MORPHABLE SHEET STRUCTURE

Abstract

The proposed morphable sheet structure comprises a succession of adjacent flexible elongated rods (10) laterally connected to each other defining a sheet structure (1), each rod (10) defining a longitudinal axis (A); wherein the rods (10) are grouped in pairs, each pair of adjacent rods (10) are connected to each other through a first connector (11) tightly connected to a second connector (12) complementary with the first connector (11), being the first connector (11) part of one rod (10) of said pair of adjacent rods (10) and being the second connector (12) part of the other rod (10) of said pair of adjacent rods (10); being the first connector (11) and the second connector (12) slidably movable to each other in the direction of the longitudinal axis (A); the first connector (11) and/or the second connector (12) extending along the entire longitude of the rod (10).

Claims

1. A morphable sheet structure morphable from a flat or singly curved shape into a doubly curved shape with non-zero Gaussian curvature, the morphable sheet structure comprising: a succession of adjacently disposed and flexible elongated rods laterally connected to each other defining a sheet structure, each flexible elongated rod comprising two ends and defining a longitudinal axis from one end to the other end, each one of the succession of adjacently disposed and flexible elongated rods being grouped in pairs, each pair of adjacently disposed and flexible elongated rods being connected to each other through a first connector, the first connector being tightly connected to a second connector complementary with the first connector, the first connector disposed on a first one of the pair of adjacently disposed flexible elongated rods and the second connector disposed on a second one of the pair of adjacently disposed flexible elongated rods; the first connector and the second connector being slidably movable to each other in along the longitudinal axis; at least one of the first connector and the second connector extending along the entire length of a corresponding flexible elongated rod; and each one of the succession of adjacently disposed flexible elongated rods being bendable along the longitudinal axis simultaneously with the sliding movement of a relative position between adjacently disposed flexible elongated rods.

2. (canceled)

3. The morphable sheet structure according to claim 1, wherein at least some of the succession of adjacently disposed and flexible elongated rods comprise at least one of: a group of driven rods configured to produce the driven controlled bending thereof, a group of linked rods connected to each other through an internal actuator configured to produce a relative sliding movement between the linked rods, causing the bending thereof; and a group of externally actuated rods connected to an external actuator configured to produce a local movement of parts of the sheet structure, causing the deformation of the sheet structure and the bending of at least some of the rods.

4. The morphable sheet structure according to claim 3, wherein at least each one of the group of driven rods, each one the group of linked rods comprising an internal actuator, or each one of the group of externally actuated rods comprises structures made of a driven material configured to changes its shape under predefined conditions.

5. The morphable sheet structure according to claim 4, wherein the driven material is at least: configured to change the longitude of at least one of the group of driven rods, the driven material being further configured to bend under predefined conditions and being eccentrically attached to at least one of the group of driven rods, imposing the bending to the at least one of the group of driven rods; integrated into at least one of the group of driven rods, the driven material being configured to change the longitude of at least one of the group of drive rods, the driven material being further configured to bend under predefined conditions and being eccentrically attached to at least one of the group of driven rods, imposing the bending to the at least one of the group of driven rods; and at least some of the group of driven rods comprising structures made of the driven material on two opposed sides thereof; integrated into at least one of the group of linked rods and configured to change a longitude thereof, the driven material being further configured to bend under predefined conditions, the driven material being connected to at least some of the group of linked rods and configured to impose a sliding movement between at least two adjacently disposed ones of the group of linked rods; or integrated into at least one of the group of externally actuated rods and configured to change a longitude thereof, the driven material further configured to bend under predefined conditions, the driven material being connected to at least some the group of externally actuated rods.

6. (canceled)

7. (canceled)

8. (canceled)

9. The morphable sheet structure according to claim 3 wherein at least each one of the group of driven rods, each one of the group of linked rods comprising an internal actuator or each one of the group of externally actuated rods comprises structures made of a driven material configured to change its shape under predefined electrical conditions, the driven material being connected by wires to a control device configured to provide controlled amounts of electric current to the driven material, producing a controlled shape transformation thereof.

10. The morphable sheet structure according to claim 1 wherein each one of the succession of adjacently disposed and flexible elongated rods are inextensible and incompressible in a longitudinal direction parallel to the longitudinal axis.

