Expandable Truss Paraboloidal Antenna

Abstract

This invention relates to an expandable truss paraboloidal antenna structure in which the truss structure of the reflector comprises hinged struts that form interconnecting, hinged, triangular truss modules that are aligned in two geometric planes with the struts terminating at junctions on the inner and outer surfaces of the paraboloidal shaped structure. The combination of hinge struts is packaged in a compact unit and then is deployed by being automatically unfolded outwardly by spring means in certain of the hinges.

Description

BACKGROUND OF THE INVENTION

There are several different types of antenna structures that are used in communication and navigation systems. While each type is unique in its application, paraboloidal-type antennas have been found to be particularly useful in many of such systems. However, the use of paraboloidal antennas is normally limited because of the reflector size, the surface and contour tolerance that can be maintained when using higher frequencies and their weight. Thus while in many applications it is particularly advantageous to use large paraboloidal reflectors, it is often necessary to build up the structure in rather inaccessible or inconvenient places which makes their use impractical in these inaccessible places. As for example, it is difficult to use a parabolic reflector antenna of large size in space, because of the difficulty of lifting such a large structure into space and assembling it there. Further, it is usually impractical to use large paraboloidal antennas on, for example, small ships or the like where space is limited. Thus, in many such applications smaller paraboloidal antennas are used when larger ones are desired.

There are several expandable antenna structures that have been used in attempts to solve the foregoing problems. Examples of these antenna structures are assembled rigid panelled modules, hinged rigid panels, and inflatable structures. Such structures are either constructed or expanded at point of use into the large paraboloidal reflector. In using such structures, it is necessary that the imperfections in the structure be held at a minimum since as the wavelength becomes shorter, the imperfections in the structure becomes an appreciable fraction of the wavelength. In this regard, the rigidity of inflatable-type structures is difficult to maintain. Modular-type construction and hinged rigid panels are limited in use by their heavy weight and because they are difficult to assemble at point of use, and because it is difficult to package them compactly. It would therefore be advantageous to have a relatively lightweight, expandable paraboloidal antenna that is easily and automatically expanded into a paraboloidal reflector at point of use and which paraboloidal antenna, when expanded, has a rigid truss-type structure that assures a contour tolerance that will permit the transmitting or receiving of higher frequency signals.

SUMMARY OF THE INVENTION

The expandable truss paraboloidal antenna of my invention utilizes the expandable truss structure of my invention to provide a reflector truss structure. This truss structure comprises connected struts that, when deployed, lie in two geometric surfaces forming the inner and outer surface of the structure. Diagonal struts join the surface struts at their apex and form a rigid triangular three dimensional truss structure. The structural elements lying in the two geometric surfaces are hinged at both ends and at their midpoints. The diagonal struts are hinged at both ends and are rigid throughout their length. The ends of the diagonal struts and the surface struts in the geometric surfaces are connected by spider connector joints as apex points with the surface struts on the geometric surfaces and the diagonal struts forming a plurality of triangular truss modules between the two geometric surfaces. When packaged, the surface struts are broken at their midpoints and are folded inwardly, or outwardly, to a vertical, contracted package. The folding of the surface struts also draws the diagonal struts into the package.

When deployed, the surface struts are resiliently biased to an extended position and are locked in this position. The diagonal struts are automatically forced into a position where the composite structure forms a plurality of modules of near equilateral triangular trusses. Thus the elements of the entire structure are joined in groups at "spider" coupling joints, which joints as convergent points. When the spider joints are drawn together in collapsing or folding the antenna structure, all the structural struts are brought into vertical orientation from their truss positions and the struts are then strapped together as a whole in a physically compact unit for later expansion at point of use. The compact, integrated, packaged unit has high strength and rigidity and is ideally suited to withstand transportation and handling conditions. When deployed or expanded, the structure has a high rigidity against dynamic distortion and vibration and forms a parabolic antenna reflector that has broad frequency application, high-gain, lightweight, large-size potential and basic electrical simplicity.

The antenna structure of this invention may function as a receiver or as a transmitter with the employment of an expandable antenna feed that is connected to the expandable truss structure at predetermined spider joints and is supported by telescoping expandable feed support legs. A webbing, screening, or the like is used to cover the concave surface of the expandable truss structure. This screen material is folded with the contraction of the expandable truss structure of the antenna in an integrated manner. When expanded, the screen material follows the concave surface of the antenna forming the paraboloidal reflector surface.

