Geometric modeling for kinematics and inspection of multibody systems

点击翻译按钮获取中文摘要

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.