11. The morphable sheet structure according to claim 1 wherein the first connector and the second connector are configured to retain at least two adjacent ones of the succession of adjacently disposed and flexible elongated rods at a constant distance.

12. The morphable sheet structure according to claim 1 wherein the first connector and the second connector are inextensible and incompressible in a transversal direction perpendicular to the longitudinal axis.

13. The morphable sheet structure according to claim 1 wherein: each one of the succession of adjacently disposed and flexible elongated rods comprises a first connector and a second connector; or each one of the succession of adjacently disposed and flexible elongated rods of a first group of flexible elongated rods comprises two first connectors and each one of the succession of adjacently disposed and flexible elongated rods of a second group of flexible elongated rods comprises two second connectors, each one of the flexible elongated rods of the first group and each one of the flexible elongated rods of the second group being alternated.

14. The morphable sheet structure according to claim 1 wherein at least the first connector is placed on opposed sides of a corresponding one of the succession of adjacently disposed and flexible elongated rods.

15. The morphable sheet structure according to claim 1 wherein: the first connector comprises a channel accessible through a narrowed mouth slot; the second connector comprises a flap of equal thickness or thinner than the narrowed mouth slot, and a thickened end of the flap being thicker than the narrowed mouth slot; the flap of each rod being tightly fitted on a narrowed mouth slot of an adjacent rod and the corresponding thickened end being inserted into the corresponding channel of the adjacent rod.

16. The morphable sheet structure according to claim 1 wherein at least one of the succession of adjacently disposed and flexible elongated rods is elastically bendable in a transversal direction perpendicular to the longitudinal axis, defining a stable shape of the at least one of the succession of adjacently disposed and flexible elongated rod and at least one of a plurality of stable shapes of the morphable sheet structure.

17. The morphable sheet structure according to claim 12 wherein different ones of the succession of adjacently disposed and flexible elongated rods comprise different stable shapes.

18. The morphable sheet structure according to claim 1 wherein each rod comprising at least a first connectors comprises a single material.

19. The morphable sheet structure according to claim 1 further comprising a tubular shape.

20. The morphable sheet structure according to claim 1 wherein at least one of the succession of adjacently disposed and flexible elongated rods contains a responsive element selected from the group consisting of: shape-memory material bimorph piezoelectric element responsive polymer, responsive hydrogel, and pneumatically inflatable element; the material of the responsive element being configured to produce a plurality of stable shapes.

21. The morphable sheet structure according to claim 1 wherein an external actuator is connectable to the morphable sheet structure by applying forces thereto producing the sliding movement between adjacent ones of the succession of adjacently disposed and flexible elongated rods and a deformation of the sheet structure.

22. The morphable sheet structure according to claim 1 wherein the first connector and the second connector of two adjacent ones of the succession of adjacently disposed and flexible elongated rods are actuatable by an internal actuator producing the relative sliding movement thereof.

23. The morphable sheet structure according to claim 1 wherein: each one of the succession of adjacently disposed and flexible elongated rods comprises a constant cross section along the longitudinal axis.

24. The morphable sheet structure according to claim 1 wherein each one of the succession of adjacently disposed and flexible elongated rods comprises a non-constant cross section along the longitudinal axis.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0099] The foregoing and other advantages and features will be more fully understood from the following detailed description of an embodiment with reference to the accompanying drawings, to be taken in an illustrative and non-limitative manner, in which:

[0100] FIG. 1 shows a morphable sheet structure according to a first embodiment;

[0101] FIG. 2 shows the morphable sheet structure shown on FIG. 1 after a sliding movement produced between adjacent rods;

[0102] FIG. 3 shows a morphable sheet structure according to a second embodiment;

[0103] FIG. 4 shows the morphable sheet structure shown on FIG. 3 after a sliding movement produced between adjacent rods;

[0104] FIG. 5 shows a perspective view of a sheet structure having a flat shape;

[0105] FIG. 6 shows a perspective view of the sheet structure shown on FIG. 5 after its deformation without producing sliding movement between adjacent rods but bending said rods producing a wavy surface;

[0106] FIG. 7 shows five different views of the same tubular morphable sheet structure having different longitudes and diameters but the same area, the five different views corresponding to morphed shapes of the same tubular sheet structure obtained by twisting both ends of the tubular sheet structure on opposed directions in different degrees, producing sliding displacement between adjacent rods;

