AF:Medium:Collaborative:RUI:Structure in Motion:Algorithms for Kinematic Design

机器人（微型制造），计算生物学（DNA组装），材料科学（纳米技术），甚至折纸的新技术和技术在运动学设计中产生了新的问题？移动组件的设计。 该项目针对运动设计中的一些基本问题的理论和相应的算法。目标是设计（可变形）几何对象的形状，沿着其变形轨迹的一个或一个族。例如，在机器人技术中，人们可能希望构建一个能够将其末端执行器从源域中的任何点移动到目的域中的任何点的机器人手臂（几何结构设计），以避免奇点和碰撞（轨迹设计）的方式。在制造业和CAD中，人们对设计可以从标准的较小零件组装的结构感兴趣;例如，多面体表面可以由刚性三角形件组装而成，三角形件的边连接在一起。另一个例子是从一张有折痕的（平的）纸折叠3D折纸形状：3D形状和折叠轨迹都必须提前设计。预计这些结果将对正在使用几何建模和几何模拟的几个科学领域产生影响，包括力学、机器人、计算生物学和材料科学（纳米技术）。 该项目将吸引不同层次的学生（博士后、研究生和本科生）。PI将开发与新兴的多学科联系相关的新教材。新的运动学设计原则依赖于移动性和结构的相互依赖。PI机器人手臂奇异性和精确的位置工作空间确定的最新结果提供了一个综合的方法，协调结构参数和路径规划的见解和技术。对于具有拉胀能力的超材料的创新模式，周期性框架的严格几何理论将与框架生成和可视化的有效算法相结合。推进这些方法将为晶体的构象变化和生物自组装问题带来新的曙光。

New technologies and techniques in robotics (miniature fabrication), computational biology (DNA assembly), material science (nano-technology), and even origami give rise to new questions in kinematic design ? the design of moving assemblies. This project addresses the theory and corresponding algorithms for a number of fundamental problems in kinematic design. The goal is to design the shape of a (deformable) geometric object, along with one or a family of its deformation trajectories. In robotics, for instance, one may want to build a robot arm capable of moving its end-effector from any point in a source domain to any point in a destination domain (geometric structure design), in a way that would avoid singularities and collisions (trajectory design). In manufacturing and CAD, one is interested in designing structures that can be assembled from standard smaller parts; for example, a polyhedral surface might be assembled from rigid triangular pieces whose sides are joined together. Another example is folding a 3D origami shape from a creased piece of (flat) paper: both the 3D shape and the folding trajectories have to be designed in advance. The results are anticipated to have an impact on several scientific fields where geometric modeling and geometric simulations are being used, including mechanics, robotics, computational biology and materials science (nano-technology). The project will engage a diverse population of students, at all levels (post-doc, graduate and undergraduate). The PIs will develop new educational materials related to emerging multidisciplinary connections.New kinematic design principles rely on the mutual dependence of mobility and structure. Recent results of the PIs on robot-arm singularities and precise positional workspace determination provide insights and techniques for an integrated approach, which coordinates structural parameters and path-planning. For innovative patterns of metamaterials with auxetic capabilities, a rigorous geometric theory of periodic frameworks will be combined with efficient algorithms for framework generation and visualization. Advancing these methods will throw new light on conformational changes in crystals and biological self-assembly problems.