Abstract
An assembly for converting motion has a first member; a second member pivotally connected at a first position to a first position on the first member; a third member pivotally connected at a first position to a second position on the first member; and a fourth member pivotally connected at a first position to a second position on the second member and pivotally connected at a second position to a second position on the third member; wherein the distance between the first position on the second member and the second position on the second member is a distance X and the distance between the first position on the fourth member and the second position on the fourth member is a distance Y; wherein X is equal to Y.
Claims
1. An assembly for converting motion, the assembly comprising: a first member; a second member pivotally connected at a first position on the second member to a first position on the first member; a third member pivotally connected at a first position on the third member to a second position on the first member, the second position on the first member being spaced apart from the first position on the first member; and a fourth member pivotally connected at a first position on the fourth member to a second position on the second member and pivotally connected at a second position on the fourth member to a second position on the third member, the second position on the second member being spaced apart from the first position on the second member and the second position on the third member being spaced apart from the first position on the third member; wherein the distance between the first position on the second member and the second position on the second member is a distance X and the distance between the first position on the fourth member and the second position on the fourth member is a distance Y; wherein the distance X is equal to the distance Y; and wherein the second member extends from the first position on the second member in the direction of the second position of the second member beyond the second position on the second member.
2. The assembly according to claim 1, wherein in an extended position the second member extends from the second position on the second member in the direction of the first position on the second member beyond the first position on the second member to or beyond the first member.
3. The assembly according to claim 1, wherein the first, second, third and fourth members have the same length.
4. The assembly according to claim 1, further comprising: a fifth member pivotally connected at a first position on the fifth member to the second position on the third member and the second position on the fourth member; and a sixth member pivotally connected at a first position on the sixth member to a third position on the second member, wherein the third position on the second member is spaced from the second position on the second member in the direction extending from the first position on the second member to the second position on the second member, and a second position on the fifth member, the second position on the fifth member being spaced apart from the first position on the fifth member.
5. The assembly according to claim 4, wherein the fifth member is of a sufficient length that a point P on the fifth member spaced from the first and second positions on the fifth member and beyond the second position in the direction from the first to the second position on the fifth member moves in a substantially straight line as the assembly moves between the retracted position and an extended position; the assembly further comprising: a seventh member pivotally connected at a first position on the seventh member to the point P on the fifth member; and an eighth member pivotally connected at a first position on the eighth member to the third position on the second member and pivotally connected at a second position on the eighth member to a second position on the seventh member, the second position on the seventh member being spaced apart from the first position on the seventh member.
6. The assembly according to claim 1, wherein the distance between the first and second position on the first member is A and wherein X and Y have a length represented by the following formula (I):
A/(1+ϕ) (I) where ϕ is as follows:
1ϕ≤2.
7. The assembly according to claim 6, wherein ϕ is from 1.1 to ≤2.
8. The assembly according to claim 6, wherein an angle α is formed between the first member and the third member when the assembly is in an extended position, the angle α defined by formula (II):
α=arccos(ϕ/2) (II) and ϕ has a value to give an angle α of from 5° up to 59°.
9. The assembly according to claim 6, wherein ϕ has the value of 1.285, SQRT(2), 1.532, [(SQRT(5)+1)/2], or SQRT(3).
10. A method for providing an assembly for converting motion, the method comprising: providing a first member; providing a second member pivotally connected at a first position on the second member to a first position on the first member; providing a third member pivotally connected at a first position on the third member to a second position on the first member, the second position on the first member being spaced apart from the first position on the first member; and providing a fourth member pivotally connected at a first position on the fourth member to a second position on the second member and pivotally connected at a second position on the fourth member to a second position on the third member, the second position on the second member being spaced apart from the first position on the second member and the second position on the third member being spaced apart from the first position on the third member; wherein the distance between the first position on the second member and the second position on the second member is a distance X and the distance between the first position on the fourth member and the second position on the fourth member is a distance Y; wherein the distance X is equal to the distance Y; and wherein the second member extends from the first position on the second member in the direction of the second position of the second member beyond the second position on the second member; the method further comprising: determining the extent of straight line motion required to be generated by the assembly and the deviation of this motion from a straight line; and selecting the value of X and Y to provide the predetermined motion.
