CA1048781A - Mobile geometrical form - Google Patents

Mobile geometrical form

Info

Publication number
CA1048781A
CA1048781A CA74214942A CA214942A CA1048781A CA 1048781 A CA1048781 A CA 1048781A CA 74214942 A CA74214942 A CA 74214942A CA 214942 A CA214942 A CA 214942A CA 1048781 A CA1048781 A CA 1048781A
Authority
CA
Canada
Prior art keywords
strip
geometrical form
mobile
opposing
edge
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired
Application number
CA74214942A
Other languages
French (fr)
Inventor
Francis Rebajes
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Individual
Original Assignee
Individual
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Individual filed Critical Individual
Application granted granted Critical
Publication of CA1048781A publication Critical patent/CA1048781A/en
Expired legal-status Critical Current

Links

Classifications

    • BPERFORMING OPERATIONS; TRANSPORTING
    • B44DECORATIVE ARTS
    • B44CPRODUCING DECORATIVE EFFECTS; MOSAICS; TARSIA WORK; PAPERHANGING
    • B44C3/00Processes, not specifically provided for elsewhere, for producing ornamental structures

Abstract

MOBILE GEOMETRICAL FORM

ABSTRACT OF THE DISCLOSURE

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.

Description

~04~78~L
BACXGROUND OF T~ IN~E~ ION

Various geomevrlcal forms are known. Some o r these forms are ~ound in the fields of structural architecture, abstract art, complex machine parts including cams and followers and home display or decorative ob~ects. However, the present lnvention discloses a novel geometrical ~orm which has unique characteristics whlch makes the same suitable for being adapted for many varied uses.

The moblle geometrical form o~ the present invention, 1~ which is in the general shape o~ a hyperbolic parabolold, is made of a semi-rigid flexible material. Once the form is established, in accordance with the method to be described, the strip assumes the novel geometrical form in an infinite number of relative positions of the strip. Translatory motion o~ the strip, within a general path outlined by the form, redlstrlbutes the stresses established ln the strip ln each position of the latter to malntain the shape of the geometrlcal form. The forces required to translate the strlp within its general outline or shape are a function of the flexibility o~
; 20 the material ~rom which it is made and can be reduced to mlnimal values.

Accordlngly, the novel and aesthetically pleasing form of the present invention can be utilized both for ornamental purposes as well as other mechanical utilitarian purposes. For exa~ple, the lor~ is p~rticularly suitable as a reclprocating movement or rotion devlce. Also, the novel form can be utilized to convert linear lnto curvillnear move~ents or vice versa. Other important uses of the device include amusement and exercise. For example, as wlll become evident from the descriptlon that follows, the form can be continuously or reciprocally advanced while continuously maintaining a fixed grip on two points of the form. This suggests possible use in physical therapy applications to provide exercise to muscles ,O in the arms and wrists.

SUMMARY OF THE INVENTION

Accordingly, it is an ob~ect of the present invention to provlde a novel geometrlcal form which exhibits new and unusual propertles not known heretofore in prior art geometrical forms.

It is another ob~ect of the present invention to~
provide a novel and useful geometrical form which is simple in construction and economical to manufacture.

It is still another ob~ect o~ the present invention to provide a novel geometrlcal form which is made of a continuous strip of semi-rigid flexible material and which can be either continuously or reciprocally translated along a path generally defined by the novel shape.

Tt i-~ ~et another o~;Ject of the present ln~ention to provlde a mobll~ g~ometrical form whlch is in the general shape of a hyperbolic paraboloid but hav~ng an internal edge forming an opening centrally of the form and which is made of a continuous strip of material.

It is a further object of the present invention to provlde a mobile geometrical form of the type above suggested which can be utilized for ornamental as well as mechanically utilitarian purposes.

It is still a further ob~ect of the present invention to provide a mobile geometrical form of the type generally under discusslon which can translate linear into curvilinear motion and vice versa.

