Abstract

AbstractEric Lord has observed: In nature, helical structures arise when identical structural subunits combine sequentially, the orientational and translational relation between each unit and its predecessor remaining constant. A complete version of this paper proves this. If a robot is composed of modular structural subunits that can change their shape or relation, the shape of the robot can change. If they all change in the same way, the robot will be a segmented helix of varying length and curvature. Closed-form expressions are given for the parameters of the segmented helix generated from the intrinsic properties of a chained object and its conjoining rule. The construction of these from the rule for conjoining repeated subunits of arbitrary shape is provided, allowing the complete parameters describing the unique segmented helix generated by arbitrary stackings to be easily calculated. Free-libre open-source interactive software and a website is provided which performs this computation for arbitrary prisms along with interactive 3D visualization [13]. A theorem, proved in a longer version [11], is stated that any chain can be transformed continuously between a toroid-like helix and a maximally-extended helix by varying joint-face normal twist.KeywordsSolid geometrySegmented helixRoboticsChemistry

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