US3695617A

US3695617A - Tensegrity structure puzzle

Info

Publication number: US3695617A
Application number: US152055A
Authority: US
Inventors: Geoffrey A Mogilner; Rodney D Johnson
Original assignee: Individual
Current assignee: Individual
Priority date: 1971-06-11
Filing date: 1971-06-11
Publication date: 1972-10-03
Anticipated expiration: 1989-10-03

Abstract

A puzzle comprising a cage-like tensegrity structure including a plurality of rigid columns having flexible tension members connected between the opposite ends thereof and having a slot at each end thereof. Each of the columns is slidably supported at opposite ends thereof by the tension members of adjacent columns, which tension members extend through the slots in the columns. A solid or hollow object is positioned within the cage-like structure, the object having an outer dimension which is sufficiently large so as to prevent removal thereof from the structure except when the structure is manipulated to one of a limited number of geometric shapes. According to a preferred embodiment of the present invention, the structure comprises twelve columns and forms a polyhedron having six quadrilateral sides and eight hexagonal sides. The object may be removed from the cage-like structure by contracting four of the six quadrilateral sides and then expanding one of the two remaining quadrilateral sides.

Description

United States Patent Mogilner et al.

154] TENSECRITY STRUCTURE PUZZLE [72] Inventors: Geoffrey A. Mogilner, 2070 California St., W., San Diego, Calif. 92110; Rodney D. Johnson, San Diego, Calif.

[73] Assignee: said Mogilner, by said Johnson [22] Filed: June 11, 1971 [21] Appl. No.: 152,055

[56] References Cited UNITED STATES PATENTS 3/1891 Lyon ..273/156 11/1962 Fuller ..52/646 OTHER PUBLICATIONS The Dymaxion World of Buckminster Fuller by Robert W. Marks, publ. by Reinhold Publishing Corp., New York, pages 156- 163 51 Oct. 3, 1972 Primary Examiner-Anton O. Oechsle Att0rneyBernard Kriegel [57] ABSTRACT A puzzle comprising a cage-like tensegrity structure including a plurality of rigid columns having flexible tension members connected between the opposite ends thereof and having a slot at each end thereof. Each of the columns is slidably supported at opposite ends thereof by the tension members of adjacent columns, which tension members extend through the slots in the columns. A solid or hollow object is positioned within the cage-like structure, the object having an outer dimension which is sufficiently large so as to prevent removal thereof from the structure except when the structure is manipulated to one of a limited number of geometric shapes. According to a preferred embodiment of the present invention, the structure comprises twelve columns and forms a polyhedron having six quadrilateral sides and eight hexagonal sides. The object may be removed from the cage-like structure by contracting four of the six quadrilateral sides and then expanding one of the two remaining quadrilateral sides.

13 Claims, 4 Drawing Figures I PATENTEDUBT 3 I972 SHEET 1 [IF 2 INVENTOR. Gt'OFFREYA. MOG/LA/E? B RODNEY a c/Of/NSO/V ATTORNEYS PATENTEDHU 3 I872 SHEET 2 BF 2 INVENTOR. GEOFFREY A M0614 NEE B RQDA/EY D JOHNSON ATTOE/VE'YS TENSEGRITY STRUCTURE PUZZLE BACKGROUND OF THE INVENTION 448,974 issued to Leonard M. Lyon for a Puzzle inl cluding four concentric rings and a ball which was positioned within the third and fourth rings. As stated in the specification, the idea of the puzzle was to remove the ball from the rings by suitable manipulation thereof. According to the objects of that patent, there was produced an ornamental, interesting and inexpensive puzzle which would interest and entertain both adults and children and which was quickly solved by a person understanding it.

Another early example of this type of puzzle is disclosed in U. S. Patent No. 1,050,141 issued Jan. 14, 1913 to Sam S. Joy. Again, there is shown a puzzle including a number of rings which encircle a ball which is releasable from the device only by disassembling the rings in accordance with a predetermined solution.

