Patent ID: 8384613

Claim:
A deployable and collapsible structure comprising: a strut being straight, rigid and having a fixed length; a quadrilateral loop comprised of four of the struts being connected end-to-end at nodes, with the respective lengths being L 1 , L 2 , L 3 and L 4 , and satisfying a constraint equation defined as L 1 −L 2 +L 3 −L 4 =0; each of the nodes providing the connected struts with multiple degrees of rotational freedom; a plurality of the quadrilateral loops, including adjacent quadrilateral loops having in common one of the struts; the struts being approximately parallel when the quadrilateral loops are collapsed, whereby the structure is collapsed; the nodes having, loci forming a plurality, i, of concentric, circles when the structure is deployed; each of the circles having a radius, r, whereby the deployed structure forms a radial grillage; the radial grillage having a geometric center; a plurality, n, of the struts lying radially with respect to the center; a cross section of the radial grillage being planar when r i + 1 r i = 1 + sin ⁢ π n 1 - sin ⁢ π n wherein: r i the radius of circle i; and r i+1 =the radius of the next larger circle; a diagonal being a straight line that intersects two of the nodes and also forms an respectively, with each of the four struts comprising one of the quadrilateral loops when the structure is deployed; a pair of opposing nodes being comprised of the two nodes that intersect each one of the diagonals; and the loop being collapsed by translating each of the two pairs of opposing nodes in opposite directions.