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. Morphable sheet structure comprising a succession of adjacent flexible elongated rods laterally connected to each other defining a sheet structure, each rod having two ends and defining a longitudinal axis from one end to the other end; the rods are grouped in pairs, and: each pair of adjacent rods are connected to each other through a first connector tightly connected to a second connector complementary with the first connector, being the first connector part of one rod of the pair of adjacent rods and being the second connector part of the other rod of the pair of adjacent rods; being the first connector and the second connector slidably movable to each other in the direction of the longitudinal axis; the first connector and/or the second connector extending along the entire longitude of the rod; the flexible elongated rods are bendable or twistable along the longitudinal axis simultaneously with the sliding movement of the relative position between adjacent rods; the morphable sheet structure is morphable from a flat or singly curved shape into a doubly curved shape with non-zero Gaussian curvature.

2. The morphable sheet structure according to claim 1, wherein at least some of the rods are: driven rods configured to produce driven controlled bending or twisting thereof, and/or linked rods linked to each other through an internal actuator configured to produce a relative sliding movement between the linked rods, causing the bending or twisting thereof; and/or externally actuated rods connected to an external actuator configured to produce a local movement of parts of the sheet structure, causing deformation of the sheet structure and the bending or twisting of at least some of the rods.

3. The morphable sheet structure according to claim 2, wherein each driven rod, or each internal actuator or each external actuator is made or comprises structures made of a driven material which changes a shape thereof under predefined conditions.

4. The morphable sheet structure according to claim 3, wherein the driven material integrated in the driven rods or in the structures attached to the driven rods is configured to change the longitude thereof, bend or twist under predefined conditions and is eccentrically attached to the driven rod, imposing the bending or twisting to the driven rod; or the driven material integrated in the driven rods or in the structures attached to the driven rods is configured to change the longitude thereof, bend or twist under predefined conditions and is eccentrically attached to the driven rod, imposing the bending or twisting to the driven rod and at least some of the driven rods comprises structures made of driven material on two opposed sides thereof; or the driven material integrated in the internal actuator is configured to change the longitude thereof, bend or twist under predefined conditions and is connected to the linked rods, imposing a sliding movement between the two linked rods; or the driven material integrated in the external actuator is configured to change the longitude thereof, bend or twist under predefined conditions and is connected to the externally actuated rods.

5. The morphable sheet structure according to any preceding claim 3 wherein the predefined conditions producing the driven material to change the shape thereof are predefined electrical conditions, and the driven material is connected by wires to a control device configured to provide controlled amounts of electric current to the driven material, producing the controlled shape transformation thereof.

6. The morphable sheet structure according to claim 1 wherein the rods are inextensible and incompressible in a longitudinal direction parallel to the longitudinal axis.

7. The morphable sheet structure according to claim 1 wherein the first connector and the second connector are configured to retain adjacent rods at a constant distance.

8. 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 (A).

9. The morphable sheet structure according to claim 1 wherein each rod comprises one first connector and one second connector; or each rod of a first group of rods comprises two first connectors and each rod of a second group of rods comprises two second connectors, being the rods of the first group and the rods of the second group alternated.

10. The morphable sheet structure according to claim 1 wherein the first and/or second connectors are placed on opposed sides of each single rod.

11. 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 equal or thinner than the narrowed mouth slot and a thickened end of the flap thicker than the narrowed mouth slot; being the flap of each rod tightly fitted on a narrowed mouth slot of an adjacent rod and being the correspondent thickened end inserted into the correspondent channel of the adjacent rod.

12. The morphable sheet structure according to claim 1 wherein at least one rod is elastically bendable in a transversal direction perpendicular to the longitudinal axis, defining a stable shape of the at least one rod and one or a plurality of stable shapes of the sheet structure.

13. The morphable sheet structure according to claim 12 wherein different rods have different stable shapes.

14. The morphable sheet structure according to claim 1 wherein each rod, comprising the first and/or second connectors, is made of a single material.

15. The morphable sheet structure according to claim 1 wherein the sheet structure is a tubular structure.

16. The morphable sheet structure according to claim 1 wherein at least one rod contains a responsive element selected among: shape-memory material; bimorph piezoelectric element; responsive polymer; or responsive hydrogel, pneumatically inflatable element, and the material is tuned or controlled to produce a plurality of stable shapes or to modify a stable shape thereof.

17. The morphable sheet structure according to claim 1 wherein an external actuator is connectable to the sheet structure applying forces thereto producing the sliding movement between adjacent rods and the deformation of the sheet structure.

18. The morphable sheet structure according to claim 1 wherein the first connector and the second connector of two adjacent rods are actuatable by an internal actuator producing the relative sliding movement thereof.

19. The morphable sheet structure according to claim 1 wherein: each rod has a constant cross section along the longitudinal axis; or each rod has a non-constant cross section along the longitudinal axis.

20. 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

(1) 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:

(2) FIG. 1 shows a morphable sheet structure according to a first embodiment;

(3) FIG. 2 shows the morphable sheet structure shown on FIG. 1 after a sliding movement produced between adjacent rods;

(4) FIG. 3 shows a morphable sheet structure according to a second embodiment;

(5) FIG. 4 shows the morphable sheet structure shown on FIG. 3 after a sliding movement produced between adjacent rods;

(6) FIG. 5 shows a perspective view of a sheet structure having a flat shape;

(7) 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;

(8) 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;

(9) 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;

(10) 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;

(11) 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;

(12) 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;

(13) 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;

(14) 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;

(15) 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).

(16) 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

(17) 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:

(18) 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.

(19) 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.

(20) Each pair of two adjacent rods 10 are connected to each other by a first connector 11 tightly connected with a second connector 12.

(21) 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.

(22) 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.

(23) 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.

(24) 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.

(25) A succession of pairs of adjacent rods 10 generate a morphable sheet structure 1.

(26) On FIGS. 2 and 4 it is shown the shape modification obtained by the sliding movement produced between adjacent rods 10.

(27) 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.

(28) 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.

(29) Preferably the first and second connectors 11 and 12 are made of the same material than the rod 10 being also flexible.

(30) 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.

(31) 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.

(32) 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.

(33) FIG. 5 shows a completely flat sheet structure 1 made of straight rods 10 in perspective.

(34) 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.

(35) 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.

(36) 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.

(37) 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.

(38) 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.

(39) 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.

(40) 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.

(41) The sliding displacement between adjacent rods 10 is a Gaussian function of the length along the rod 10.

(42) 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.

(43) 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.

(44) 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.

(45) 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.

(46) 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.

(47) 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).

(48) Also, a collapse of the tubular sheet structure 1 can be produced.

(49) 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 30, or applying an external force to the sheet structure 1, for example using an external actuator 31.

(50) 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.

(51) 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.

(52) 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.

(53) 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.

(54) 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.

(55) 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.

(56) 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.

(57) 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.

(58) 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.

(59) 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

(60) 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.

(61) 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.

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

(63) $\mathrm{.Math.}\left(\right)\frac{r_0^2}{n{}_{0}T}\frac{1}{2}\left[{\left({\sin }^2\cos -r_0{u}_2^{*}\right)}^2+{\left(\sin {\cos }^2-r_0{u}_3^{*}\right)}^2\right]$
wherein:
u.sub.2* is the spontaneous curvature of the rods 10;
u.sub.3* is the spontaneous torsion of the rods 10;
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.

(64) 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.

(65) 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.

(66) 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.