BACKGROUND

Known methods and systems for wheels having changeable diameters use linkages, i.e., bars connected with pivots, to expand and contract the wheels. Such methods and systems lack solutions for incorporating coatings or "tires" into the wheels due to the change in dimensions. Although there are some known "origami flasher" mechanisms that accomplish diameter change, such mechanisms are in need of actuation from the outside, or a secondary mechanism, and these operate on the rim. in some known mechanisms in some of those other origami and non-origami methods, the wheel's height is traded for against its width. All these restrictions severely limit their functionality.

SUMMARY

According to one aspect a wheel is provided made of flexible, semi-stiff material that can fold and change its diameter by actuation of a central, fixed-sized huh.

This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Brief Description of the Figures and the Detailed Description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.

According to one aspect a wheel is provided, comprising:

an edge-compressed cylinder formed out of a rolled-up parallelogram-shaped sheet, the sheet comprising: two short edges; two long edges, accordion folds in a parallel corrugation pattern of accordion pleats skewed in a skew- angle in relation to the long edges and extending between the two long edges; a pair of reflection folds extending between the two short edges and being essentially equi-distant from the long edges. and sheet units bound by the intersection of the reflection folds and the accordion folds, the sheet units comprising skewed waterbomb-based folds;

wherein the wheel comprises:

the sheet rolled up in a direction of the long edges;

in the rolled-up sheet:

the two short edges compressed into two adjoined hub units, rotatable in directions opposite to each other;

the waterbomb-based folds comprising a run of the wheel,

the reflection folds reflecting the accordion pleats in the wheel and inverting the skew angle in relation in relation to the long edges such as to allow controlled compression or expansion of the rim.

Some embodiments are configured to allow inflation and deflation thereof in tandem with the controlled rotation.

In some embodiments the parallelogram-shaped sheet further comprises abrasion-resistant materials situated at locations thereon where there will be expected abrasion of the wheel during rotation on a surface. In some embodiments the abrasion-resistant materials are deposited on the sheet.

In some embodiments the accordion pleats comprise a retractable material that allows winding up the wheel. In some embodiments the retractable material consists of one or more of the group consisting of polypropylene, plastics, steel, invar, copper, wire meshes, and shape- memory alloys.

In some embodiments the retractable material has a thickness of 0.06 to 0. 16 mm.

According to another aspect a robot is provided, comprising a plurality of the wheels.

Glossary

"waterbomb base" is an "origami waterbomb-base pattern". It's a well-known pattern for accomplishing collapse of (usually) a square, or square units within a sheet.

BRIEF DESCRIPTION OF FIGURES

The figures illustrate generally, by way of example, but not by way of limitation, various embodiments discussed in the present document.

For simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity of presentation. Furthermore, reference numerals may be repeated among the figures to indicate corresponding or analogous elements. The figures are listed below.

The number of elements shown in the Figures should by no means be construed as limiting and is for illustrative purposes only.

Figure 1 depicts a side view of the wheel unfolded (above) and folded (below);

Figure 2 illustrates a side view of the wheel being folded, actuation by counter-rotation of hubs; Figure 3 shows a wheel rim:

Figure 4 is a diagram, demonstrating skewed angled corrugations;

Figure 5 depicts a cylinder, before collapse into a wheel;

Figure 6a is a schematic side view of a robot that includes the wheels, and

Figure 6b is a schematic frontal view of the robot shown in Figure 6a.

DETAILED DESCRIPTION

The following description provides specific details for an understanding of various examples of the technology. One skilled in the art will understand that the technology may be practiced without many of these details. In some instances, structures and functions may not have been shown or described in detail or at all to avoid unnecessarily obscuring the description of the examples of the technology. It is intended that the terminology used in the description presented below be interpreted in its broadest reasonable manner, notwithstanding that it is exemplified by specific examples and not every possible permutation is shown in full detail. Although certain terms may be emphasized below, any terminology intended to be interpreted in any restricted manner will be overtly and specifically defined as such in this Detailed Description section.

Structure of selected embodiments

Referring to Figure 1 and Figure 2, at first side 110 and opposite second side 120 of the wheel 100, the hub units 112, 122 can rotate m directions opposite to each other as viewed from a common viewpoint, and such counter-rotation causes the spokes of the wheel to wind up around the hub units and to unwind. This pulls in or spools out the spokes and thus precisely controls the diameter of the wheel. [Fig. 2. Actuation by counter-rotation of hubs.] At any given degree of counter-rotation the wheel remains at a specific size subject only to deformations of pressure from loads or road bumps. Thus the change to any size within the range can be effected while the wheels are rolling on the road, forward or backward.