It is yet a further ob~ect of the present invention to provide a mobile geometrical form as suggested in the above ob~ects which can be utilized both for a.museme~t. and exercise purposes.

It is an additional ob~ect of the present invention to provide a method for easily assembling and forming the
2~ moblle geometrical form above described.

4.

1~)48781 In order to achleve the above obJects, as well as others which ,lill beco~e apparent hereafter, a mobile geo~etrical form in ~ccordance ~ith the present invention comprises a double-slded continuous strip of material, each side having fou~ points of inflection to thereby result in four surface portions having excessive concave and convex contours. Opposing surface portions of said strip bet~reen the same inflection points have opposing concave and con~ex contours. The double-sided continuous strip of ~aterial is 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, the portions facing each other and the portions directed in opposing directions being symmetrically disposed about and substantially parallel to respective planes which are normal to one another. Generally, the novel mobile geometrical form of the present invention is in the form of a hyperbollc paraboloid which, when formed from a continuous strip of material, exhibits both an external edge and in internal edge, with the internal edge forming an opening centrally of the form.

Advantageously, the strip of material is made from a semi-rigid flexible material. In this manner, the strip assumes the 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 to maintain the shape of the geometrical form.

1~)4~
icco~d1 n~ to so~.e nresen-tl~ preferred embodiments, the exterr.al ar.d i~ternal edges of the form are s~ooth.
However, protuberances in the form of pro~ections may be provided on the internal, external or both edges. With such protuberances, the mobile geometrical form adds extra dimensions for posslble uses to whlch it can be applied. As suggested above, such a geometrical form can be utilized for ornamental, amusement, exercislnæ, and mechanical uses.

BRIEF DESCRIPTION OF THE DRAWINGS

With the above and additional ob~ects and advantages in view, as will hereinafter appear, this invention comprises the devices, combinations and arrangements of parts hereinafter descrlbed and lllustrated in the accompanylng drawings of a preferred embodiment ln which:

FIGURES 1 and 2 are top plan views of slitted annular strips from which the mobile geometrical form in accordance with the present invention may be formed;

FIGURE 3 is a side elevational view of the two annuIar strips shown in FIGURE 1 when the strlps are concentrically 2~ disposed and opposing edges are ~olned to permit the connected annular strips or resultant strip to be stretched along the general direction of the axis into the general shape of a helicoid;

~, . , 16~48781 FIGURE 4 is a perspec~ive vlew of the helicoid shown in FIGURE 3, showing the manner in which the hellcoid ls formed by separation of the free ends of the respectlve annular strips;

FIGURE 5 is'a front elevational view Or the connected strips after one of the free ends of the resultant strip ls bent to bring portlons Or one of the resultlng surfaces of the helicoid onto itself whereby portlons of a single surface face each other;

1'0 FIGURE 6 is slmilar to FIGURE 5, showing the condltlon when one of the free ends ha3 been brought ad~acently to the other free end and wherein the free ends are aligned to bring the corresponding surfaces at the,free ends to posltlon~ generally facing the same direction;

FIGUR~ 7 ls slmilar to FIGURE 6,-showlng the condltlon when the free ends are ~oined to each other to thereby cause each of the original helicold surface~ to form a contlnuous surface once all the opposlng edges have been connected;

FIGURE 8 ls a front elevatlonal vlew of the novel geometrical form resultlng from the above suggested and illustrated construction, the form being generally in the shape of a hyperbolic paraboloid which deflnes an external edge and an internal edge, with the internal edge forming an openlng centrally of the form;

,............................... ~

~6)4878~

FIGURES 9 and 10 are perspective vlews of the geometrlcal form shown in FIGURE 8, taken from different angles to clearly illutrate the novel form;