While antennas made with the expandable truss structure of this invention may be used in ground installations, where the antennas are expanded at point of use and supported by supporting means, the antennas have many other uses as, for example, they may be expanded on ships such as submarines, destroyers and other small ships and then contracted after use and returned to a small package for storage.

The expandable paraboloidal antenna of my invention has particular application for use in space where the antenna is packaged in a small unit and lifted into space by a missile. When in space the structure is released by appropriate radio control means to expand automatically through resilient biasing means at certain of the hinge points into a rigid and locked paraboloidal antenna structure of extremely large size. The screen is unfurled by the expansion of the antenna and forms the reflector surface of the antenna. In addition the expandable feed mechanism for the antenna is carried as a part of the package and is secured to the antenna for transmission as desired. Thus it is possible through my invention to place a large paraboloidal antenna or transmitter into space and automatically assemble it without requiring the use of astronauts or the like. However, astronauts or the like may easily assemble parts of my antenna structure in space where desirable, since the main structural elements would already be joined together and expanded into a correct and rigid orientation through the expandable resiliently, biased mechanism of the antenna structure. Further my invention has interlocking forces that assures expansion of the entire structure even though certain of the mechanisms in the hinge structure may fail to function properly.

It is therefore an object of this invention to provide a new and improved expandable truss.

It is another object of this invention to provide a new and improved expandable truss paraboloidal antenna.

It is another object of this invention to provide a new and improved expandable truss structure that is capable of unfolding from a compact, rigid, high-density packaged unit to a large, rigid, low-density, expanded truss structure having a definite shape.

It is another object of this invention to provide a new and improved expandable truss paraboloidal antenna that has a broad frequency application, high gain, relatively lightweight and basic electrical simplicity.

It is another object of this invention to provide a new and improved expandable truss paraboloidal antenna that may be packaged in a small size unit, carried to point of use and then automatically expanded to a rigid antenna having a smooth and stable reflector surface.

It is another object of this invention to provide a new and improved expandable truss structure that expands automatically into an expanded structure from a small packaged unit and which force of expansion is sufficient to expand malfunctioning components in the structure.

It is another object of this invention to provide a new and improved expandable truss paraboloidal antenna that may be carried in a small package by a space missile or the like into space and automatically expanded in space providing a paraboloidal reflector and feed mechanism that will transmit and receive signals, without requiring the application of human hands in the assembly thereof in space.

These and other objects and advantages of my invention will become more apparent upon a reading of the following specification and a consideration of the attached drawings in which like referenced numerals designate like parts throughout the figures and wherein:

FIG. 1 is a view illustrating the lifting of the packaged antenna structure and feed structure into space by missile propulsion.

FIG. 2 is a partial side view in perspective of an embodiment of the expandable truss paraboloidal antenna in the state of being partially expanded.

FIG. 3 is a perspective view of an embodiment of the expandable truss structure in expanded condition.

FIG. 4 is a partial view of an embodiment of the expandable truss frame structure with the reflector mesh mounted thereon and which structure is partially expanded.

FIG. 5 is a partial view of an embodiment of the expanded truss structure.

FIG. 6 is a top view of the spider and attachment joint in the expandable truss structure.

FIG. 7 is a side view of the spider and attachment joints.

FIG. 8 is a side view of the spring-loaded knee joint in the surface struts of the expandable truss structure.

FIG. 9 is a side view of a modified spring-loaded knee joint in the surface struts.

FIG. 10 is a view taken along lines 10--10 of FIG. 9.

FIG. 11 is a view partly in section with parts broken away taken along lines 11--11 of FIG. 9.

FIG. 12 is a side view of the spring-loaded midstrut knee joint of FIG. 9 in the parted condition.

FIG. 13 is a diagrammatic illustration of the spider joints, surface struts and diagonal struts in the collapsed or packaged condition.

FIG. 14 is a diagrammatic illustration of the spider joints, surface struts and diagonal members in the transition from packaged to expanded condition.

FIG. 15 is a diagrammatic illustration of the structures in FIGS. 13 and 14 in the expanded condition.

FIG. 16 is a side view with parts broken away of the means of attaching the reflector mesh onto the surface struts and the spider joints.