Another type of decorative puzzle, that has been referred to as a Jumbo Puzzle, includes a number of wood struts which are held in place by notches to form a cage. A ball or other object is positioned within the cage. The purpose of the puzzle is to selectively remove certain of the struts so that the ball can be removed from the cage.

Each of these puzzles, as well as the myriad of other known types of puzzles, rely for their appeal on their particular characteristics. More specifically, when introducing a puzzle on the market, its ultimate success will be determined by its price, how attractive it is, how interesting it is to work with, and also its degree of uniqueness.

SUMMARY OF THE INVENTION According to the present invention, there is provided a novel puzzle of the type discussed previously including a cage-like structure enclosing a solid or hollow object such as a ball where the structure may be manipulated to a unique geometric shape to remove the ball. The present puzzle differs from heretofore known puzzles by forming the cage-like structure in a manner heretofore unknown in the puzzle art.

Briefly, the present puzzle comprises a cage-like tensegrity structure including a plurality of rigid columns having flexible tension members connected between the opposite ends thereof and having a slot at each end thereof. Each of the columns is slidably supported at opposite ends thereof by the tension members of adjacent columns, which tension members extend through the slots in the columns. A solid or hollow object is positioned within the cage-like structure, the object having an outer dimension which is sufficiently large so as to prevent removal thereof from the structure except when the structure is manipulated to one of a limited number of geometric shapes. According to a preferred embodiment of the present invention, the structure comprises twelve columns and forms a polyhedron having six quadrilateral sides and eight hexagonal sides. The object may be removed from the cage-like structure by contracting four of the six quadrilateral sides and then expanding one of the two remaining quadrilateral sides.

It is therefore an object of the provide a novel puzzle.

It is a further object of the present invention to provide a unique, interesting and decorative puzzle.

It is a still further object of the present invention to provide a puzzle of the type including a cage-like structure enclosing a solid or hollow object.

It is another object of the present invention to provide a puzzle utilizing tensegrity, a structural system incorporating continuous tension and discontinuous compression.

Still other objects, features and attendant advantages of the present invention will become apparent to those skilled in the art from a reading of the following detailed description of the preferred embodiment constructed in accordance therewith, taken in conjunction with the accompanying drawings wherein like numerals designate like parts in the several figures and wherein:

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an elevation view of the basic building block of the present tensegrity structure including a rigid column having a slot at each end thereof and a flexible tension member connected between such opposite ends;

FIG. 2 is a plan view of twelve of the columns of FIG. 1 showing the manner in which they may be interconnected to form a polyhedron having six quadrilateral sides and eight hexagonal sides;

FIG. 3 is a perspective view of the constructed polyhedron of FIG. 2 in one position shaped as a cube and enclosing a solid or hollow object such as a sphere; and

FIG. 4 shows the manner in which the object may be removed from the tensegrity structure of FIG. 3.

DESCRIPTION OF THE PREFERRED EMBODIMENT The present puzzle includes, as one of two major parts thereof, a cage-like tensegrity structure. Accordingly, before discussing in detail the construction of the present puzzle, a brief discussion of tensegrity is provided. The word tensegrity" was coined by the well-known, modern, structural designer, R. Buckminster Fuller, to describe his invention of a structural system using continuous tension and discontinuous compression. Tensegrity structures are described in detail in Buckminster Fullers US. Pat. No. 3,063,521 as well as in Mr. Fullers book entitled Ideas and Integrities, Prentice Hall Publishing Co., 1963. Articles about Mr. Fullers work and, more specifically, his tensegrity structures, include The Dymaxion World of Buckminster Fuller by Robert W. Marks, Southern Illinois University Press; World Design Science Decade 1965-1975, Phase I (1964), Document 2, The Design Initiative, World Resources Inventory, Southern Illinois University, Pages 28 and 35-39; and Portfolio and Art present invention to News Annual, No. 4, Pages 112-125, The Art Foundation Press, Inc., 1960.