FIGURES 11-16 are front elevatlonal views similar to FIGURE 8, each view showing two points at sllghtly translated positions, the FIGURES showlng the manner in whlch the form of the present invention permits, when made of a semi-rigid flexible material, translation or movement of the strip along a path generally deflned by the extent of 1~ the latter. The strip may thus assume an infinite number of relative positions with the stresses established in the strip redistributing themselves in each relative position to maintain the shape of the geometrical form. While FIGURES 11-16 illùstrate translatory movement of the strip to thereby result in all points on the strip ving, it is also possible to fix one point- on the strip. When one point on the strip is rixed, movement of the type suggested in FIGURES 11-16 causes the geometrical form to reciprocate from side to ~ide about the fixed point while includlng curvllinear nutating-type movement;

FIGURES 17 and 18 are similar to FIGURES 1 and 2, but showing a plurality of pro~ections along the length of the internal edge extending in the direction generally centrally of the annular discs; and . . ... .... . . . .... .. . . ..
,' .~

104878~.
FIGURE 19 1~ a perspective view of a second embodiment o~ a mobile geometrlcal form in accordance with the present invention made from the discs shown ln FIGURES 17 and 18.

DESCRIPTION OF THE PREFERRED EMBODI~ENTS

Referrlng now to the FIGURES, ln which identical or similar parts have been designated by the same reference -numerals throughout, and first referring to FIGURES 1 and 2, the mobile geometrical form in accordance with the present r 1~0 invention will be de~cribed as being formed of two slitted annular strips 10 and 30. Whlle the descrlption will be outlined in the order in which the strips are assembled to ultimately form the novel form or shape, it is pointed out that the same or similar form need not be formed ~rom two individual strips but may be molded or constructed from a single continuous strip.

The annular strip 10 includes a disc 12 having an upper sur~ace 14 and a lower sur~ace 16, as viewed in FIGURE
1. The disc 12 ls provided with a slit 18 to form an end ; ~D portlon 20, marked with an A, and an opposing end portion 22, marked with a B.

.. .... . . . ... . . ..

Similarly, the annular strip 30 includes a disc 32 havlng an upper sur~ace 34 and a lower surface 36, as viewed in FIGU~E 2. The disc 32 is provlded with a slit 38 to thereby form opposlng end portions 40 and 42, respectively designated by the letters B and A.

The annular strip 10 ls provided with a central openlng 24. In the presently preferred embodiment, the central opening 24 is defined by a smooth internal edge 26.
The external periphery or edge contour is de~ined by a smooth edge 28. To facllitate the descriptlon o~ the novel geometrical form and the principle which makes it possible, the internal and external edges 26 are shown as simple concentrlc circular edges. Modl~ications o~ the internal and external edges will be more fully described in connection with FIGURES 17-19.

Similarly, the annular strip 30 is provided with a central opening 44 de~ined by a circular smooth internal edge 46. The external circular edge 48 is concentric with the internal edge 46 and is similarly smooth.

The upper ldes or surfaces 14 and 34, as well as the lower surfaces 16 and 36 are so defined for facilitating the description o~ the invention. These sur~aces have no other significance and, clearly, inversion o~ the discs would reverse the roles of the described surfaces.

10 .

-, . .. .. ..

1~4~78~1 ~ 11th the annular strips disposed as shown in FIGURES 1 and 2, it is pointed out that the end portlon 20, shown to the left Or the sllt 18 in FIGURE 1, is deslgnated by the letter A. On the other hand, the end portion 40, to the left of the slit 38, is designated by the letter B. Simllarly, the end portions 22 and 42, respectively to the right of slits 18 and 38, are respectlvely marked by the letters B and A.