The hub units 112, 122 define a central hole 130. The holes 130 remain of fixed size during counter-rotation and can be plugged, with allowances for air movement. The wheel itself remains at essentially constant width during the changes in its diameter.

The spokes essentially consist of folds in the surface of the wheel which fan out to the rim; they have the stability (compressive strength and resistance to bending) that a fan of flexible material gams from its corrugations. The rim itself has folds that turn inward to accommodate the shrinking diameter and outward during expansion. [Fig. 3. Wheel rim 140, shown in perspective side view above and frontal view below]. The entire constructed wheel includes material that m its chief mode of manufacture can be a single, continuous flat sheet which is glued into a cylinder and collapsed along straight-line folds. Since the original surface out of which it is made can be unperforated, the constructed wheel also hermetically encloses a volume of air that changes m amount with the changing diameter. That means the interior can also be inflated and deflated, adding to the ability of the wheel to sustain loads beyond the mechanical stiffness of the wheel material itself. It also means that in some embodiments the wheel unit functions as a pump or as a valve within a pipe or artery for example.

The cylinder that collapses into a wheel shape is made from a parallelogram-shaped surface of flat, flexible material, which is rolled into a cylinder and then has the two skewed edges joined by glue or heat-fusing. Alternatively, the cylinder can be made directly by extrusion. The flat surface, before rolling or forming into a cylinder, has folds in a parallel corrugation pattern of accordion pleats that meet the long edge of the parallelogram at an angle that is skewed m relation to the long edge. See Fig. 4. diagram, illustrating a sheet 10 with skewed angled corrugations. The thick arrow shows the direction of folding. The sheet 10 comprises: two short edges 12; two long edges 14, accordion folds in a parallel corrugation pattern of accordion pleats 16 skewed in a skew angle s in relation to the long edges 14 and extending between the two long edges 14; a pair of reflection folds 17 extending between the two short edges 12 and being essentially equi-distant from the long edges 14, and sheet units bound by the intersection of the reflection folds and the accordion folds, the sheet units comprising skewed waterbomb-based folds 18.

When in a cylinder form 200 the skew is also noticeable. See Fig. 5, showing a cylinder 200, before collapse into a wheel. Referring to Figures 1-4 as well:

The sheet is rolled up in a direction of the long edges 14. In the rolled-up sheet: the two short edges 12 are compressed into two adjoined hub units 112, 122, rotatable in directions opposite to each other; the waterbomb-based folds 18 comprising a rim 140 of the wheel 100. The reflection folds 17 reflect the accordion pleats 16 in the wheel 100 and invert the skew angle s in relation in relation to the long edges 14 such as to allow controlled compression or expansion of the rim 140.

The angle of skew and the length of the parallelogram together determine the optimal size of the hub units, relative to the overall wheel size. This means that various compression ratios, as desired, can be achieved between the wheel in its smallest and largest states. The compression ratios selected as optimal are also a function of the material chosen for the wheel, in particular the width and stiffness of the material . Paper, polypropylene, fabric with or without further implanted stiff material, as well as thin metals (such as 0.1 mm steel or tape-measure grade stock) are some of many foldabl e materials that work to form a wheel of this kind.

The skewed accordion pl eats that reach from the lower to upper edges of the parallelogram are divided by a pair of folds, of any shape that accomplishes reflection, which run across the length of the parallelogram at its middle, creating what wall be the rim of the wheel. [Fig 3. Rim.] This pair of folds intersects the accordion corrugations on the plane of the surface material but at a total of 180 degrees effectively reflecting the corrugations across the rim area. An illustration of a reflection in its simplest (but not unique) form is provided in Figure 4.

The reflection folds across the middle of the parallelogram reflect the accordion pleats which intersect them. Since those accordion pleats are slightly skewed, their angle of incidence with the reflection folds is equal to their angle of exit, but in the opposite direction. E.g., if the accordion pleats hit the reflection folds at 80 degrees, after reflection, once the wheel is formed, they emerge at 100 degrees. These skew angles are listed for illustration purposes only; the angle chosen in practice, which controls the size of the hub relative to the expanded wheel, may be different.