As discussed in these publications, the word tensegrity is a contraction of tensional integrity, a structure the shape of which is guaranteed by the tensional behaviors of the system and not by the compressional behaviors. A tensegrity structure includes a plurality of rigid, column-like compression members having flexible tension members connected between the opposite ends thereof, the compression members being held in axially spaced relationship to one another by the tension members. More specifically, the ends of the column-like compression members are connected to the tension members of adjacent compression members. As can be gathered from thepublications cited above, such tensegrity structures may be constructed to form a polyhedron having any number of compression mem- Cord B may be connected between the opposite ends of stick A in any convenient manner. According to a preferred embodiment of the present invention, first and second parallel holes 50 and 51 are bored through bers. For example, Buckminster Fullers book entitled Ideas and Integrities, cited supra, between pages 192 and 193, includes a photograph of a 90 strutminiature tension integrity sphere.

According to the present invention, a tensegrity structure is modified so as to provide a unique and interesting puzzle. The modification of such tensegrity structure is two-fold. In the first instance, each of the column-like compression members is providedwith a slot at each end thereof so that the tension member connected to one compression member extends through the slot in an adjacent compression member.

In this manner, each of the compression members is slidably supported at its opposite ends by the tension members of adjacent compression members. Secondly, a solid or hollow object, such as a sphere, a ball, a cube, an octahedron or any irregular cobble-shaped object, is positioned within the space enclosed by the tensegrity structure. The object essentially entirely fills such space so that the object is sufficiently large to prevent removal thereof from the structure in its normal, uniform orientation. On the other hand, since the compression members are slidably supported, the structure may be manipulated to form an unlimited number of different geometric shapes. According to the present invention, a limited number of such shapes permit removal of the object so that the modified structure is, indeed, a puzzle.

Referring now to the drawings and, more particularly, to FIG. 1 thereof, there is shown one element with which the present tensegrity structure and puzzle therefrom are to be constructed. More specifically, the first basic element of the present puzzle is a rigid, column-like, compression member A, having a flexible tension member B connected between the opposite ends thereof. As shown in FIG. 1, tension member B has a length which is greater than the distance between its attaching points to column A so that it remains loose and manipulatable. As will appear hereinafter, the length of tension member B relative to compression member A is not critical, but selected to satisfy the necessity of keeping the constructed polyhedron firm when assembled. A rather elaborate discussion of the theoretical considerations, in a structural element, of the length of the tension members compared to the length of the compression members may be found in the beforementioned R. B. Fuller US Patent No. 3,063,521.

' cordance with the present invention, such connection is made so that each stick A is slidably supported at its opposite ends by the cord B of an adjacent stick A. For this purpose, stick A is constructed by cutting a slot, 54 and 55, at ends x and y thereof, adjacent holes 50 and 51, respectively, the plane of slots 54 and 55 being perpendicular to holes 50 and 51. The width of slots 54 and 55 is approximately equal to the diameter of cord B. More specifically, slots 54 and 55 should be narrow enough to firmly hold cord B, but wide enough to permit cord B to readily slide through slots 54 and 55.

Although not shown, an alternate technique for connecting the opposite ends of cord B to the ends of stick A is to knot the ends of cord B and to insert cord B into slots 54 and 55. When this is done, the knots prevent removal of the end of cord B from slots 54 and 55 when cord B is placed under tension.

According to the present invention, any number of sticks A may be connected together to form a tensegrity structure in accordance with the teachings of R. Buckminster Fuller. In accordance with the present invention, the completed tensegrity structure, forming a polyhedron, may be manipulated to form an unlimited number of different geometric shapes. An object, generally designated 40, and as shown in FIGS. 3 and 4 as a ball, for convenience, is positioned within the space enclosed by the polyhedron. By manipulating the polyhedron to one of a limited number of geometric shapes, ball 40 may be removed.

Referring now to FIGS. 2-4, according to a preferred embodiment of the present invention, a preferred configuration for a puzzle includes 12 sticks A interconnected to form a polyhedron having six quadrilateral sides and eight hexagonal sides. The completed structure, generally designated 45, is shown in FIGS. 3 and includes 12 sticks 1 through 12, sticks 1-12 having cords 21-32, respectively, connected between the opposite ends thereof, in the manner shown in FIG. 1. The manner of interconnecting sticks 1-12 to form structure 45 may be best understood with reference to FIG. 2. More specifically, a l2-stick polyhedron may be constructed by starting with stick 1 and extending cord 21 through the slot at end x of stick 2. Cord 22 is then extended through the slot at end x of stick 3 and cord 23 is then extended through the slot at end x of stick 4.