The first step in assembling the annular strips 10 1;0 and 30 is to dispose the strips one on top of the other in a concentric fashion whereby the discs 12 and 32 overlap wlth the slits 18 and 38 aligned. In this condition, the end portion 20 is disposed contiguous to the end portlon 40 while the`end portion 22 is contiguous to the end portion 42. An end portion to the right Or the slit of one o~ the strips ls now ~oined t~ an end portion to the left of a respective slit on the other strip. mus, either the end portion 20 may be ~oined to the end portion 42 or the end portion 22 may be ~oined to the end portion 40. The particular set of end portions which are connected in this manner ls not critical and the same ultimate results are obtained, as will become evldent hereafter. As suggested in FIGURES 3 and 4, the end portions 20 and 42 have been ~oined in the example presently being descrlbed. The ~oint 50 may be ~ormed by connecting the end portions 20 and 42 in any conventional means, such as with screws and wing nuts 52.

, ... . . . .

1~)4t~78~
The r~sultlng form is generally described as a right helicoid when the remaining free end portions 22 and 40 are separated from each other or the re3ulting strlp i~
stretched generally along the axis Or symmetry.

In FIGURE 4, the resultlng hellcoid ls shown when the end portions 22 and 40 are moved ln opposing directions.
It should be noted that the effect of ~olning the two annular strips 10 and 30 in this fashion causes the upper surfaces 14 and 34 to merge and define a continuous helical surface.
Slmilarly, the lower surfaces 16 and 36 of the respective a~nular strips 10 and 30 slmllarly merge to form a helical surface. Thus, the upper surfaces 14 and 34 generally ~ace a single directlon along the axis o~ the resultlng hellcold while the lower surfaces 16 and 36 similarly face a single opposing directlon along the axis.

Also shown in FIGURE 4 are cutout portions 54 at the end portlon 22 while bolts 56 are shown pro~ecting from the end portion 40 which are adapted to be received within the cutout portions 54 when the free ends of the helicoid are ~oined in a manner to be described hereafter.

As suggested above, the annular strips 10 and 30 are made of a semi-rigid flexible material. This material may either be sheet metal or a sheet of elastomeric plastic material.

12.

1~487~.1 The thickness and hardness o~ the annular strips will determine the ease with which the resulting geometrlcal form can be shifted or translated along ltself, as will become evldent hereafter.

Referrlng to FIGURE 5, the next step in the assembly of the construction of the form is the bending of one free end of the resulting spiral or helicoid shown in FIGURE 3 to cause, in the example shown in FIGURE 5, lower surface portions 16' and 36' to face each other. The configuratlon wl~û shown in FIGURE 5 ls achieved by bending the disc 32 at the end portlon 40 inwardly or towards the end portions 20 and 42 and bringing the lower surface 36 ln the region of the end portion 40 to a facing condition with respect to the lower surface 16 of the disc 12. Once the disc 32 has been so deformed, the end portion 40 is continuously moved along the lower surf'ace 16 in a generally counter-clockwise direction, as viewed in FIGURE 4, until the end portion 40 is dfsposed ad~acent to the end portion 22.

The transformation ~etween the shapes shown in 2 D FIGURES 5 and 6 are effected by twisting the resulting end portions 22 and 40 tcwards each other to dispose the lower surface portions 16' and 36' in a common plane. The free ends and end portions 22 and 40 are then aligned to dispose the edges at the free end portions coextensively with one another and cause the upper surfaces 14 and 34 and lower surfaces 16 and 36 at the free end portions to generally face the same dlrections.

104~7~/1 The final step o~ the constructlon process ls the Joining Or the free ends to each other at a second ~oint 58, shown in FIGURE 7. The resulting mobile shape or ~orm is generally designated by the reference numeral 60.
I~ will be noted that the form 60 merges the original upper surfaces 14 and 34 into a continuous sur~ace. Similarly, the original lower surfaces 16 and 36 of the component annular strlps are similarly merged lnto a continuous surface.

It is also noted that the novel mobile form 60 now lo includes an internal edge 62 which represents the origlnal internal edges 26 and 46 which merge when the annular strlps are ~oined as described. Similarly, a new continuous external edge 64 is defined by the form 60 which replaces the original external edges 28 and 48 of the two component strips. The above described continuous edges and surfaces are shown ln FIGURES 7 and 9.

