Abstract: Reversibly expanding covering elements for truss structures made up of scissor-assemblies that are connected together by hub elements structures. These covering elements are comprised of a folded sheet of flexible material such as cardboard or a plastic sheet, or alternatively, comprised of planar panels that are hinged together. As the truss structure expands and contracts, the covering element is compressed and expanded along with it.

Abstract: A folding linkage is hereby disclosed that is comprised of four links, each link having a bevel gear on its end, where each link is in geared contact with a neighboring link, such that both links are held together by a hub element that is small relative to the two links. An alternate embodiment of the invention has links that have a spur gear on each end, whereby each gear end is engaged with a central rack (linear gear).

Abstract: This invention discloses tongs-linkage, which, in its extended position, provides an essentially triangular-shaped surface, whereby the links of the tongs-linkage are themselves the panels that form the surface. Such assemblies may be planar, or, by use of intermediate hub elements, may form a surface with curvature. As such an assembly is compressed, the panel-links slide over one another, compressing down to a compact stack. Such tongs-linkages may be joined to similar linkages by pivots lying along their respective edges thereby forming extended structural surfaces. Surfaces that are planar, cone-shaped and doubly-curved surfaces of revolution are disclosed. In each case when the structure is retracted it compresses down to a compact linear element or ring.

Abstract: Reversibly expanding covering elements for truss structures made up of scissor-assemblies that are connected together by hub elements structures. These covering elements are comprised of a folded sheet of flexible material such as cardboard or a plastic sheet, or alternatively, comprised of planar panels that are hinged together. As the truss structure expands and contracts, the covering element is compressed and expanded along with it.

Abstract: This invention discloses tongs-linkage, which, in its extended position, provides an essentially triangular-shaped surface, whereby the links of the tongs-linkage are themselves the panels that form the surface. Such assemblies may be planar, or, by use of intermediate hub elements, may form a surface with curvature. As such an assembly is compressed, the panel-links slide over one another, compressing down to a compact stack. Such tongs-linkages may be joined to similar linkages by pivots lying along their respective edges thereby forming extended structural surfaces. Surfaces that are planar, cone-shaped and doubly-curved surfaces of revolution are disclosed. In each case when the structure is retracted it compresses down to a compact linear element or ring.

Abstract: Improved reversibly expandable structures are formed from novel loop assemblies comprising a plurality of links, each of said links having at least one center pivot joint and a plurality of end pivot joints, each of at least two of said plurality of end pivot joints proximate to the outer edge of said loop assembly and connected to another link; each of said plurality of links being connected to another one of said plurality of links by at least two end pivot joints thereby forming a link pair, said loop assembly comprising at least three link pairs, each of said at least three link pairs connected to at least two other link pairs through at least one of said end pivot joints; each of said at least three link pairs connected to a central piece that is central to the loop assembly, said central piece being rotatable around a central axis, wherein the rotation of the central piece reversibly expands said loop assembly.

Abstract: A new hub element is disclosed for building reversible expandable three-dimensional truss structures. The hub element can directly connect a pin joint towards the center of a scissor linkage to a pivot located near the extremity of another out-of-plane scissor linkage. It has the advantages of being more compact than previously known hub elements and can be used to create foldable structures that are more structurally sound than previously possible. The use of this novel hub element can also reduce the number of pieces required for a given foldable structure, thereby reducing manufacturing and assembly costs.

Abstract: Reversibly expandable structures are formed from loop assemblies comprising interconnected pairs of polygonal shaped links. Each loop assembly has polygon links with at least three pivot joints and at least some of the polygon links have more than three pivot joints. Additionally, these links lie essentially on the surface of the structure or parallel to the plane of the surface of the structure. Each polygon link has a center pivot joint for connecting to another link to form a link pair. Each link also has at least one internal pivot joint and one perimeter pivot joint. The internal pivot joints are used for connecting link pairs to adjacent link pairs to form a loop assembly. Loop assemblies can be joined together and/or to other link pairs through the perimeter pivot joints to form structures.

