Geometric modeling for kinematics and inspection of multibody systems

对这一建议的简短描述可能是通过应用“力学中的几何”来“针对极端环境进行设计”。这样的环境包括一些不寻常的环境，比如活动脉的内部或热钢转炉，以及更普通的快速、精确的测量和材料处理系统，它们必须在恶劣的环境中运行。背景是申请人参加了NSERC/McGill设计工程教席的团队。问题通常是用几何方法解决的，通常是在尺寸大于3的空间中。几何方面的考虑是因为，例如，插入冠状动脉支架需要弯曲，而像道路涵洞一样，它必须径向僵硬。这种管子的穿孔图案是一种设计特征，它应该与其表面上的某些曲线相关，称为测地线。这些曲线或其合理近似出现在道路结构中，例如曲线上的管桥元件。相反，这里需要很高的抗弯强度。最后，这些(可能)最短的曲线出现在“面果”上，在规划路径时，只有肘关节和手腕关节的简单机械臂必须遵循这条路径，才能尽可能接近一条直线。这种联合安排不允许它准确地这样做。试着用手中的指针和你的上臂不动来做。如果后者看起来很琐碎，没有实际重要性，但它对于微型自动机器人挖掘机的运动编程仍然很有用，这些挖掘机用于准备维也纳和加尔各答等地的下水道重新铺设。这种面团坚果被称为圆环。这一点和二次曲面，称为二次曲面，在拟议研究的理论部分中扮演着主要的几何角色。例如，二次曲面的性质被用来揭示机器人中不应该存在的笨拙，即在具有足够多数量的专门为避免这种尴尬而设计的关节的机器人中。建议将这些技术扩展到其他类型的机械手和机器人系统，并扩展到圆柱形和类似形状零件的相机辅助精密测量。

A short description of this proposal might be "Design for Extreme Environments" via application of "Geometry in Mechanics". Such environments include unusual ones like the inside of a living artery or a hot steel convertor and the more ordinary fast, precise measurement and material handling systems that must operate in hostile surroundings. Context is the applicant's participation in the NSERC/McGill Design Engineering Chair's team. Problems are solved using geometric methods, often in spaces of dimension greater than 3. Geometric considerations arise because, for example, inserting a coronary stent requires it to bend while, like a road culvert, it must be radially stiff. The perforation pattern of this tube is a design feature that should be related to certain curves on its surface called geodesics. These curves, or fair approximations thereof, appear in roadway structures, e.g., elements of a tubular bridge on a curve. In contrast, here high bending strength is required. Finally these (possibly) shortest curves-on-the-"dough-nut" appear in planning the path that a simple robot arm, with only elbow and wrist joints, must follow to stay as close as possible to a straight line. This joint arrangement does not permit it to do so exactly. Try to do it with a pointer in your hand and your upper arm immobile. If the latter appears frivolous and without practical importance it was nevertheless useful for motion programming of a miniature, automated robotic excavator used to prepare sewers for relining in places like Vienna and Calcutta. The dough-nut is called a torus. This and surfaces of 2nd degree, called quadrics, play the major geometric role in the theoretical part of the proposed research. Properties of quadrics are used, for example, to reveal awkwardness in robots, called "singularity", where it should not exist; that is in robots with a more than sufficient number of joints designed specifically to avoid such embarassment. It is proposed to extend these techniques to other types of manupulators and robotic systems and also to the camera-aided precision metrology of cylindrical and similarly shaped parts.