The novel mobile shape or form 60 defines an interesting mathematical warped surface resembling, in certain respects, the doubly ruled hyperbolic paraboloid. However, it should be noted 20 that the hyperbolic paraboloid is formed of a solld warped or deformed planar sheet. On the other hand, the form 60 of the present invention is in the form of a continuous warped strip having a ~inite width. For this reason, an internal edge 62 is defined which forms a central opening exhibited by the form 60. It is the provision of the internal edge 62, and the 14.

16~48781 central opening which it represents, which substantially increases the versatility of the form 60 since this permits the translatory and reciprocating movements which have been suggested above and which will be further described hereafter in connection with FrGURES 11-16.
An interesting characteristic of the novel form 60 is its ability to maintain the shape shown in the FIGURES even though the form may be made from a semi-rigid flexible material.
The tendency for the form 60 to maintain its shape exists even when limited external forces are applied to the form, In-this connection, reference is had to FIGURES 8 and 10 wherein the mobile form 60 is viewed at a particular instance of time.
In the confiyuration shown, the form 60 exhibits four lines of inflection 66. These lines are inflection separate or divide each of the surfaces, i.e., the original merged lower surfaces or the original merged upper surfaces, into four surface portions each having successive concave and convex contours. Clearly, opposing surface portions of the resulting strip between the same inflection lines have opposing concave and convex contours. The concave surfaces or contours are designated by the reference numeral 68 while the convex surfaces or contours are designated by the reference numeral 70. In this connection, the form 60 can be described as a continuous strip of material which is twisted in such a manner to cause each continuous looped surface to include two portions thereof which substantially face each other and two portions which are substantially directed away from one another. The portions which face each other and the portions directed in opposing directions being 1C)4~781 symmetrically disposed about ancl substantially parallel to respective planes which are normal to one another. In the example illustrated in FIGURE 10, the surface portlons which face each other are alway~ the convex surfaces 70 whlle the surface portions which are directed away from each other are always the concave surfaces.

The lines of inflection 66 which are exhibited ln the form 60 are caused by and represent a dlstr~bution of stresse~ within the resulting contlnuous strlp whlch tends ~lo to maintain the strlp in the shape shown ln FIGURES 8-16.
However, referring to FIGURES 11-16, it will become clear that the strlp may assume the same geometrical ~orm in an infinite number of relative positions of the strip. In each case, the stresses established in the strip redistribute themselves ln each relative posltlon of the strip to malntain its shape of the geometri¢al form 60. In this sense, the restoring forces at any single point on the continuous loop tend to revert that portion into the planes of the original flat annular strips 10 and 30. It is these restoring forces 20 which maintaln the curved or warped conditlon of the form 60 ln a state of equllibrium or stability.

The mobility or ability of the form 60 to move or translate along itself is based on the semi-rigid characterlstic of the resulting strip, the central openlng defined by the lnternal edge 62 and the ability of the resulting shape to reach a stable equilibrlum and distributlon of stresses which tend to maintaln the strip in the desired shape or form. Referring to 16.

.. .. . .. .. .. . ..
.

B7~1 ~IGURE3 11-16, the resulting form 60 is shown ln each FIGURE with markings 72 and 711. The markings 72 and 74 are provlded on the strip to indicate flxed points on the strip to illustrate the translatory movement of which the present form 60 is capable of achieving. To best understand this type of movement, it may be helpful to imagine an imaginary continuous path or corridor which is flat and shaped to receive lnternally thereof the form 60. If such a shaped path or guide corridor could be imagined, the translatory lo motion which is illustrated in FIGURES 11-16 is comparable to the constant advancement of each point on the continuous strip of the form within the lmaginary guide path or corridor.
Stated otherwise, the movement illustrated in the FIGURES
ls such that each fixed point on the resulting form 60 can continuously move along a path generally defined by the form itself. Thus, the point 72 is shown in the lower left corner ln FIGUÆ 11 whlle the marking 74 is in the upper right corner.
However, with sliding or translatory motion of the entire strip in the direction indicated by the dashed arrows, the 20 point or marking 72 is advanced towards the middle left while the marking 74 is moved towards the middle right of the form.
With continued movement of the resulting strip in the direction of th0 dashed arrow~, the points 72 and 74 ultimately move to the rear of the form in FIGURE 14 and continue to advance-to positions shown in FIGURE 16. A FIGURE subsequent to FIGURE 16 would appear similar to FIGURE 11 wherein the point A has m~ved from the rear onto the upper right corner 17.