[0107] FIG. 8 shows four different views of the same tubular morphable sheet structure having different longitudes and shapes (with regions of positive, negative and zero Gaussian curvature) but the same area, the four different views corresponding to morphed shapes of the same tubular sheet structure obtained by twisting two portions of the tubular sheet structure on opposed directions, producing sliding displacement between adjacent rods in an intermediate region of the tubular sheet structure generating a bulge between the two portions twisted;

[0108] FIG. 9A shows two different views of the same tubular morphable sheet structure having different longitudes and shapes (now doubly curved with negative Gaussian curvature), obtained by twisting one end of the tubular sheet structure keeping the opposed end of the tubular sheet structure untwisted, producing sliding displacement between adjacent rods on one end generating a trumped shape;

[0109] FIG. 9B shows the same tubular morphable sheet structure shown on FIG. 9A, but in which the sheet structure has a trumpet-shape stable shape morphable into a cylindrical shape, and being the sheet structure collapsible;

[0110] FIG. 10 shows thirteen different examples of shapes obtained from the same tubular morphable sheet structure, all having the same area, including cylinder-shape, cone-shape, disc-shape, trumpet-shape, spindle-shape, sphere-shape and tire-shape;

[0111] FIG. 11 shows the flat sheet structure shown on FIG. 5 but each rod including holes regularly distributed along its longitude, modifying the flexibility of the resulting rod and generating a porous sheet structure;

[0112] FIG. 12 shows a perspective view of an alternative embodiment in which the width of each rod is constantly increasing along its longitude, producing a truncated conical sheet structure;

[0113] FIG. 13 shown a graph of the stored elastic energy for a cylindrical sheet structure composed of 20 rods as a function of the helix angle (inclination of the rods axis with respect to the cylinder axis).

[0114] On most of those Figures the rods have been shown as flat bands with lateral edges in contact. It will be understood that said flat bands are a schematic view of the rods described on this document and shown in detail in FIGS. 1 to 4.

DETAILED DESCRIPTION OF AN EMBODIMENT

[0115] The foregoing and other advantages and features will be more fully understood from the following detailed description of an embodiment with reference to the accompanying drawings, to be taken in an illustrative and not limitative, in which:

[0116] FIGS. 1, 2, 3 and 4 shows a flat morphable sheet structure 1 produced by four parallel rods 10 made of flexible material such plastic.

[0117] On those Figs. each rod 10 is shown having a straight shape, defining on its center a longitudinal axis A. It will be understood that the bending or twisting of said flexible rods 10 will produce also the bending or twisting of said longitudinal axis A.

[0118] Each pair of two adjacent rods 10 are connected to each other by a first connector 11 tightly connected with a second connector 12.

[0119] On those examples the first connector 11 includes a channel 13 extending along the entire longitude of one rod 10, being said channel 13 accessible through a narrowed mouth slot 14 extending also along the entire longitude of the correspondent rod 10.

[0120] The second connector 12 includes a flap 15 with a thickened end 16 on its end, both the flap 15 and the thickened end 16 also extending along the entire longitude of one rod 10.

[0121] The thickened end 16 of the second connector 12 of one rod 10 is tightly fitted inside the channel 13 of one first connector 11 of one adjacent rod 10, passing the flap 15 through the correspondent narrowed mouth slot 14.

[0122] This solution produces the connection between two adjacent rods 10 allowing the sliding movement of the first connector and the second connector to each other in the direction of the longitudinal axis A of the correspondent rods 10 modifying the shape of the morphable sheet structure 1 and maintaining said adjacent rods 10 at a constant distance.

[0123] A succession of pairs of adjacent rods 10 generate a morphable sheet structure 1.

[0124] On FIGS. 2 and 4 it is shown the shape modification obtained by the sliding movement produced between adjacent rods 10.

[0125] FIGS. 1 and 2 shown a first embodiment of the morphable sheet structure 1 in which each rod 10 includes one first connector 11 and one second connector 12, being all the rods 10 identical.

[0126] FIGS. 3 and 4 shown a second embodiment of the morphable sheet structure 1 in which each rod 10 of a first group of rods 10A include two first connectors 11, and each rod 10 of a second group of rods 10B include two second connectors 12, being the rods of the second group of rods 10B alternated with the rods 10 of the first group of rods 10A.

[0127] Preferably the first and second connectors 11 and 12 are made of the same material than the rod 10 being also flexible.