FIG. 17 is a side view of a reflector mesh support member for attachment to the surface struts.

FIG. 18 is a top partial view of a reflector edge support.

FIG. 19 is a side view with parts in section of the expandable truss paraboloidal antenna with expandable feed structure in the expanded condition and being supported on the ground for vertical reception and radiation.

FIG. 20 is an exploded view of a reflector screen attachment.

FIG. 21 is a schematic diagram of a pyrotechnic deployment initiation circuit for releasing the straps holding a packaged expandable truss structure.

FIG. 22 is a schematic diagram of a pressure means for expanding the telescoping feed structure.

Referring now to FIGS. 4, 5, 13, 14 and 15, the expandable truss structure of my invention comprises interconnecting surface struts 20 and 24 that are connected to spider junctions 30 and 31 and when expanded lie in two geometrical planes or in inner and outer surfaces. Diagonal struts 22 interconnect the spider joints 30 forming a triangular truss structure within the inner and outer surfaces having a given width. All struts 22 are substantially equal in length unless it is desired that the top and bottom faces of the packaged unit be other than flat. The struts 20, 22 and 24 have varying lengths relative to each other and the surface struts 24 have varying shorter lengths relative to the surface struts 20 in the outer surface causing an overall difference in length of the two geometrical surfaces. Thus when expanded, the surface struts on the geometric surfaces form substantially equilateral triangular truss modules on the two surfaces with the peripheral distance of the concave surface being shorter than the convex surface giving the desired curvature. The diagonal struts 22 are also connected to form isosceles triangles relative to the surface struts 20 and 24 forming triangular pyramid truss modules whose height equals the thickness of the antenna frame structure. The truss modules are thus wrapped on the curve forming the parabolic surface 1.

Each of the diagonal struts 22 and the surface struts 20 and 24 are connected by hinge means 34 to the spider junctions 30. These hinge means permit the struts to pivot relative to the spider junctions 34. The surface struts 20 and 24 are hinged 35 at a point midway along their length to allow the struts to bend inwardly or outwardly and be moved as a unit into a compact structure as illustrated in FIG. 13. Each of the hinged structures 35 are resiliently biased to force the surface struts 20 and 24 to an extended condition as illustrated in FIG. 15 and to force diagonal struts 22 to the inclined position. Thus the structure as compressed in FIG. 13, when released, automatically expands by passing through the transition stage illustrated in FIG. 14. It should be recognized that this particular expandable truss structure may have many uses other than in the particular expandable truss antenna antenna embodiment of this invention.

While the truss members may be constructed from any suitable materials such as metal or the like, it has been found particularly advantageous to construct the truss members of aluminum alloy tubing. In a representative construction, the surface struts 20 on the inner surface have a length of approximately 36 inches and the surface struts 24 on the outer surface have a length of approximately 40 inches and the diagonal struts 22 have a length somewhere between 36 and 40 inches. Of course, these dimensions will vary with the size of the antenna and the particular curvature and the depth of structure of the paraboloidal reflector desired.

Referring to FIGS. 2, 3, and 4, the reflector surface comprises a conductive, highly reflective material flexible enough to be folded into the packaged configuration and stretched onto the expanded structure without wrinkling when deployed. A wire mesh reflector 26 is used to permit maximum solar transmission and to minimize shadowing the antenna structure. The effects of thermal distortion of the antenna are thereby diminished. An example of a mesh that can be used is that constructed of high tensile strength aluminum with approximately a 0.03-inch spacing that provides a strong flexible fabric with 80 percent solar transmission. Etched foil sheet and hold punched foil sheet and other mesh may also be used for the reflector surface. The surface of the mesh is normally coated with a white pigmented Teflon for temperature control and reduction of intermesh drag during deployment. It should also be recognized that a folding plastic screen of monofilament nylon or mylar can be used that is dip coated with polyimide and then plated successively with aluminum and silicon oxide. The reflector mesh 26 is supported on the structure in a manner that will be more specifically described hereinafter.