~V4~781 Or the form and the marking 74 from the rear to the lower left corner of the form as shown in FIGURE 11. It ls pointed out in connection with FIGURES 11-16 that the translatory motlon there shown results when every point o~ the form ls moved relative to a fixed point externally of the form. It is for this reason that the strip is permltted to advance while the overall form appears to be statioary, with the exception to the reference to markings 72 and 74.

A substantially different effect is observed when l~o the translatory motion above described is applied to a form 60 which is fixed at one point thereof. When this is done, the form exhibits the above translatory motion, but additionally reclprocates from side to side about the fixed point in a cyclical motion not unlike a nutating motion.

Uses of the form 60 are numerous. In additlon to ornamental, artistic and amusement devlces or ob~ects, the present inventlon exhibits properties which are useful in mechanical arrangements. The translatory motion descrlbed ln connectlon with FIGURES 11-16 may be utlllzed ln a cammlng 2~ actlon. With one polnt fixed, a reciprocating motion can be achieved which exhibits both linear as well as curvilinear components. As described above, the fixlng of one point causes the form 60 to reciprocate from side to side about the fixed point, this being a useful feature in some forms of machines.

18.

." .

1~487~1 In this connection, the reciprocatory motion may be mechanlzed by alternating a~plying o~posing forces to the continuous strip proximate or ad~acent to the flxed point. The frequency of reclprocation then corresponds to the frequency at which the opposlng forces are applied to the portions of the strip ad~acent to the fixed point.

While the above described forms exhibit smooth internal and external edges, it is pointed out that pro~ections of varlous shapes can be provided along these edges. Referring to FIGURES 17 and 18, discs 76 and 77 are shown which are similar to the discs 12 and 32 shown in FIGURES 1 and 2. The discs 76 and 77 are each provided with slits 78 and opposing end portions 80 and 82. Each of the discs is provided with a plurality of equally angularly spaced radial slits 84 which together define central openings or holes 86. In order to prevent the overlap o~ two triangular pro~eCtions when the disCS are assembled, a space 88 is provided on each disc which permits the overlapping o~ the end portions 80 and 8-2 without resulting in an overlap of triangular pro~ections or extensions.

m e procedure for assembling the discs 76 and 77 is identical to that described in connection with discs 12 and 32.
Ihe resulting form is designated by the reference numeral 60' shown in FIGURE 19. Clearly, the forms are very similar, with the exception that the form 60' includes a plurallty of triangular pro~ections which pro~ect centrally into the form. The ends or 19 .

' ' ' ', 1()4~781 tlps of each Or the proJections together define a square-like opening 90. The mobile property of the form 60' are slmilar to those described in connection with the form 60.

Likewise, while the external edge 64 Or the form 60 has been shown and described as being smooth, suitable protuberances or pro~ections may similarly be provided along the external edge 64. Such pro~ections generally extend in a direction away from the central region of the rorm.
Accordlng to one embodlment of the present inventlon, the external edge 64 has a predetermined length. In this embodiment, two extensions are provided at points along the predetermined length to form therebetween two equal length portions. Each extension extends in a direction substantially normal to the external edge portion ~rom which it pro~ects and each extension is provided wlth a surface at the free end thereof which is substantially parallel to the respective external edge portion.
The form 60 is supportable on the two end sur~aces when the extensions, in the form of legs, are dispo~ed ad~acently to .. . .
one another in opposing relation. As suggested above, when 20 one of these extenslons or legs is fixed in space relative - to the other extenslon, the other pro~ection is movable between two positions. In one position, the extensions are dlsposed ln ad~acent, substantially parallel and opposing positions. In the other position, the sur~aces of the extensions, which faced each other in the first or initial position, face away from 20.

