Geometric methods for mechanical system design and analysis

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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.