A retractable structure based on Bricard linkages and rotating rings of tetrahedra

Retractable structures which alter their geometries according to practical requirements are widely used in roof structures of stadiums for their versatility. A retractable structure based on threefold-symmetric Bricard linkages and rotating rings of tetrahedra is proposed and developed in this paper. By replacing each link of a threefold-symmetric Bricard linkage with a tetrahedron, a retractable structure is obtained which can repeatedly open and close by rotating the tetrahedra. The geometric relationship between the retractable structure and the threefold-symmetric Bricard linkage is derived and ranges of main geometric parameters are determined to ensure a continuous and smooth movement in the deployment of the structure. Then the relative displacement of the support and the open rate of the structure, two main parameters concerned in practical applications, are investigated. Preferred ranges of main geometric parameters are proposed and a physical model is manufactured to verify them. A discussion on some possible improvements and modifications of the structure is also presented.