Referring now to FIGS. 6 and 7, the spider joint 30 comprises a flat connector structure having six tubular connector members for pivotally securing the surface struts 20 and 24. The spider joints 30 and 31 also have inwardly projecting members to which are connected the three diagonal struts 20. The surface struts are pivotally secured through a pivot connection 34 having a connecting pin 38 and a sleeve 36. The connection of the end of the surface strut 24 abuts against the end of the tubular member 30 as illustrated in FIG. 7 when in the extended position forming a rigid extended structure. The diagonal strut 22 is connected through a threaded clevis 40 that allows pivoting in the vertical direction and also has a sufficiently loose connection that will permit 10.degree. of rotation as is necessary in the collapse of the structure to a packaged unit. Also the connection 40 may comprise a well-known spherical bearing connection that provides vertical pivoting action and a limited bearing rotation of approximately 10.degree. . Each of the three diagonal members 22 are connected to the spider joints 30 in the manner previously described and illustrated in FIG. 7 and each of the horizontal strut members are also connected to the spider structure as described and illustrated in FIGS. 6 and 7.

Each of the surface struts 20 and 24 have hinged sections or knee joints 35, see FIG. 8, by which the surface strut may be folded. A bearing pin 47 is connected to vertical arm members 45 and 49 that are secured by welding or the like to the ends of the respective parts of the surface strut. A spiral spring 46 having projecting ends 51 that contact the inner surface of struts 24, bias the two parts of the surface struts 50 and 52 into the extended or longitudinal position. When extended to the longitudinal position a spring lock detant 54 hooks over a shoulder portion 58 and locks the structure together.

An alternate midstrut, knee joint structure is illustrated in FIGS. 9, 10, 11 and 12 and may be used in place of the hinged junction 35 illustrated in FIG. 8. It comprises a scissor-type pivoting means 64 that pivots around a bearing pin connection 62. A longitudinal spiral spring 67 extends through the knee joint and is held at each end by spring anchor clips 69 that passes through eyelets 68 and hooks through a pair of apertures in the surface strut portions 50 and 52. As may be seen in FIG. 12, when in the broken condition, spring 67 exerts a pulling force on the knee joint resiliently biasing the knee joint and the parts of the surface struts to the extended, longitudinal position. A known spring-biased, ball-detent, locking structure 74 having a tongue 70 with side recesses 72 projects into a center recess of end 66 to lock the joint structure together in the extended position.

The reflector mesh connectors 27, 42 and 61 are secured to the inner or concave surface of the paraboloidal expandable truss structure at the spider joints, at the knee joints of the surface struts and also at points along the surface struts. A cylindrical projection 32 projects from the spider joints 30 and 31 and has a threaded stud 42 on which the reflector mesh 26 may be secured by a grommet connection or the like positioned in the mesh 26. The knee joints also have a similar structure, as for example in FIGS. 8 and 9, in which tubular members 44 and 60 have studs thereon for receiving and holding the reflector mesh 26. Positioned along the surface struts 24 are a plurality of reflector mesh supports 27 that are pivotally connected by a stud, bolt or the like to the struts. A stud is threaded into the U-shaped member 27 for holding the reflector mesh 26.

Also the reflector mesh 26 may be connected to the connectors 27, 42, 44 and 61 by a line 25 or the like that is secured at one end to the connectors and at the other end to the reflector mesh at a point spaced from said connectors. By suitably adjusting tension in this line 25, it is possible to control the mesh 26 to closely conform to the true paraboloidal curvature.

It may thus be seen that upon the bending of the various spring-biased hinges in the entire structure, the mesh 26 is drawn or folded with the parts to which it is connected into spaces within the structure and thereby cover the collapsed spiders an surface struts as illustrated in FIG. 4. The mesh is secured at its outer edge to the outermost surface struts 24 by a band connection 74 in which a stud 76 holds a wire 72 that passes through a grommet in the reflector mesh 26, (see FIG. 18). The mesh 26 at its outer edge has a longitudinal flexible member made from plastic or other suitable materials that passes through a hem in the edge of the mesh structure 26.