Cord 24 is then extended through the slot at end x of stick 1 as well as through the slot at end at of stick 5. Cord 25 is then extended through the slot at end x of stick 6. Cord 26 is then extended through the slot at end x of stick 7 and cord 27 is extended through the slot at end yof stick 4. Cord 28 is then extended through the slot at end x of stick and cord 30 is extended through the slot at end x of stick 9, as well as the slot at end x of stick 11. Cord 29 is then extended through the slot at end y of stick 6 and cord 32 is extended through the slot at end y of stick 10. This completes the connections shown in FIG. 2, which enable sticks 1-12 to lie relatively flat.

In order to form the configuration of a polyhedron shown in FIG. 3, the following additional steps are followed. Cord 21 is extended through the slot at end y of stick 7 so that end y of stick 7 is positioned between end x of stick 2 and end y of stick 1. Cord 27 is then extended through the slot at end y of stick 9 that end y of stick 9 is positioned between end yof stick 4 and end y of stick 7. Cord 29 is then extended through the slot at end x of stick 12 so that end x of stick 12 is positioned between end y of stick 6 and end y of stick 9. Cord 32 is then extended through the slot at end y of stick 1 so that end y of stick 1 is positioned between end x of stick 12 and end y of stick 10. Cord 22 is then extended through the slot at end y of stick 12 that end y of stick 12 extends between end y of stick 2 and end x of stick 3. Cord 31 is now extended through the slots at ends y of sticks 2 and 8 so that end y of stick 2 is closest end x of stick 11 and end y of stick 8 is closest end y of stick 11. Next, cord 25 is extended through the slot at end y of stick 3 so that end y of stick 3 is closest end y of stick 5.

At this time, any further connections of the sticks and slots will prevent the insertion or removal of ball 40 except when structure 45 is manipulated to one of a limited number of geometric shapes. Accordingly, at this time, sphere 40 is positioned within tensegrity structure 45. Thereafter, in order to complete structure 45, cord 28 is extended through the slot at end y of stick 5 so that end y of stick 5 is positioned between end x of stick 10 and end y of stick 8. Finally, cord 23 is extended through the slot at end y of stick 11 so that end y of stick 11 is positioned between end x of stick 4 and end y of stick 3. 1

FIG. 3 shows the appearance of a tensegrity structure 45 having 12 sticks and assembled in accordance with the instructions previously given with respect to FIG. 2. However, it will be apparent that the assembly procedure just given is exemplary only and that many more are possible. From FIG. 3, it may be seen that tensegrity structure 45 forms a polyhedron having six quadrilateral sides and eight hexagonal sides, the quadrilateral sides being arranged in three mutually orthogonal directions to form a cube having four sides, a top and a bottom. More specifically, and with reference to FIG. 3, one quadrilateral side namely the front side, designated 60, is formed by

cords

21, 22, 23 and 24, connected between ends x of sticks 1, 2, 3 and 4. Another quadrilateral side, namely the left side as viewed in FIG. 3, designated 61, is formed by

cords

23, 25, 28 and 31. The right quadrilateral side as viewed in FIG. 3, designated 62, is formed by

cords

21, 27, 29 and 32. The top, bottom and rear quadrilateral sides,

designated 63-65, respectively, are formed in a similar manner. An example of a hexagonal side, designated 66, is shown in the upper left hand corner of FIG. 3 and includes

cords

23, 24 and 25, each of which has two separate sections extending between different ends of different sticks. Seven more of such hexagonal sides exist.

