Geometric methods for mechanical system design and analysis

机械系统的运动几何常常是极其难以理解和表征的。这个简单的事实导致了机械系统的设计、综合和分析中看似无穷无尽的未解决问题。因此，提出的研究结合了机器人、机构理论、欧几里得和非欧几里得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、性能评估和增强以及运动控制开发新的和实质上改进的方法。四个相互支持，但不同的子项目已经发展。首先是开发一种新颖的运动平台（车辆模拟器），可以提供无限的角位移。这可以让飞行员有机会进行训练，以应对不太可能发生但极其危险的情况：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行平台的不可控自由度。这些是六条腿的飞行模拟器平台，在它们能达到的任何配置中都可以折叠。动作非常僵硬和坚定。我们建议将其中的六个平台以适当的方式串联起来，结果将是一个非常僵硬的六自由度机器人手臂，具有并联平台的负载重量比优势，但具有串联机器人的灵巧能力。三是整合机构的数量、类型、维度综合任务。目前，确定机构中关节的数量和类型，然后使用方法来估计连杆的大小和关节的位置。如果在维度的优化中包含数量和类型，则结果将是用于指定任务的最佳机制。第四是对工业机器人的温度和应变引起的变形进行建模，以消除在编程之前对机器人进行“预热”的需要。积极的结果可能会使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一些新的机构综合、机器人运动学分析、机器人性能评估和一种全新的定向装置的方法。

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.