.. . ... . . . .. . .. . . .

1~)4~7t31 each other in t~e other or secorld position. By successively fixing each of the legs or extensions, the form can be advanced along a linear directlon.

It will thus be noted from the above description that the novel geometrical form o~ the present invention can exhiblt various forms of motion while it does not have any moving parts.

While reference has been made throughout to annular strlps, it is pointed out that this phrase is not intended to be limited to circular annular strips, as suggested, for example, in FIGURES 1 and 2. The term annular strip in the context of the present description and claims is intended to include any flat sheet of arbitrary peripheral or edge contours or outlines.
This may include square, triangular or any shaped sheets. Each sheet, lrrespective to its outside contour or edge configuration is provided with an internal opening, which may again assume an arbltary shape. The internal opening may be disposed anywhere within the external edge boundaries, not necessarily centrally located. The slits above described now extend between an internal and external edge boundary.

Numerous alterations of the structure herein disclosed will suggest themselves to those skilled in the art. However, it is to be understood that the present disclosure relates to a preferred embodiment of the invention which is for purposes of illustration only and is not to be construed as a limitation of the invention.

21.

.. ..
?

.

Claims (22)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. A mobile geometrical form comprising a double-sided continuous strip of material of uniform width, 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 of uniform width, 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 of uniform width 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.

24.
17. A mobile geometrical form as defined in claim 15, 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 25.

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 of uniform width 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 services 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 of uniform width 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.

27.
CA74214942A 1973-12-26 1974-11-29 Mobile geometrical form Expired CA1048781A (en)

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US428201A US3884462A (en) 1973-12-26 1973-12-26 Mobile geometrical form

Publications (1)

Publication Number Publication Date
CA1048781A true CA1048781A (en) 1979-02-20

Family

ID=23697950

Family Applications (1)

Application Number Title Priority Date Filing Date
CA74214942A Expired CA1048781A (en) 1973-12-26 1974-11-29 Mobile geometrical form

Country Status (13)

Country Link
US (1) US3884462A (en)
JP (1) JPS6052958B2 (en)
BE (1) BE823655A (en)
CA (1) CA1048781A (en)
DE (1) DE2453045C2 (en)
DK (1) DK659774A (en)
ES (2) ES433325A1 (en)
FR (1) FR2256044B1 (en)
GB (1) GB1494488A (en)
IL (1) IL46227A (en)
IT (1) IT1029639B (en)
NO (1) NO744660L (en)
SE (1) SE429117B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7220105B2 (en) 2004-10-20 2007-05-22 Gene Schobinger Ornamental wind turbine apparatus

Families Citing this family (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4214747A (en) * 1978-04-07 1980-07-29 Francis Rebajes Mobile geometrical form
US4384717A (en) * 1981-11-12 1983-05-24 Morris Daniel L Mobius strip puzzle
CH647121GA3 (en) * 1981-11-25 1985-01-15 Christian Glauser Wristwatch case
US5324037A (en) * 1993-06-24 1994-06-28 Greeson Ewell E Mobius strip puzzle
US6250988B1 (en) * 1999-09-24 2001-06-26 Martin Fleet Hand manipulable device
US6595519B1 (en) * 1999-11-30 2003-07-22 Mcgoveran David O. Dimensional puzzle
US20110212798A1 (en) * 2007-12-17 2011-09-01 Tangle, Inc. Segmented ball with lighted elements
US20080090486A1 (en) * 2006-10-11 2008-04-17 Tangle, Inc. Resilient Ball Containing Looped Segments
US7867115B2 (en) * 2007-12-17 2011-01-11 Tangle, Inc. Segmented ball with lighted elements
USD692510S1 (en) 2007-12-17 2013-10-29 Tangle, Inc. Ball
USD623247S1 (en) 2008-02-14 2010-09-07 Tangle, Inc. Baseball
US9115508B2 (en) * 2009-04-21 2015-08-25 Medi-Mag Ltd. Flexible segmented support structure
USD956880S1 (en) * 2019-05-16 2022-07-05 Minghuan Xu Puzzle cube
CN113388958A (en) * 2021-06-07 2021-09-14 上海帽仕汇服饰有限公司 Decorative belt and using method thereof

