Expandable space frames

Expandable space frames having essentially infinite periodicity limited only by practical considerations, are described. Each expandable space frame comprises a plurality of hinge joint assemblies having arms that extend outwardly in predetermined symmetrically related directions from a central or vertex point. The outer ends of the arms form one part of a hinge point. The outer expandable space frame also comprises a plurality of struts. The outer ends of the struts from the other part of the hinged joint. The struts interconnect the plurality of hinge point in sychronism, the spaceframes can be expanded or collapsed. Three-dimensional as well as two-dimensional spaceframes of this general nature are described

Space Frames with Multiple Stable Configurations

This paper is concerned with beamlike spaceframes that include a large number of bistable elements, and exploit the bistability of the elements to obtain structures with multiple stable configurations. By increasing the number of bistable elements, structures with a large number of different configurations can be designed. A particular attraction of this approach is that it produces structures able to maintain their shape without any power being supplied. The first part of this paper focuses on the design and realization of a low-cost snap-through strut, whose two different lengths provide the required bistable feature. A parametric study of the length-change of the strut in relation to the peak force that needs to be applied by the driving actuators is carried out. Bistable struts based on this concept have been made by injection molding nylon. Next, beamlike structures based on different architectures are considered. It is shown that different structural architectures produce structures with workspaces of different size and resolution, when made from an identical number of bistable struts. One particular architecture, with 30 bistable struts and hence over 1 billion different configurations, has been demonstrated

Every Hilbert space frame has a Naimark complement

Naimark complements for Hilbert space Parseval frames are one of the most fundamental and useful results in the field of frame theory. We will show that actually all Hilbert space frames have Naimark complements which possess all the usual properties for Naimark complements with one notable exception. So these complements can be used for equiangular frames, RIP property, fusion frames etc. Along the way, we will correct a mistake in a recent fusion frame paper where chordal distances for Naimark complements are computed incorrectly.Comment: Changes after Refereein

Vibrational characteristics of linear space frames

Digital computer program for determining modes and frequencies of arbitrary linear space frame