Mobile geometrical form

• US 3,884,462 A
• Filed: 12/26/1973
• Issued: 05/20/1975
• Est. Priority Date: 12/26/1973
• Status: Expired due to Term

• Current Assignee: Francis Rebajes
• Original Assignee: Francis Rebajes
• Inventors: Rebajes, Francis
• Primary Examiner(s): Schulz, William E.
• Application Number:
  US05/428,201
• Time in Patent Office: 510 Days
• Field of Search: 161/7 D34/15A 35/73 46/23,24
• US Class Current: 472/57
• CPC Class Codes: B44C 3/00 Processes, not specifically provided for elsewhere, for producing ornamental structures

Abstract

A mobile geometrical form in the general shape of a hyperbolic paraboloid is described as made from a continuous strip of material to form a continuously twisted shape having both an external edge and an internal edge. The internal edge of the form defines an opening centrally in the form. The form has two distinct continuous surfaces on opposing sides of the strip from which the form is made. Each side or surface has four lines of inflection to result in four surface portions having successive concave and convex contours. Opposing surface portions of the strip between the same inflection lines have opposing concave and convex contours. The form is made of a semi-rigid flexible material such as sheet metal. In this manner, the strip can assume the predetermined geometrical form in an infinite number of relative positions of the strip. The stresses established in the strip redistribute themselves in each relative position of the strip as the latter translates along a path generally defined by the form itself to maintain the shape of the same.

Claims

1. A mobile geometrical form comprising a double-sided continuous strip of material, each side having four points of inflection to thereby result in four surface portions having successive concave and convex contours, opposing surface portions of said strip between the same inflection points having opposing concave and convex contours.

2. A mobile geometrical form as defined in claim 1, wherein said strip of material is made of a semi-rigid flexible material, said strip assuming the geometrical form in an infinite number of relative positions of said strip, the stresses established in said strip redistributing themselves in each relative position of said strip to maintain the shape of the geometrical form.

3. A mobile geometrical form as defined in claim 2, wherein said material is a sheet of metal.

4. A mobile geometrical form as defined in claim 2, wherein said material is a sheet of elastomeric plastic.

5. A mobile geometrical form comprising a double-sided continuous strip of material, said strip being twisted to cause each surface to include two portions thereof which substantially face each other and two portions which are substantially directed away from one another, said portions facing each other and said portions directed in opposing directions being symmetrically disposed about and substantially parallel to respective planes which are normal to one another.

6. A mobile geometrical form as defined in claim 5, wherein said strip of material is made of a semi-rigid flexible material, said strip assuming the geometrical form in an infinite number of relative positions of said strip, the stresses established in said strip redistributing themselves in each relative position of said strip to maintain the shape of the geometrical form.

7. A mobile geometrical form as defined in claim 6, wherein said material is a sheet of metal.

8. A mobile geometrical form as defined in claim 6, wherein said material is a sheet of elastomeric plastic.

9. A mobile geometrical form in the general shape of a hyperbolic paraboloid, said form comprising a continuous strip of material to thereby form both an external edge and an internal edge, said internal edge forming an opening centrally of said form.

10. A mobile geometrical form as defined in claim 9, wherein said internal edge is smooth.

11. A mobile geometrical form as defined in claim 9, wherein said internal edge is smooth and includes at least one extension extending in a direction generally centrally of the form.

12. A mobile geometrical form as defined in claim 11, wherein a plurality of extensions are provided along the length of said internal edge each extending in a direction generally centrally of the form.

13. A mobile geometrical form as defined in claim 12, wherein said extensions are triangular.

14. A mobile geometrical form as defined in claim 9, wherein said external edge is smooth.

15. A mobile geometrical form as defined in claim 9, wherein said external edge is smooth and includes at least one extension extending generally away from the central region of the form.

16. A mobile geometrical form as defined in claim 15, wherein a plurality of extensions are provided each extending in a direction generally away from the central region of the form.

17. A mobile geometrical form as defined in claim 16, wherein said strip is made of a semi-rigid flexible material, said strip assuming the geometrical form in an infinite relative positions of said strip, the stresses established in said strip redistributing themselves in each relative position of said strip to maintain the shape of the geometrical form.

18. A mobile geometrical form as defined in claim 17, wherein said external edge has a predetermined length, and wherein two extensions are provided at points along said predetermined length to form therebetween two equal length portions.

19. A mobile geometrical form as defined in claim 18, wherein each extension extends in a direction substantially normal to the external edge portion from which it projects, each extension being provided with a surface at the free end thereof which is substantially parallel to the respective external edge portion, the form being supportable on said end surfaces when said extensions are disposed adjacently to one another in opposing relation.

20. A mobile geometrical form as defined in claim 18, wherein one of said extensions is fixed in space relative to the other extension, the other extension being movable between two positions, one position wherein said extensions are disposed in adjacent substantially parallel and opposing positions, and another position wherein the surfaces of said extensions which face each other in said one of said positions facing away from each in the other of said positions.

21. A mobile geometrical shape formed by two concentric annular strips each having first and second opposite surfaces respectively facing the same direction and each having adjacent first and second opposing edges, with respective first and second edges of each of said strips being disposed adjacently to each other, and a first edge of one strip being connected to a second edge of the other strip to result in a spiral wherein said first surfaces and second surfaces of each said strips respectively merge, one of the free ends of said strips being bent to bring portions of one of said surfaces into a facing condition, said one of the free ends being brought adjacently to the other free end and said free ends being twisted and joined to cause said first and second surfaces to respectively merge, whereby both said first and second surfaces become continuous when all said opposing edges have been joined.

22. A method of forming a mobile geometrical shape comprising the steps of A. Disposing two slotted annular strips concentrically to each other, each of said strips having first and second opposing surfaces respectively facing the same directions and first and second opposing edges;

B. Connecting a first edge of one strip with a second edge of the other strip to cause said first and second surfaces to merge at the point of connection, the resulting shape being a spiral having said first surfaces generally facing one direction and said second surfaces generally facing an opposing direction;

C. Bending one free end of the resulting spiral to cause portions of one of said surfaces to face each other;

D. Bringing said edges at the free ends of the spiral into proximity to each other;

E. Aligning the free ends and opposing edges to bring corresponding first and second surfaces at the free ends to positions generally facing the same direction; and

F. Joining said free ends to each other, whereby said first and second surfaces each form a continuous loop when all the opposing edges have been connected.