Geometric methods for mechanical system design and analysis

机械系统的运动几何学通常是非常难以理解和描述的。这一简单的事实导致了在机械系统的设计、综合和分析中似乎没有解决的一系列问题。因此，拟议的研究结合了机器人学、机构理论、欧几里得和非欧几里德几何以及数字图像处理的元素，目的是为机械系统的设计、运动学分析、性能评估和改进以及运动控制开发新的和显著改进的方法。已经形成了四个相互支持但又不同的子项目。一是开发一种新型的可提供无限角位移的运动平台(车辆模拟器)。这可以用来让飞行员有机会为不太可能但极其危险的情况进行训练：例如，在没有动力的情况下从旋转的自由落体中逃生。二是利用结构奇异并联平台的不可控自由度。这些是六条腿的飞行模拟器平台，它们可以达到的任何配置都会坍塌。这项动议是非常僵硬和坚定的。我们建议以适当的方式串联其中的六个平台，结果将是一个非常刚性的六自由度机械臂，具有并联平台的负重比优势，但又具有串联机器人的灵巧能力。三是整合机构数、型、维综合任务。目前，机构中关节的数量和类型是确定的，然后使用方法来估计杆件的大小和关节的位置。如果将数量和类型包括在维度的优化中，结果将是满足规定任务的最好机制。第四个是对工业机器人中的温度和应变引起的变形进行建模，以消除在对机器人进行编程之前对其进行热身的需要。积极的结果可能会将机器人工作单元的生产率提高一个数量级。这项研究已经产生了几种用于机构综合、机器人运动学分析、机器人性能评估的新方法，以及一种全新的定位装置。

The kinematic geometry of mechanical systems is often extremely difficult to understand and characterize. This simple fact leads to a seemingly endless range of unsolved problems in the design, synthesis and analysis of mechanical systems. Thus the proposed research combines elements of robotics, mechanism theory, Euclidean and non-Euclidean geometries, and digital image processing with the objective of developing new and substantially improved methods for the design, kinematic analysis, performance assessment and enhancement, and motion control of mechanical systems. Four mutually supportive, yet distinct sub-projects have evolved. The first is to develop a novel motion platform (vehicle simulator) that can provide unlimited angular displacements. This could be used to give pilots the opportunity to train for unlikely, but extremely dangerous scenarios: escape from a spinning free-fall without power, for example. The second is to exploit the uncontrollable degree-of-freedom (DOF) of so called architecture singular parallel platforms. These are six-legged flight simulator platforms that collapse in every configuration they can attain. The motion is very stiff and sure. We propose to serially connect six of these platforms in an appropriate way, the result will be a very stiff six DOF robot arm with the load-to-weight ratio advantages of a parallel platform, but possessing the dexterous capabilities of a serial robot. The third is to integrate the tasks of number, type, and dimensional synthesis of mechanisms. Currently, the number and type of joints in a mechanism is decided then methods are used to estimate the size of the links and locations for the joints. If number and type were included in the optimization of the dimensions, the result would be the very best mechanism for the prescribed task. The fourth is to model the temperature and strain-induced deformations in industrial robots to eliminate the need to "warm-up" the robot before programming it. Positive outcome could improve the productivity of robotic work cells by an order of magnitude. Several novel methods for mechanism synthesis, robot kinematic analysis, robot performance assessment, and a radically novel orienting device have already resulted from this research.