Reflection of the corrugations, by this or any comparable fold, has the effect of reversing the direction of the skew and, when the structure is collapsed into a wheel, also creates an opposed chirality to the fanwheels on the left and right sides. This reversed chirality' is what allows opposed rotation of the hubs and the controlled change of the wheel size. [Fig 2]

The reflection is optimally accomplished in two folds rather than one, projecting out of the plane at 90 degrees and then again to be parallel to it in the opposite direction. Using two folds allows a rim with a width to form rather than a single narrow- edge. The folds extend between the two shorter edges of the parallelogram and in their simplest version are made as straight lines.

Operation of the size change is by counter-rotation, or by rotating one side of the wheel by its hub against the other while the latter is held fixed. Turn it one way and the wheel expands; the other and it contracts. This mode of actuation of the size change, by hub rotation rather than perimeter actuation, is one of the chief novel properties of this wheel.

Manufacture

All the folds can be scored on a flat sheet of an appropriate flexible semi-stiff material (e.g. , paper, polypropylene, tape-measure grade metals) using conventional scoring equipment. Pre-folding of corrugations may take advantage of existing machinery for production of corrugations. In some embodiments the process is done starting with a rectilinear sheet that has orthogonal folds, later trimmed to form the parallelogram and the skewed angles.

At present I believe that these embodiments operate most efficiently, but the other embodiments are also satisfactory.

When the corrugations are made the sheet is flattened in a flat accordion state.

The sheet is opened again to its extended flat shape and is rolled into a cylinder core to acquire a cylindrical shape; the core is then removed. The short edges of the parallelogram, now shaped as a cylinder with a slit, are glued or heat-fused. This produces a long cylinder with all the folds in place.

The cylinder is then compressed from both ends to form the wheel.

The fact that this wheel's manufacture can start from a flat sheet, means that it can take advantage of existing roll-to-roll manufacturing techniques, standardized for production of objects from the flat state. Scoring of areas to be folded can be done in the flat-printed state, as can deposition of materials where there will be expected abrasion in the 3D state, etc.

Some embodiments allow the wheel to hold up at different size configurations a greater weight, by further comprising inflation'' deflation ability of such a wheel, in tandem with the mechanical action, i.e., counter-rotation, that causes it to expand and contract.

For example the load-bearing ability of the wheel is increased by making the surface out of which the wheel is to be formed, slightly corrugated (the corrugations running along the skewed lines of the crease pattern), e.g., with a material that still allows winding up, such as the material used in retractable tape measures. Often this material is 0.1 1 mm ± 0.05mm thickness steel. Comparisons to other wheels

An origami wheel that changes its diameter using a different principle exists, and has been used in the design of a robot by researchers at the University of Seoul See:

https://www.youtube.com/watch?v=2XVQF94ShCg , based on

https://spectrum.ieee.org/automaton/robotics/robotics-har dware/robots-get-flexible-and-torqued-up- with-deformable-origami-wheels

The Koreans' wheel is based on what they call a“traditional” origami pattern (in actuality a pattern invented by Yuri and Katrin Shurnakov) known as the“Magic Ball”. When the bail is squeezed laterally it narrows into a wheel and when stretched it forms a cylinder. A deforming wheel of this kind becomes substantially wider as it loses height and narrower as it gams height. By contrast, our wheel remains at roughly the same width during the size transformation. It thus can fit and operate in narrower crawl spaces and can be housed in robotic vehicles of a more standard form.

So-called“origami flashers” (wheel-shapes that wind up around a central core) from flexible material exist and are known in the literature. (For a recent example see

https://www.youtube.com/watch?v=QNZaHC2z7uo , based on

https : //www. resear chgate. net/publicati on/261416064_Deformable_wheel_robot_based_on_origami_str ucture ) These are of various shapes but consist primarily of single sheets of a roughly circular form where the hub is located in the center and the material wraps around it.

Paterns like this are known in the art; the researcher whose name is associated with this form is Simon Guest, see http://www2.eng.cam.ac.uk/~sdg/dstruct/wrapping.html . Note that the folding units are effectively triangles with the narrow angled apex touching the hub. In our flasher construction, the folding units are quadrilateral.

Wheels of this prior-art kind, or any single- wheel version, do not have a built-in mode of actuation. The wheel can indeed change size but by only by pulling and pushing at the perimeter. As the material needs to be flexible to allow winding about the core there is little that can be done to keep the wheel from sagging as it is pressed against a surface; the single-surface therefore needs to be stiffened. Our construction by contrast begins from a sheet first formed into a cylinder rather than a circle. This is already different from most flashers. Our construction further develops two flashers from that cylinder where other flashers that instead begin from a circle make only one (and can easily make only one). With two counteracting flashers, control is enabled from the hub over the degree of deployment.