Abstract: This application is directed to a linkage system which provides continuous rotation to two or more interconnected quadrilaterals. The basic element of the linkage system is a multi-level link which provides firstly, a non-rotatable connection between two sub-links lying, in separate parallel planes and secondly, a rotatable connection for a further link lying in another parallel plane between the planes of the sub-links. By various interconnections between link elements, the quadrilaterals the linkage system will form various geometric patterns as the linkage is rotated. As the quadrilaterals lie in different planes, they may be continuously rotated with respect to each other. The linkage system may be used as a toy, a novelty item and as an educational tool.

Abstract: Reversibly expandable structures are formed from loop assemblies comprising interconnected pairs of polygonal shaped links. Each loop assembly has polygon links with at least three pivot joints and at least some of the polygon links have more than three pivot joints. Additionally, these links lie essentially on the surface of the structure or parallel to the plane of the surface of the structure. Each polygon link has a center pivot joint for connecting to another link to form a link pair. Each link also has at least one internal pivot joint and one perimeter pivot joint. The internal pivot joints are used for connecting link pairs to adjacent link pairs to form a loop assembly. Loop assemblies can be joined together and/or to other link pairs through the perimeter pivot joints to form structures.

Abstract: Self-supporting structures of diverse shapes are disclosed that may be collapsed down to compact bundles. Structures of this type are comprised of units which are comprised of two strips having non-parallel pleat lines. By pleating these strips according to a special pleat pattern, these structures may collapse down and expand out in a smooth manner.

Abstract: A loop-assembly is disclosed which is comprised of at least three scissors-pairs, at least two of the pairs comprising:two essentially identical rigid angulated strut elements, each having a central and two terminal pivot points which do not lie in a straight line, each strut being pivotally joined to the other of its pair by their central pivot points,each pair being pivotally joined by two terminal pivot points to two terminal pivot points of another pair such that both scissors pairs lie essentially in the same plane, oreach pair being pivotally joined by two terminal pivot points to two terminal pivot points of another pair in that the terminal points of a scissors-pair are each pivotally joined to a hub element, and these hub elements are in turn joined to the terminal pivot points of another scissors-pair,whereby a closed loop-assembly is thus formed of scissors pairs, and this loop-assembly can fold and unfold, anda line that intersects and is perpendicular to the axes of any two terminal pivot points

Abstract: Self-supporting structures of diverse shapes are disclosed that may be collapsed down to a compact bundle. In them, units are employed that are comprised of a central tapered strip bordered by two elongated strips. The tapered strip is pleated along a series of lines that cross it widthwise and each elongated strip is pleated along a series of lines that cross it widthwise. The central tapered strip is joined to each of the two elongated strips by a series of pleat lines that are connected end-to-end. When the unit is folded, each of the two elongated strips fold into a stack, and the central tapered strip folds in a zig-zag fashion, such that the planes of the tapered strip lie essentially orthogonal to the planes of the stacked elongated strips. The two stacked elongated strips fold towards each other, such that the stacks lie in line with one another.

Abstract: A loop-assembly is disclosed which is comprised of at least three scissors-pairs, at least two of the pairs comprising:two essentially identical rigid angulated strut elements each having a central and two terminal pivot points with centers which do not lie in a straight line, each strut being pivotally joined to the other of its pair by their central pivot points,each pair being pivotally joined by two terminal pivot points to two terminal pivot points of another pair in that,(a) the terminal pivot points of each of the scissors-pairs are pivotally joined to the terminal pivot points of the adjacent pair such that both scissors-pairs lie essentially in the same plane, or(b) the terminal pivot points of a scissors-pair are each pivotally joined to a hub element which is small in diameter relative to the length of a strut element, and these hub elements are in turn joined to the terminal pivot points of another scissors-pair, such that the plane that one scissors-pair lies in forms an angle with the plane that