11. The method according to claim 10, wherein the distance between the first and second position on the first member is A and wherein X and Y have a length represented by the following formula (I):
A/(1+ϕ) (I) wherein ϕ is as follows:
1<ϕ≤2.
12. The method according to claim 11, wherein ϕ is less than 2.
13. The method according to claim 12, wherein ϕ is from 1.1 to ≤2.
14. The method according to claim 11, wherein ϕ has a value up to 1.95.
15. The method according to claim 11, wherein an angle α is formed between the first member and the third member when the assembly is in an extended position, the angle α defined by formula (II):
α=arccos(ϕ/2) (II) and ϕ has a value to give an angle α of from 5° up to 59°.
16. The method according to claim 11, wherein ϕ has the value of 1.285, SQRT(2), 1.532, [(SQRT(5)+1)/2], or SQRT(3).
17. An assembly comprising an assembly according to claim 1, wherein the first member is provided by a fixed structure, operation of the assembly providing movement of the members of the assembly with respect to the fixed structure.
18. The assembly according to claim 17, comprising a plurality of assemblies according to claim 1.
19. The assembly according to claim 18, wherein one or more members of a first assembly are directly connected to a member of a second assembly.
20. The assembly according to claim 18, wherein one or more members of a first assembly are indirectly connected to a member of a second assembly by way of one or more additional members.
Description
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
[0154] The principles and operation of the assembly of the present invention and embodiments employing the assembly will be further explained by reference to the accompanying figures, in which:
[0155] FIG. 1 is a diagrammatic representation of an assembly according to one embodiment of the present invention;
[0156] FIG. 2 is a diagrammatic representation of an assembly according to a second embodiment of the present invention;
[0157] FIG. 3 is a diagrammatic representation of an assembly according to a third embodiment of the present invention;
[0158] FIG. 4 is a diagrammatic representation of an assembly according to a fourth embodiment of the present invention;
[0159] FIG. 5 is a diagrammatic representation of an assembly according to a fifth embodiment of the present invention;
[0160] FIG. 6 is a diagrammatic representation of an extendable structure of one embodiment of the present invention comprising a plurality of interconnected assemblies according to the embodiment of FIG. 3;
[0161] FIG. 7a is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 4, for which the value of ϕ is 1.285;
[0162] FIG. 7b is a diagram of the members required to construct the structure of FIG. 7a;
[0163] FIG. 7c is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising an assembly generally according to the embodiment of FIG. 4, for which the value of ϕ is 1.285;
[0164] FIG. 7d is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 3, for which the value of ϕ is 1.285;
[0165] FIG. 7e is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising an assembly generally according to the embodiment of FIG. 4, for which the value of ϕ is 1.285;
[0166] FIG. 7f is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 3, for which the value of ϕ is 1.285;
[0167] FIG. 8a is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 4, for which the value of ϕ is 1.414;
[0168] FIG. 8b is a diagram of the members required to construct the structure of FIG. 8a;
[0169] FIG. 8c is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising an assembly generally according to the embodiment of FIG. 4, for which the value of ϕ is 1.414;
[0170] FIG. 8d is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 3, for which the value of ϕ is 1.414;
[0171] FIG. 8e is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising an assembly generally according to the embodiment of FIG. 4, for which the value of ϕ is 1.414;
[0172] FIG. 8f is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 3, for which the value of ϕ is 1.414;
[0173] FIG. 9a is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 4, for which the value of ϕ is 1.532;
[0174] FIG. 9b is a diagram of the members required to construct the structure of FIG. 9a;
[0175] FIG. 9c is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising an assembly generally according to the embodiment of FIG. 4, for which the value of ϕ is 1.532;
[0176] FIG. 9d is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 3, for which the value of ϕ is 1.532;
[0177] FIG. 9e is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising an assembly generally according to the embodiment of FIG. 4, for which the value of ϕ is 1.532;
[0178] FIG. 9f is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 3, for which the value of ϕ is 1.532;
[0179] FIG. 10a is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 4, for which the value of ϕ is 1.618;
[0180] FIG. 10b is a diagram of the members required to construct the structure of FIG. 10a;
[0181] FIG. 10c is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising an assembly generally according to the embodiment of FIG. 4, for which the value of ϕ is 1.618;
[0182] FIG. 10d is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 3, for which the value of ϕ is 1.618;
[0183] FIG. 10e is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising an assembly generally according to the embodiment of FIG. 4, for which the value of ϕ is 1.618;
[0184] FIG. 10f is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 3, for which the value of ϕ is 1.618;
[0185] FIG. 11a is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 4, for which the value of ϕ is 1.732;
[0186] FIG. 11b is a diagram of the members required to construct the structure of FIG. 11a;
[0187] FIG. 11c is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising an assembly generally according to the embodiment of FIG. 4, for which the value of ϕ is 1.732;
[0188] FIG. 11d is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 3, for which the value of ϕ is 1.732;
[0189] FIG. 11e is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising an assembly generally according to the embodiment of FIG. 4, for which the value of ϕ is 1.732; and
[0190] FIG. 11f is a diagrammatic representation of an extendable structure of a further embodiment of the present invention comprising a plurality of interconnected assemblies according generally to the embodiment of FIG. 3, for which the value of ϕ is 1.732.
