它们可以生成的几何约束进行分类;以及（4）一个交互式的、虚拟现实（VR）使能的设计环境，将机构设计问题解决为形状识别和检索问题。如果成功，本研究的结果将导致一个新的，多学科框架称为“变分运动几何。“这将使机制设计中概念生成这一经常难以捉摸的任务变得更加容易处理。建议的设计环境将能够解决高度复杂的运动生成问题，而不需要从用户的运动学的先进知识。 研究结果将通过软件分发到其他领域，如生物力学、结构化学和蛋白质运动学，以及运动学发挥重要作用的微米和纳米系统。 虚拟设计工具将被用作教学和学习空间可视化和推理以及探索几何和运动之间相互作用的教育工具。拟议努力的教育和外联活动将有助于促进代表性不足的群体和高中学生对科学和工程的兴趣。

The research objective of this award is to develop a new, constraint based paradigm for task-driven mechanism design in a virtual environment. Concepts in variational geometry for constraint based geometric modeling will be extended from geometric domain to kinematic domain for representing and resolving kinematic constraints that define a given motion. This facilitates a constraint based analysis, classification, and synthesis of rigid body motions by applying and adapting existing methods in the field of computational shape analysis. Deliverables include: (1) a B-spline motion generation tool for specifying a motion task; (2) a novel motion trajectory analysis tool for converting a prescribed planar or spherical motion into a set of geometric primitives; (3) a database of basic planar or spherical mechanism constructs sorted by the geometric constraints that they can generate; and (4) an interactive, virtual-reality (VR) enabled design environment that solves the problem of mechanism design as a shape identification and retrieval problem.If successful, the results of this research will lead to a new, multidisciplinary framework called "Variational Kinematic Geometry." It will make the often elusive task of concept generation in mechanism design more tractable. The proposed design environment will be capable of solving highly complex motion generation problems without requiring advanced knowledge of kinematics from the user. The results will be disseminated through the software distribution to other fields such as biomechanics, structure chemistry and protein kinematics, as well as micro- and nano-systems, in which kinematics plays an important role. The virtual design tool will be used as an education tool for teaching and learning spatial visualization and reasoning and for exploring the interplay between geometry and motion. The education and outreach activities of the proposed effort will help promote interest for science and engineering from underrepresented groups and high school students.