An antenna feed mechanism 16 and 18 comprises a telescoping tripod support mechanism 64 and 66 that is initially collapsed into a package and is capable of being expanded in a manner that will be more specifically described hereinafter upon expansion of the expandable truss paraboloidal antenna structure. The support of the tripod are connected to appropriately positioned ones of the said spider joints 30 by any known swivel connection such as by spherical bearing connections, clevises, or the like. While the telescoping legs 64 and 66 are telescoped in the packaged condition as shown in FIG. 1, they are expanded through expansion of the antenna structure itself as shown in FIG. 3. Also a positive means may be provided to expand the telescopic legs such as by spring means or other known means. For example, see FIG. 22, a tank 110 provides a supply of pressurized gas. The gas passes through a pair of explosive control valves 112, through a manifold 114 and through inlet ports 120 to the respective hollow telescoping members 64 and 66. Thus, upon actuation from a ground control unit, such as by radio control or the like, the explosive valves 112 are ignited opening the valves an allowing the pressurized gas 110 to pass through the manifold 114 and into the telescoping members forcing the members 64 into the extended position. The system can be held in this pressurized condition over a period of time holding the telescoping members in the extended position. Also the telescoping members can be locked in a manner similar to that illustrated in FIG. 8 or in FIG. 12 or by any other known locking means. In the latter structure, an explosive release valve 116 would be ignited opening the valve 116 and venting the compressed gas.

In the packaged condition the collapsed antenna structure 10 is held by straps 11. These straps 11 may be automatically released, as for example, in space, by using explosive charges on the straps. The explosive charges are ignited by a conventional ground control unit connected by radio control or the like. As for example, in FIG. 21, a schematic circuit is illustrated for igniting three explosive units on each strap. A battery 112 provides a source of voltage that is connected through a switch 104 to lines 108 and 110 and to a plurality of pyrotechnic deployment initiation circuits 106. In operation, the switch 104 is closed prior to sending the unit into space, then a ground control signal operates the control unit 100 to close the circuit igniting the pyrotechnic deployment initiation charges that explode and sever the straps 11. This then allows the packaged antenna to expand in the manner previously described.

In operation to deploy and erect the antenna and feed mechanism in space, the antenna is packaged and held by straps 11 and carried into space by a missile 12. A booster missile 14 normally carries the antenna unit to the desired position in space. The control unit 100 is then actuated by a ground unit through a known radio control system to provide electricity to the pyrotechnic igniting units 106 that explode charges that sever the straps 11. The spring mechanisms in the hinge elements of the surface struts, that are spring loaded for deployment, are released causing the struts to expand outwardly and move the spider joints laterally outwardly in a folding-out action as previously described. Simultaneously with this, the explosive valves 112 are exploded from a ground control unit providing gas pressure to the telescoping feed mechanism 16 that extends outwardly as previously described. The antenna structure thus assumes the operative position as illustrated in FIG. 3 of the drawings.

The antenna structure can also be used as a ground installation by transporting the packaged antenna unit and feed mechanisms to an appropriate site, releasing the mechanism and supporting it on a plurality of vertical support members 70 (see FIG. 19). In a ground installation, the vertical support members 70 abut and are fixed to the respective spider joints 30 on the inner and outer surfaces of the parabolic structure. Since the spider joints 30 are offset from the other, it is possible to project the vertical support members 70 through the width of the antenna structure. The other ends of members 70 are supported on ground 81 in the known manner. The feed mechanism 16 is expanded by any of several known means, such as by using the gas actuated system as illustrated in FIG. 22. The reflector mesh 26 may be attached to the expanded structure in the manner previously described. An alternative structure for installing the reflector mesh is illustrated in FIG. 20 wherein a web assembly 86 is secured to the surface struts 24 and spiders 30 by appropriate connections 88 and 97. The reflecting mesh 95 is attached by lacing the mesh to the web assembly 93 and 94. The panels are each laced together by a line or the like 92. A plurality of lines 90 may be threaded through the web assembly and pulled as tight as desired to give curvature to the reflecting mesh 95 and provide a more concave surface across the triangular truss members 24.

It is understood that minor variations from the form of my invention disclosed herein may be made without departing from the spirit and scope of the invention, and that the specification and drawings are to be considered as merely illustrative rather than limiting.

Claims

Having described my invention, I now claim:

1. In an expandable truss paraboloidal antenna structure having a folded condition and an expanded condition and having two substantially geometric surfaces in the expanded condition with a paraboloidal surface,

a plurality of coupling joints having multiple connections for being positioned on said geometric surfaces,

each of said coupling joints being interconnected by a plurality of pivotally connected surface struts for lying in said geometric surfaces,

a plurality of pivotally connected diagonal struts for interconnecting said coupling joints in one surface with said coupling joints in the other surface,

said struts forming triangular trusses,

said surface struts being pivoted at their midpoints forming knee joints,

and resilient means at said knee joints for biasing said surface struts to an extended condition.