[0191] In the embodiments shown in the accompanying figures, the assemblies are formed from a plurality of members. Each of the members is represented as an elongate bar or arm. However, it is to be understood that the members may take other forms, as generally described above.
DETAILED DESCRIPTION OF THE INVENTION
[0192] Turning first to FIG. 1, there is shown a diagrammatic representation of an assembly according to one embodiment of the present invention. The assembly, generally indicated as 2, comprises a first member 4, a second member 6, a third member 8 and a fourth member 10. The assembly 2 is shown in FIG. 1 in an extended position.
[0193] In the assembly 2 of FIG. 1, the second member 6 is pivotally connected to the first member 4 at a position 12 forming a first position on the first member and a first position on the second member. The third member 8 is pivotally connected to the first member 4 at a position 14 forming a second position on the first member and a first position on the third member. The fourth member 10 is pivotally connected to the second member 6 at a position 16 forming a second position on the second member and a first position on the fourth member. The fourth member 10 is further pivotally connected to the third member 8 at a position 18 forming a second position on the third arm 8 and a second position on the fourth arm 10.
[0194] In the assembly of FIG. 1, the distance between the positions 12 and 16 along the second member 6 is the distance X. Similarly, the distance between the positions 16 and 18 along the fourth member 10 is the distance Y. In the assembly of FIG. 1, the distances X and Y are equal.
[0195] Turning to FIG. 2, there is shown an assembly according to a second embodiment of the present invention. The assembly, generally indicated as 2a, comprises first, second, third and fourth members arranged as shown in FIG. 1 and described above. The components and features common to FIGS. 1 and 2 are indicated using the same reference numerals and are as described above. Differences between the assemblies of FIGS. 1 and 2 are as follows:
[0196] In the assembly 2a of FIG. 2, the second member 6a extends in the direction from the position 12 to the position 16 beyond the position 16 and beyond the third arm 8. Optionally, a locking mechanism 20 is provided to lock the second member 6 and the third member 8 in the extended position.
[0197] Turning to FIG. 3, there is shown an assembly according to a third embodiment of the present invention. The assembly, generally indicated as 2b, comprises first, second, third and fourth members arranged as shown in FIGS. 1 and 2 and described above. The components and features common to FIGS. 1, 2 and 3 are indicated using the same reference numerals and are as described above. Differences between the assemblies of FIGS. 1, 2 and 3 are as follows:
[0198] In the assembly 2b of FIG. 3, the fourth member 10a extends in the direction from the position 18 to the position 16 beyond the position 16 and beyond the first arm 4. Optionally, a locking mechanism 22 is provided to lock the fourth member 10 and the first member 4 in the extended position.
[0199] In the assembly 2b of FIG. 3, the assembly is formed from four members 4, 8, 6a and 10a of equal length.
[0200] Turning to FIG. 4, there is shown an assembly according to a fourth embodiment of the present invention. The assembly, generally indicated as 2c, comprises first, second, third and fourth members arranged as shown in FIGS. 1 and 2 and described above. The components and features common to FIGS. 1, 2 and 4 are indicated using the same reference numerals and are as described above. Differences between the assemblies of FIGS. 1, 2 and 4 are as follows:
[0201] The assembly 2c further comprises a fifth member 24. The fifth member is pivotally connected to the position 18 forming a first position on the fifth member, such that the fifth member 24 is pivotally connected to both the third member and the fourth member at the position 18.