As explained previously, since each of sticks 1-12 is slidably supported at opposite ends thereof by cords B connected to adjacent sticks A, tensegrity structure 45 may be manipulated to form an unlimited number of different geometric shapes, the uniform cube shown in FIG. 3 being only one of such shapes. However, in accordance with the present invention, and regardless of the number of sticks A used and the particular polyhedron formed, there is at least one unique geometric shape which will permit the removal of ball 40 from the center of structure 45. With a l2-stick polyhedron, as shown in FIGS. 3 and 4, ball 40 may be removed by contracting four of the six quadrilateral sides and then expanding one of the two remaining quadrilateral sides. For example, and with reference to FIG. 4, the ends of sticks l-12 may be slid along cords 21-32 until the

sides

60, 61, 62 and 65 of the cube are contracted to a small size as shown. Then, by sliding the ends of sticks 4, 5, 6 and 7 on

cords

24, 25, 26, and 27, top 63 of the cube may be expanded to remove ball 40, as shown in phantom in FIG. 4.

As set forth previously, any number of sticks A may be connected together to form a tensegrity structure in accordance with the teachings of R. Buckminster Fuller. The completed tensegrity structure, forming a polyhedron, may be manipulated to form an unlimited number of different geometric shapes. An object, such as ball 40, may be positioned within the space enclosed by the polyhedron. By manipulating the polyhedron to one of a limited number of geometric shapes, the ball may be removed.

By way of example, three sticks A may be subtracted from or added to the structure shown in FIG. 2 and then such sticks may be interconnected to form a ninestick polyhedron or a l5-stick polyhedron, respectively. More specifically, a nine stick polyhedron may be constructed by arranging sticks 1 through 9 as shown in FIG. 2 and entirely eliminating sticks 10, 11, and 12. The directions previously given. for converting the structure of FIG. 2 to the polyhedron of FIG. 3 would also be applicable to converting sticks 1 through 9 to a nine-stick polyhedron if the instructions for sticks 10, 1 1 and 12 are applied to

sticks

6, 8 and 9, respectively. The resulting polyhedron would have two triangular sides, three quadrilateral sides and six hexagonal sides. As in the case of tensegrity structure 45, the nine stick polyhedron may be manipulated to form an unlimited number of different geometric shapes, at least one of such shapes permitting the removal of an object positioned within the center thereof. In the case of the nine stick polyhedron, the object may be removed by contracting the triangular sides and two of the three quadrilateral sides and then expanding the remaining quadrilateral side.

A l5-stick polyhedron may be constructed by arranging sticks 1 through 12 as shown in FIG. 2 and then adding three more sticks 13-15 which would be interconnected and connected to sticks 11 and 12 in the exact same manner as sticks 10-12 are connected to .sticks 8 and 9. In addition, the directions previously given for converting the structure of FIG. 2 to the polyhedron of FIG. 3 would also be applicable to converting sticks 1 through 15 to a l5-stick polyhedron if the instructions for sticks 10, 11 and 12 are applied to sticks 13, 14 and 15, respectively. The resulting polyhedron would have two pentagonal sides, five quadrilateral sides and hexagonal sides. As in the case of tensegrity structure 45, the l5-stick polyhedron may be manipulated to form an unlimited number of different geometric shapes, at least one of such shapes permitting the removal of an object positioned within the center thereof. In the case of the l5-stick polyhedron, the object may be removed by contracting the five hexagonal sides and then expanding one of the two pentagonal sides.

It can therefore be seen that in accordance with the present invention, there is provided a novel puzzle of the type including a cage-like structure enclosing a solid or hollow object such as a ball where the structure may be manipulated to a unique geometric shape to remove the ball therefrom. The present puzzle differs from heretofore known puzzles by forming the cagelike structure in a manner heretofore unknown in the puzzle art. More specifically, and in accordance with the present invention, a tensegrity structure is modified so as to be manipulatable into an unlimited number of different geometric shapes, a limited number of such shapes permitting removal of the ball therefrom.

