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

该奖项的研究目标是为虚拟环境中的任务驱动机制设计开发一种新的、基于约束的范式。基于约束的几何建模的变分几何概念将从几何域扩展到运动学域，以表示和解决定义给定运动的运动学约束。通过应用和适应计算形状分析领域的现有方法，这有助于基于约束的刚体运动分析、分类和综合。可交付成果包括：(1)用于指定运动任务的b样条运动生成工具；(2)一种新的运动轨迹分析工具，可将规定的平面或球面运动转换为一组几何基元；(3)根据所能产生的几何约束进行排序的基本平面或球面机构结构数据库；(4)交互式虚拟现实（VR）设计环境，将机构设计问题作为形状识别和检索问题解决。如果成功，这项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”。它将使机构设计中经常难以捉摸的概念生成任务变得更加容易处理。提出的设计环境将能够解决高度复杂的运动生成问题，而不需要用户的高级运动学知识。研究结果将通过软件分发传播到其他领域，如生物力学，结构化学和蛋白质运动学，以及微纳米系统，其中运动学起着重要作用。虚拟设计工具将用作教学和学习空间可视化和推理的教育工具，并用于探索几何和运动之间的相互作用。拟议努力的教育和推广活动将有助于提高代表性不足的群体和高中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.