[0202] The assembly 2c further comprises a sixth member 26. The sixth member 26 is pivotally connected to the second member at a position 28 forming a third position on the second member and a first position on the sixth member. The sixth member 26 is further pivotally connected to the fifth member 24 at a position 30 forming a second position on the fifth member 24 and a second position on the sixth member 26.
[0203] The fifth member 24 has a position P thereon. In operation, when the assembly 2c is moved between a retracted position, in which the members of the assembly lie adjacent each other, and the extended position shown in FIG. 4, the point P moves in a substantially straight line extending perpendicular to the first member 4.
[0204] Turning to FIG. 5, there is shown an assembly according to a further embodiment of the present invention. The assembly, generally indicated as 2d, comprises the components of the assembly of FIG. 4, which are indicated in FIG. 5 using the same reference numerals and are as described above.
[0205] The assembly 2d of FIG. 5 further comprises a seventh member 32, pivotally connected at a first position on the seventh member to the point P on the fifth member 24. An eighth member 34 is pivotally connected at a first position on the eighth member to the position 28, thereby pivotally connected to the second member 6a and the sixth member 26a. The eighth member 34 is further pivotally connected to the seventh member 32 at a position 36, forming a second position on the eighth member 34 and a second position on the seventh member 32.
[0206] The sixth member 26a extends beyond the fifth member 24 towards the seventh member 32 and can be provided with a locking mechanism to lock the sixth and eighth members together in the extended position shown.
[0207] Referring now to FIG. 6, there is shown a structure, generally indicated as 102. The structure 102 is an expandable structure and is shown in an extended position in FIG. 6. The structure comprises a plurality of the assemblies shown in FIG. 3 and described above. In particular, the structure 102 comprises four interconnected assemblies 104a, 104b, 104c, 104d. Adjacent assemblies in the structure 102 are interconnected by way of a pivotal connection between each assembly 104a, 104b, 104c, 104d and the second and fourth members 6a, 10a of each adjacent assembly.
[0208] The structure 102 of FIG. 6 is an example of the use of the assemblies of the present invention as modules in forming larger expandable structures. As will appreciated, FIG. 6a shows one example employing four assemblies in a modular manner. However, similar structures can be formed employing fewer than four assemblies or more than four assemblies, as required for a particular application.
[0209] Turning to FIG. 7a, there is shown a diagrammatic representation of a structure comprising a plurality of interconnected assemblies. The structure of FIG. 7a is formed from a plurality of assemblies in which 1=1.285.
[0210] The structure, generally indicated as 202, comprises two assemblies 204a, 204b of the general configuration shown in FIG. 4 and described above. The assemblies 204a, 204b are interconnected first by having the point P on the fifth member of the assembly 204a pivotally connected to the point P on the fifth member of the assembly 204b. Further, the sixth member of each assembly 204a, 204b is extended beyond the fifth member, with the ends of the sixth members pivotally connected to each other.
[0211] The members required to form the structure of FIG. 7a are shown in FIG. 7b. The members of the structure 202 are all equal in length, with the difference in the members being the number of pivot connections provided. More particularly, the structure 202 is formed from eight members 206 and four members 208. The members 206 are characterised by having means for forming a pivot connection provided at three positions on the member, in particular a first position at one end, a second position at a second end and a third position a distance A/(1+ϕ) from the first position, where A is the distance between the first and second positions, as indicated in FIG. 7b. The members 208 are characterised by having means for forming a pivot connection provided at two positions on the member, in particular a first position at one end and a second position at a second end.
[0212] The assembly 202 of FIG. 7a is formed from eight members 206 and four members 208 shown in FIG. 7b. The members forming the structure 202 are all equal in length.
[0213] As shown in FIG. 7a, the structure is in an extended position, with the structure extended through an angle of β, where β=2.arccos(ϕ/2), that is an angle of 100°. The angle α between the first and third members of the assembly 204b is provided by the relationship α=arccos(ϕ/2), that is an angle of 50°.
[0214] Referring to FIG. 7c, a structure according to a further embodiment of the present invention is shown. The structure, generally indicated as 232, comprises an assembly 234 of the general configuration shown in FIG. 4 and described above, for which ϕ=1.285.