[0128] According to a preferred embodiment each rod 10 is apparently inextensible and incompressible under forces applied in a longitudinal direction parallel to the longitudinal axis A below a pre-established threshold of forces intended for the normal use of that element in a particular application. So, the longitude of each rod 10 does not modify when a force is applied on said rod 10 in the direction of the longitudinal axis A.

[0129] It is also preferred the first and second connectors 11 and 12 being apparently inextensible and incompressible under forces applied in a transversal direction perpendicular to the longitudinal axis A below a pre-established threshold of forces intended for the normal use of that element in a particular application. So, the distance between adjacent rods 10 connected to each other through the first connector 11 and the second connector 12 does not modify when a force is applied on said connector in a direction perpendicular to the longitudinal axis A.

[0130] Those features assure that the area of the morphable sheet structure 1 does not changes when forces are applied to it, and also permits to forecast the shape of the morphable sheet structure 1 to be obtained when forces are applied to it with higher precision.

[0131] FIG. 5 shows a completely flat sheet structure 1 made of straight rods 10 in perspective.

[0132] FIG. 6 shows a morphed shape of the same sheet structure 1 shown on FIG. 5 obtained without sliding the adjacent rods 10 but only bending the sheet structure producing a wavy shape.

[0133] The morphable sheet structure 1 can also be configured as a tubular sheet structure in which one initial rod 10 of the sheet structure 1 is connected to one end rod 10 of the same sheet structure 1 producing a continuous sheet structure with a tubular nature. FIGS. 7 to 10 shown different embodiments of said tubular sheet structures 1.

[0134] A tubular sheet structure 1 in the shape of a cylinder will have the longest longitude and the smaller diameter when the rods 10 are straight extending along the entire longitude of the cylinder.

[0135] A uniform sliding movement between adjacent rods 10 will morph the shape of each rod 10 acquiring a helical shape. As sliding increased, cylinders become shorter and with increasing diameter, and the pitch of the helical rods 10 becomes shorter.

[0136] FIG. 7 shown a cylindrical sheet structure 1 including twenty rods 10 at distinct values of the helix angle. The helix angle value of the rods 10 on each embodiment shown are 0, 30, 50, 70 and 80 deg from left to right of the FIG. 7.

[0137] FIG. 8 shown different alternative shapes which can be obtained starting from a cylindrical sheet structure 1, producing a cylindrical shape with a bulge in a central region thereof.

[0138] Surfaces involving non-constant Gaussian curvature (zero, negative and positive) are also possible, producing a localized bulge which can be placed or moved along an otherwise cylindrical sheet structure 1.

[0139] The sliding displacement between adjacent rods 10 is a Gaussian function of the length along the rod 10.

[0140] In this case those shapes can be achieved through a sliding movement affecting only a central portion of the first and second connectors 11 and 12, each rod 10 having a helical shape only on said central region, so producing a non-constant sliding movement along the rods 10.

[0141] This can be produced for example rotating cylindrical end portions of the cylinder on opposed directions being the bulge produced between said cylindrical end portions.

[0142] If the sliding between adjacent rods 10 affects only one end portion of each rod 10 then, starting from a cylinder, a trumpet-shape is generated as shown on FIG. 9A. This shape can be produced rotating one end of the cylinder sheet structure while an opposed end portion of the cylindrical sheet structure is kept un-twisted.

[0143] Many different shapes can be obtained starting from a cylinder sheet structure 1. As shown on FIG. 10 also cone-shapes, disc-shapes, trumpet-shapes (flared), sphere-shapes and tire-shapes can be obtained controlling the sliding movement between adjacent rods 10.

[0144] A tire-shape is a solid of revolution obtained from a C-shape generatrix with its open side facing the axis of revolution of said solid of revolution.

[0145] Starting from a cylindrical sheet structure, a wide family of shapes is achievable by sliding rod elements non-uniformly along their length. The figure illustrates some of the possible deformation paths involving axisymmetric shapes, and includes shapes of zero Gaussian curvature (cylinders, disks and cones), surfaces with constant positive Gaussian curvature (spindles, spheres and bulges), and surfaces of constant negative Gaussian curvature (trumpet-shapes or pseudo-spheres).

[0146] Also, a collapse of the tubular sheet structure 1 can be produced.

