Two types of foldable rings are designed using polynomial continuation. The first type of ring, when deployed, forms regular polygons with an even number of sides and is designed by specifying a sequence of orientations which each bar must attain at various stages throughout deployment. A design criterion is that these foldable rings must fold with all bars parallel in the stowed position. At first, all three Euler angles are used to specify bar orientations, but elimination is also used to reduce the number of specified Euler angles to two, allowing greater freedom in the design process. The second type of ring, when deployed, forms doubly plane-symmetric (irregular) polygons. The doubly symmetric rings are designed using polynomial continuation, but in this example a series of bar end locations (in the stowed position) is used as the design criterion with focus restricted to those rings possessing eight bars.
Designing Folding Rings Using Polynomial Continuation
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Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received December 30, 2012; final manuscript received August 8, 2013; published online December 27, 2013. Assoc. Editor: J. M. Selig.
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Viquerat, A. D., and Guest, S. D. (December 27, 2013). "Designing Folding Rings Using Polynomial Continuation." ASME. J. Mechanisms Robotics. February 2014; 6(1): 011005. https://doi.org/10.1115/1.4025857
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