It is worth pointing out in this context that both types of single- wheel flasher, circle-derived and cylinder-derived, look very similar in both their extended and compact positions, so that an image of a flasher has to be examined very' closely to notice what form it was derived from. Even an image of the double- wheel flasher, which show's only one side and does not explain the mode of operation, does not. im itself give information about its derivation or (more important) how it is supposed to be actuated; it still looks like a single flasher! A demonstration or explanation of the counter-rotation is needed in addition to a static image.

To continue with the prior art: A flasher design that uses rigid (not flexible) materials also is known m the literature, and was used m the design of projected deployable solar collectors for a space satellite. See https://www.youtube.com/watch?v=3E12ujulvgQ Journal article“Accomodating Thickness in Origami Based Deployable Arrays”

http://mechanicaldesign.asmedigitalcollection.asme.org/ar ticle.aspx?articleid=1737156 These“rigid origami” flashers are in need of a separate mechanism for deployment and thus current designs include a separate truss construction at the perimeter to unwind the panels from the core for deployment. There is no real mechanism to pull the panels back into folded form. Indeed the deployment is intended to be one-time, one way; but more to the point: the design itself is not suited for repeat opening/closing and at various degrees of opening. Our construction, by contrast is designed exactly for repeated, reversible, and size-controllable deployment.

Wheels that are not origami-based but that change their size on the fly are also known in the literature. These are often based on linkages (stiff, connected rods) and so-called“scissor arrays”. See https : // en. wikipedia. org/wiki/Hoberman_mechanism

In these and other non-origami cases, if the wheel is such that it needs a skin such as a tire, then a separate system has to be designed to allow the skin to morph while the skeleton (the set of linkages) does. That is the key difference from origami wheels, since in the later the skin is already folding/unfolding in an organized manner. In our wheel furthermore, the skin while folding also performs the“skeletal” function, i.e , the corrugation-folds work as stabilizing spokes.

Advantages of this Wheel, Disadvantages of Prior Art.

a. This wheel is act.uatable from a housing of a fixed size in its center rather than by a variable-sized perimeter control, as is the case m other origami wheels. This actuation is novel and derives from the opposed chirality that the two continuously conjoined flashers have, which m turn stems from the reflected axis of folding in the production of the flashers. Reflection is possible in cylindrical flashers (the unfamiliar form) but not easy to accomplish in circular flashers (the familiar one); that may be why it has not been thought of before.

b. The wheel as a whole does not. need to widen as it loses height (unlike the Korean origami wheel and some of the non-origami ones). As such it is more like familiar vehicular wheels. It also can perform its size change in narrower paths.

c. Like other morphing wheels, a robot with pairs of such wheels allows riding on slanted surfaces. d. The entire variable part of the wheel can be made from a single flat sheet, considerably easing problems of manufacture.

e. Since it is formed of a single hermetic sheet, inflatiom'deflation of such wheels is a further property (if the choice is made to use a hermetic rather than perforated material). Designs that begin from multiple surfaces have a harder time accomplishing hermetic control.

f. Because it begins from a flat surface, roll-to-roll manufacture of the basic shape is enabled.

g. if desired, further strengthening of the material via inlays onto the flat sheet as part of more elaborate manufacture can be accomplished without the need for elaborate 3D printing. For example: winding boom-type spokes can be added for stiffness while the material is still in its flat state. Likewise, rubber can be added in the region destined to become the rim.

One of the big differences betw-een an origami mechanism for changing a wheel's diameter and mechanisms that are familiar which use linkages (bars connected with pivots) is that the surface material does not significantly stretch or compress as the change in diameter is effected. The techniques that use linkages still need to answer the question about the coating or "tire" if there is going to be one; this method already integrates that solution into the design.

One consequence of this is that without changing or stretching the surface material during the size change, that surface still completely and hermetically encloses a volume. One essential difference between this "origami flasher" mechanism and origami flasher mechanisms known previously, is that there is now a means of actuation, internal to the mechanism, activated from the central hub; whereas other flashers are in need of actuation from the outside, or a secondary mechanism, and these operate on the rim.

Another difference befween this and other origami and non-origami methods of changing a wheel diameter, is that in some of those other methods, the wheel's height is traded for against its width (it can either be wide and short or thin and tall). Here the width of the wheel stays approximately the same size during the size transformation.

Projected sises

a. The wheel can function as part of a robotic toy, which may have one or more such wheels changing their shape. As with all such robots morphing wheels, a change in size of a left or right wheel alone gives a further means of turning such a vehicle without reorienting the wheel.

