Novel method of constructing generalized Hoberman sphere mechanisms based on deployment axes

Abstract

This study proposes a method of constructing type II generalized angulated elements (GAEs II) Hoberman sphere mechanisms on the basis of deployment axes that intersect at one point. First, the constraint conditions for inserting n GAEs II into n deployment axes to form a loop are given. The angle constraint conditions of the deployment axes are obtained through a series of linear equations. Second, the connection conditions of two GAEs II loops that share a common deployable center are discussed. Third, a flowchart of constructing the generalized Hoberman sphere mechanism on the basis of deployment axes is provided. Finally, four generalized Hoberman sphere mechanisms based on a fully enclosed regular hexahedron, arithmetic sequence axes, orthonormal arithmetic sequence axes, and spiral-like axes are constructed in accordance with the given arrangement of deployment axes that satisfy the constraint conditions to verify the feasibility of the proposed method.

Keywords

deployable mechanism / type II generalized angulated elements / Hoberman sphere mechanism / deployment axes / constraint conditions

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51905015) and China Postdoctoral Science Foundation (Grant No. 2018M631300).

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