[0147] The morphing of the tubular sheet structure 1 can be achieved producing a controlled sliding movement between adjacent rods, for example using an internal actuator, or applying an external force to the sheet structure 1, for example using an external actuator.

[0148] In the embodiments shown on FIG. 7 a twisting force applied on the two opposed ends of the cylinder in opposed directions will modify the shape of the rods 10 and will produce its sliding movement.

[0149] Alternatively, the morphing of the sheet structure 1 can be controlled through the control of the shape of the rods 10, for example using shape-memory materials, bimorph piezoelectric elements, responsive polymers; or responsive hydrogels.

[0150] Also, it is proposed the use of rods 10 being elastically bendable in a transverse direction perpendicular to the longitudinal axis A thereof, i.e. that in absence of an external force the rod 10 will adopt a predefined stable shape and when an external force produce the bending of said rod 10 it will store elastic energy which will be released when the external force disappear returning the rod 10 to the stable shape.

[0151] For example, in FIG. 9B, a morphable sheet structure having a stable trumpet shape is shown. If such sheet structure is collapsed by an external force, once the external force is released the sheet structure will spontaneously expand to recover the stable trumpet-shape.

[0152] Said sheet structure can have an additional stable shape for example in the form of a cylinder or can be morphed into the cylindrical shape by external or internal actuators or by the control of the stable shape of the rods, for example using shape-memory rods. This will allow the sheet structure to morph into the trumpet-shape or into the cylindrical shape in a controlled manner, and also will permit the recovery of one of those shapes when the sheet structure has been previously collapsed or modified by an external force.

[0153] It is also proposed that each rod 10 could have one or multiple holes or section reductions along its longitude, modifying the elastic properties and possibly the permeability of the resulting sheet structure. One embodiment of this feature is shown on FIG. 11.

[0154] It is also proposed that each rod 10 could have a variable width, producing a non-flat or non-cylindrical sheet structure. For example, in FIG. 12 it is shown one embodiment in which the rods 10 have a constantly increasing width, producing a conic sheet structure.

[0155] Other alternatives are also contemplated, for example each rod 10 having a variable width with a thickened central region and narrow ends defining a spindle-shaped rod 10 and producing a spindle-shaped or a spherical-shaped sheet structure when assembled.

[0156] Also, it is contemplated the rods 10 having a portion with a constant width and having another portion or portions having a narrowing or a thickening of the width, producing a variety of different sheet structures when assembled.

[0157] FIG. 13 shown the elastic energy stored of a cylindrical sheet structure composed of 20 rods as a function of the helix angle (inclination of the rods axis with respect to the cylinder axis), assuming that all rods 10 have the same properties

[0158] For rods 10 without spontaneous curvature or torsion, the cylindrical sheet structure has two stable low energy states. One in which the rods 10 are straight and the cylinder is long and thin, and one in which the rods 10 are bend, and the cylinder is short and fat.

[0159] The energy landscape is modified by the spontaneous curvature and torsion of the rods 10, leading to different equilibrium stable shapes (minima of the elastic energy). Note that the spontaneous torsion breaks the symmetry of the energy landscape.

[0160] Theoretical model for the elastic energy (in non-dimensional form) as a function of the helix angle.

[00001]$\mathrm{.Math.}\left(\theta \right)\frac{r_0^2}{n{\ell }_{0}T}\simeq \frac{1}{2}\left[{\beta \left({\sin }^2\theta \cos \theta -r_0{u}_2^{*}\right)}^2+{\left(\sin \theta {\cos }^2\theta -r_0{u}_3^{*}\right)}^2\right]$

wherein:
u.sub.2* is the spontaneous curvature of the rods 10;
u.sub.3* is the spontaneous torsion of the rods 10;
β is the ratio between bending and torsional rigidity of the rods 10;
r.sub.0 is the radius of the cylindrical sheet structure with straight rods 10.

[0161] Preferably each single rod 10 has a constant width on its entire longitude, but it is also contemplated said width being variable, while the first connector 11 and the second connector 12 do not change along the rod 10.

[0162] The use of non-constant width rods 10 will generate a non-flat and non-cylindrical initial sheet structure for example a cone-shape, sphere-shape, spindle-shape structures.

[0163] It will be understood that various parts of one embodiment of the invention can be freely combined with parts described in other embodiments, even being said combination not explicitly described, provided there is no harm in such combination.