Figure 6a is a schematic side view of a robot 300 that includes the wheels 100, and

Figure 6a is a schematic frontal view of the robot 300 shown in Figure 6a.

b. This wheel m particular can be used as a cladding or tire for other wheel-morphing designs that make use of rigid components or skeletal elements, but do not have a solution for a“skin”. In such a combination it can serve for heavier-duty military or rover-type applications.

c. The morphing wheel can sit inside a pipe and control flow so that gas or liquid has to pass nearer to or farther from the pipe wall, constricting such flow entirely if needed. It thus can function as a valve that functions not as an ins (hole in center) but by forcing/easmg flow near the pipe wall (eclipsed hole)

d. Such pipe-flow control can function inside the human body as well, in biomedical applications. e. The change in volume inside a hermetically closed boundary allows use of this wheel as a pump. f. With connection of two such wheels either by a band or by pressure between them, the wheels can change ratios in coordinated fashion while keeping constant tension in the band or constant pressure between them. This gives a further means of achieving the goal of having a continuously variable transmission. Good solutions to this problem currently exist for heavier systems such as vehicles but the present one adds to the range of solutions that can work for lightweight motors and m nano-scale contexts.

In the discussion, unless otherwise stated, adjectives such as "substantially" and "about" that modify a condition or relationship characteristic of a feature or features of an embodiment of the invention, are to be understood to mean that the condition or characteristic is defined to within tolerances that are acceptable for operation of the embodiment for an application for which it is intended.

It should be noted that the term "item" as used herein refers to any physically tangible, individually distinguishable unit of packaged or unpackaged good or goods. Positional terms such as

"upper", "lower" "right", "left", "bottom", "below", "lowered", "low", "top", "above", "elevated",

"high", "vertical" and "horizontal" as well as grammatical variations thereof as may be used herein do not necessarily indicate that, for example, a "bottom" component is below a "top" component, or that a component that is "below" is indeed "below" another component or that a component that is "above" is indeed "above" another component as such directions, components or both may be flipped, rotated, moved in space, placed in a diagonal orientation or position, placed horizontally or vertically, or similarly modified. Accordingly, it will be appreciated that the terms "bottom", "below", "top" and "above" may be used herein for exemplary purposes only, to illustrate the relative positioning or placement of certain components, to indicate a first and a second component or to do both.

"Coupled with" means indirectly or directly "coupled with".

It is important to note that the methods described above are not limited to the corresponding descriptions. For example, the method may include additional or even fewer processes or operations in comparison to what is described herein and/or the accompanying figures. In addition, embodiments of the method are not necessarily limited to the chronological order as illustrated and described herein.

It should be understood that where the claims or specification refer to "a" or "an" element or feature, such reference is not to be construed as there being only one of that element. Hence, reference to "an element" or "at least one element" for instance, may also encompass "one or more elements".

Unless otherwise stated, the use of the expression "and/or" between the last two members of a list of options for selection indicates that a selection of one or more of the listed options is appropriate and may be made.

It is noted that the term "perspective view" as used herein may also refer to an "isometric view" and vice versa.

It should be appreciated that certain features which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features, which are, for brevity, described in the context of a single embodiment, example and/or option, may also be provided separately or in any suitable sub- combination or as suitable in any other described embodiment. Certain features described in the context of various embodiments are not to be considered essential features of those embodiments, unless the embodiment, example, and/or option are inoperative without those elements. Accordingly, features, structures, characteristics, stages, methods, modules, elements, entities or systems disclosed herein, which are, for clarity, described in the context of separate examples, may also be provided in combination in a single example.

Conversely, various features, structures, characteristics, stages, methods, modules, elements, entities or systems disclosed herein, which are, for brevity, described in the context of a single example, may also be provided separately or in any suitable sub-combination.

It is noted that the term "exemplary" is used herein to refer to examples of embodiments and/or implementations, and is not meant to necessarily convey a more- desirable use-case.

In alternative and/or other embodiments, additional, fewer, and/or different elements may be used.

Throughout this description, various embodiments may be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the embodiments. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range.

Whenever a numerical range is indicated herein, it is meant to include - where applicable - any cited numeral (fractional or integral) within the indicated range. The phrases "ranging/ranges between" a first indicate number and a second indicate number and "ranging/ranges from" a first indicate number "to" a second indicate number are used herein interchangeably and are meant to include the first and second indicated numbers and all the fractional and integral numerals therebetween.

While the aspects have been described with respect to a limited number of embodiments, these should not be construed as scope limitations, but rather as exemplifications of some of the

embodiments.