While the invention has been described with respect to a preferred physical embodiment constructed in accordance therewith, it will be apparent to those skilled in the art that various modifications and improvements may be made without departing from the scope and spirit of the invention. For example, although puzzles have been described as comprising tensegrity structures having nine, 12 or 15 sticks, it will be apparent to those skilled in the art that a tensegrity structure may be formed having any number of sticks to form a polyhedron having any number of sides. It will be found that any polyhedron so constructed will have an unlimited number of geometrical shapes in which a limited number will permit the removal of a ball positioned thereinside and filling the space enclosed thereby. Accordingly, it is to be understood that the invention is not to be limited by the specific illustrative embodiment, but only by the scope of the appended claims.

We claim:

1. A puzzle comprising:

a tensegrity structure including a plurality of rigid columns having flexible tension members connected between the opposite ends thereof, each of said columns being slidably supported at opposite ends thereof by the tension members of adjacent columns to form a polyhedron; and

a solid or hollow object positioned within said tensegrity structure, said object having an outer dimension which is sufficiently large so as to prevent removal thereof from said structure except when said structure is manipulated to one of a limited number of geometric shapes.

2. A puzzle according to claim 1 wherein each of said columns has a slot at each end thereof, and wherein the tension member connected to one column extends through the slot in an adjacent column for slidably supporting said adjacent column.

3. A puzzle according to claim 2 wherein each of said columns has a hole bored therethrough at each end thereof, perpendicular to the plane of said slots, and wherein the opposite ends of said flexible tension members are inserted through said holes and knotted to connect said tension members to said columns.

4. A puzzle according to claim 1 wherein said tensegrity structure comprises twelve rigid columns, wherein each of said tension members slidably supports the ends of two of said columns and wherein said polyhedron has six quadrilateral sides and eight hexagonal sides.

5. A puzzle according to claim 4 wherein said object may be removed from said structure by contracting four of said six quadrilateral sides and then expanding one of the two remaining quadrilateral sides, said contraction and expansion being achieved by sliding the ends of said columns along said tension members.

6. A puzzle according to claim 4 wherein said columns may be manipulated relative to said tension members until said six quadrilateral sides of said polyhedron form a cube having four sides, a top and a bottom.

7. A puzzle according to claim 6 wherein said object may be removed from said polyhedron by manipulating said columns to reduce the size of said sides of said cube and to increase the size of said top of said cube, and then removing said object through said top of said cube.

8. A puzzle according to claim 1 wherein said tensegrity structure comprises nine rigid columns,- wherein each of said tension members slidably supports the ends of two of said columns and wherein said polyhedron has two triangular sides, three quadrilateral sides and six hexagonal sides.

9. A puzzle according to claim 8 wherein said object may be removed from said structure by contracting said triangular sides and two of said three quadrilateral sides and then expanding the remaining quadrilateral side, said contraction and expansion being achieved by sliding the ends of said columns along said tension members.

1. A puzzle according to claim 1 wherein said tensegrity structure comprises fifteen rigid columns, wherein each of said tension members slidably supports the ends of two of said columns and wherein said polyhedron has two pentagonal sides, five quadrilateral sides and ten hexagonal sides.

11. A puzzle according to claim 10 wherein said object may be removed from said structure by contracting said five hexagonal sides and then expanding one of said two pentagonal sides, said contraction and expansion being achieved by sliding the ends of said columns along said tension members.

12. A puzzle according to claim 1 wherein said object is a sphere.

13. A puzzle according to claim 12 wherein said sphere essentially entirely fills the space enclosed by said tensegrity structure.

Claims

1. A puzzle comprising: a tensegrity structure including a plurality of rigid columns having flexible tension members connected between the opposite ends thereof, each of said columns being slidably supported at opposite ends thereof by the tension members of adjacent columns to form a polyhedron; and a solid or hollow object positioned within said tensegrity structure, said object having an outer dimension which is sufficiently large so as to prevent removal thereof from said structure except when said structure is manipulated to one of a limited number of geometric shapes.

8. A puzzle according to claim 1 wherein said tensegrity structure comprises nine rigid columns, wherein each of said tension members slidably supports the ends of two of said columns and wherein said polyhedron has two triangular sides, three quadrilateral sides and six hexagonal sides.

12. A puzzle according to claim 1 wherein said object is a sphere.