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3492191A (en) * 1966-07-25 1970-01-27 James Paul Van Horn Functional decorative unit
US3450592A (en) * 1967-10-20 1969-06-17 Plykon Corp Multiple use geometrical shape
US3660213A (en) * 1970-02-02 1972-05-02 Henry Beakbone Fortox Ltd Corrugated covers

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7220105B2 (en) 2004-10-20 2007-05-22 Gene Schobinger Ornamental wind turbine apparatus

Also Published As

Publication number Publication date
SE7415837L (en) 1975-06-27
JPS6052958B2 (en) 1985-11-22
BE823655A (en) 1975-04-16
SE429117B (en) 1983-08-15
FR2256044A1 (en) 1975-07-25
IL46227A (en) 1977-03-31
ES226096U (en) 1977-04-01
ES433325A1 (en) 1978-03-16
JPS5096338A (en) 1975-07-31
DK659774A (en) 1975-08-18
US3884462A (en) 1975-05-20
FR2256044B1 (en) 1978-09-29
ES226096Y (en) 1977-08-01
GB1494488A (en) 1977-12-07
NO744660L (en) 1975-07-21
IL46227A0 (en) 1975-03-13
IT1029639B (en) 1979-03-20
DE2453045A1 (en) 1975-07-10
DE2453045C2 (en) 1984-07-05

Similar Documents

Publication Publication Date Title
CA1048781A (en) Mobile geometrical form
US1973564A (en) Toy designing block
US2875543A (en) Surface ornamentation of flexible sheet materials and method of making tools for producing such ornamentation
US5895306A (en) Polygonal puzzle kit capable of three-dimensional construction, such as toy construction
US3503832A (en) Repetitive unit sculpturing apparatus
DE68927893T2 (en) ITEM PRODUCED IN A MOLD WITH A MATTE SURFACE AND MANUFACTURE THE SAME
US4391045A (en) Drawing instrument or apparatus
US3061946A (en) Drawing appliance for producing ornamental designs
US4071248A (en) Puzzle apparatus
US3777359A (en) Method of making skeletal tetrahedrons
JPS6490067A (en) Production of patterned decorative material
JPH0433920Y2 (en)
US4258497A (en) Educational building blocks
DE69013493T2 (en) Manufacturing process of a patterned decorative material.
KR200181072Y1 (en) Intagio-embossment figured artificial fingernail
JPH0330069Y2 (en)
JPS6024833Y2 (en) decorative border
FR2591238B1 (en) PROCESS FOR PRODUCING A DECORATIVE FABRIC WITH RELIEF PATTERNS AND FABRIC THUS OBTAINED
JPS6038942Y2 (en) sculpture for Buddhist altar
USD257419S (en) Set of stackable coasters
Lavin Abstraction in Modern Painting: A Comparison
KR970001622Y1 (en) Playing game means
KR840002377Y1 (en) Molding form for making patterns
FR2632242B1 (en) PROCESS FOR PRODUCING A COMPOSITE MATERIAL BASED ON EXPANDED THERMOSETTING RESIN AND NEW MATERIAL OBTAINED
SE8605560D0 (en) MOLD