Geometric modeling for kinematics and inspection of multibody systems

这个建议的简短描述可以是“极端环境的设计”，通过“力学中的几何”的应用。这些环境包括不寻常的环境，比如活动脉或热钢转炉内部，以及必须在恶劣环境中运行的更普通的快速、精确的测量和材料处理系统。背景是申请人在NSERC/麦吉尔设计工程主席团队中的参与情况。使用几何方法解决问题，通常在维度大于3的空间中。几何上的考虑是由于，例如，插入冠状动脉支架需要弯曲，而像道路涵洞一样，它必须是径向刚性的。这种管的射孔模式是一种设计特征，它应该与其表面上的某些曲线（称为测地线）有关。这些曲线或近似曲线出现在巷道结构中，例如，曲线上的管状桥的构件。相反，这里需要高的抗弯强度。最后，“甜甜圈”上的这些（可能）最短曲线出现在规划路径时，一个只有肘部和腕部关节的简单机器人手臂必须遵循尽可能接近直线的路径。这种联合安排并不完全允许它这样做。试着在你的手上拿着一个指针，你的上臂不动。如果后者看起来很无聊，没有实际意义，但它对于微型自动机器人挖掘机的运动编程是有用的，用于维也纳和加尔各答等地的下水道修复。甜甜圈被称为环面。这和二次曲面，称为二次曲面，在提出的研究的理论部分起着主要的几何作用。例如，二次曲面的性质被用来揭示机器人的尴尬，称为“奇点”，它不应该存在；这种情况发生在机器人身上，它们有足够多的关节，专门设计来避免这种尴尬。建议将这些技术扩展到其他类型的机械手和机器人系统，以及圆柱和类似形状零件的相机辅助精密计量。

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.