2. In an expandable truss paraboloidal antenna structure as claimed in claim 1,

said surface struts and said diagonal struts forming triangular modules with their ends terminating on said surfaces when said antenna is in said expanded condition.

3. In an expanded truss paraboloidal antenna structure as claimed in claim 2,

said struts forming substantially equilateral triangles in said modules.

4. In an expanded truss paraboloidal antenna structure as claimed in claim 3,

said triangular modules being curved as a group forming a paraboloidal surface,

and individual adjacent struts being slightly shortened and lengthened to provide said curve.

5. In an expandable truss paraboloidal antenna structure as claimed in claim 1 in which,

in the folded condition, said surface struts being pivoted at said coupling joints,

said coupling joints being drawn into a pair of adjacent and substantially flat planes,

and said pivoted surface struts and said diagonal struts being parallel.

6. In an expandable truss paraboloidal antenna structure as claimed in claim 5 including,

a flexible antenna reflector screen,

and attachment means for securing said reflector screen to said coupling joints and said surface struts whereby portions of said screen are drawn into spaces between said struts when said antenna structure is in said folded condition.

7. In an expandable truss paraboloidal antenna structure as claimed in claim 1 including,

antenna-holding means for holding said antenna structure in said folded condition,

and means for releasing said antenna-holding means and allowing said antenna structure to automatically expand to said expanded condition under the force of said resilient means.

8. In an expandable truss paraboloidal antenna structure as claimed in claim 1 including,

a flexible antenna reflector screen,

and attachment means for securing said reflector screen to said coupling joints and said surface struts.

9. In an expandable truss paraboloidal antenna structure as claimed in claim 8,

said attachment means including a plurality of pivotal connectors mounted on said surface struts.

10. In an expandable truss paraboloidal antenna structure as claimed in claim 8,

line means securing said flexible screen to said attachment means for selectively providing a curved surface on areas of said screen between ones of said attachment means.

11. In an expandable truss paraboloidal antenna structure as claimed in claim 1 including,

an expandable antenna feed having telescoping support legs,

said legs being connected to ones of said coupling joints.

12. In an expandable truss paraboloidal antenna structure as claimed in claim 12,

automatic feed extension means for automatically extending said telescoping support legs.

13. In an expandable truss paraboloidal antenna structure as claimed in claim 1,

support means for supporting said antenna structure on a base,

said support means including a plurality of support members positioned on said base and contacting said coupling joints in both of said planes.

14. In an expandable truss paraboloidal antenna structure as claimed in claim 1,

a plurality of frame modules for being fixed to said surface struts on said paraboloidal surface and providing a framing network over the space between said surface struts,

an antenna reflector screen,

and portions of said screen being attached to each of said frame modules.

15. In an expandable truss paraboloidal antenna structure as claimed in claim 14,

line means for being connected between portions of said frame and said surface struts for pulling portions of said frame and said attached screen to slightly curved shape.

16. In an expandable truss paraboloidal antenna structure as claimed in claim 1,

said surface struts comprising hollow tubes,

said resilient means comprising longitudinal spiral springs positioned within said tubes and extending across said knee joints with ends of said springs being connected to said tubes.

17. In an expandable truss paraboloidal antenna structure as claimed in claim 1 including,

locking means for locking said knee joints when in the extended position.

18. An expandable truss structure comprising,

a plurality of surface struts,

junction means for pivotally joining the ends of said plurality of surface struts in radial orientation at given points in two aligned surfaces,

a plurality of pivotally connected rigid and nonfolding diagonal struts for interconnecting said junction means in one surface with ones of said junction means in said other surface,

said surface struts and said diagonal struts in the expanded condition form a three dimensional curved truss structure in which said surface struts and diagonal struts are in different planes,

and said surface struts are pivoted at their midpoints for folding said truss structures.

19. An expandable truss structure as claimed in claim 18 including,

resilient means at said midpoints for biasing said surface struts to an extending condition and expanding said truss structure.

20. An expandable truss structure as claimed in claim 19 in which,

said surface struts and said diagonal struts collapse in different planes.

21. An expandable truss structure as claimed in claim 18 in which,

said junction means at each given point of said given points has a centered axis that is normal to said two aligned surfaces,

and the axis of said junction means at each given point is spaced from the axis of the junction means at each of the other given points.