[0215] In the assembly 234, the sixth member is extended beyond the fifth member. The structure 232 further comprises a first additional member 236, pivotally connected at one end to the point P on the fifth member of the assembly 234, and a second additional member 238 pivotally connected at a first end to the end of the sixth member, with the first and second additional members 236, 238 pivotally connected to each other at a position 240 between the ends of each member.
[0216] The members required to form the structure 232 of FIG. 7c are as shown in FIG. 7b and described above. The structure 232 of FIG. 7c requires six members 206 and two members 208. Again, all the members of the structure 232 are of the same length.
[0217] It is to be noted that the first and second additional members 236, 238 are arranged in the structure 232 in a first orientation, with the first additional member 236 arranged in the opposite manner about the position 240 to the second additional member 238.
[0218] As indicated in FIG. 7c, with the structure 232 in the extended position shown, a straight line is defined by the ends of members of the structure. The straight line extends at an angle γ=arccos(ϕ/2)/2, that is 25°, to the line extending perpendicular to the first member of the assembly 234.
[0219] Referring to FIG. 7d, a structure according to a further embodiment of the present invention is shown. The structure, generally indicated as 252, comprises a first assembly 254 and a second assembly 256, both of the general configuration shown in FIG. 3 and described above, and for both of which ϕ=1.285.
[0220] In the structure 252, the first assembly 254 and the second assembly 256 are interconnected, with the first assembly inverted relative to the second assembly and the end of the third member of each assembly pivotally connected to the end of the fourth member of the other assembly.
[0221] The members required to form the structure 252 of FIG. 7d are as shown in FIG. 7b and described above. The structure 252 of FIG. 7d requires four members 206 and fourth members 208. Again, all the members of the structure 232 are of the same length.
[0222] The assembly is shown in FIG. 7d in an extended position, in which the ends of the members define a straight line extending at 90° to the line joining the first and second fixed pivots, as indicated in FIG. 7d.
[0223] Referring to FIG. 7e, a structure according to a further embodiment of the present invention is shown. The structure, generally indicated as 272, comprises an assembly 274 of the general configuration shown in FIG. 4 and described above, for which ϕ=1.285.
[0224] In the assembly 274, the sixth member is extended beyond the fifth member. The structure 272 further comprises a first additional member 276, pivotally connected at one end to the point P on the fifth member of the assembly 274, and a second additional member 278 pivotally connected at a first end to the end of the sixth member, with the first and second additional members 276, 278 pivotally connected to each other at a position 280 between the ends of each member.
[0225] The members required to form the structure 272 of FIG. 7e are as shown in FIG. 7b and described above. The structure 272 of FIG. 7e requires six members 206 and two members 208. Again, all the members of the structure 272 are of the same length.
[0226] It is to be noted that the first and second additional members 276, 278 are arranged in the structure 272 in a second orientation, opposite to the orientation in the structure 232 of FIG. 7c, again with the first additional member 276 arranged in the opposite manner about the position 280 to the second additional member 278. This results in the structure assuming an opposite configuration when in the extended position, as shown by a comparison of FIGS. 7c and 7e.
[0227] As indicated in FIG. 7e, with the structure 272 in the extended position shown, a straight line is defined by the ends of members of the structure. The straight line extends at an angle γ=arccos(ϕ/2)/2, that is 25°, to the line extending perpendicular to the first member of the assembly 274.
[0228] Turning to FIG. 7f, there is shown a diagrammatic representation of a structure comprising a plurality of interconnected assemblies. The structure of FIG. 7f is formed from a plurality of assemblies in which ϕ=1.285.
[0229] The structure, generally indicated as 292, comprises two assemblies 294a, 294b of the general configuration shown in FIG. 4 and described above. The assemblies 294a, 294b are interconnected first by having the point P on the fifth member of the assembly 294a pivotally connected to the point P on the fifth member of the assembly 294b. Further, the sixth member of each assembly 294a, 294b is extended beyond the fifth member, with the ends of the sixth members pivotally connected to each other.
[0230] The members required to form the structure of FIG. 7e are shown in FIG. 7b. The assembly 292 of FIG. 7f is formed from eight members 206 and four members 208 shown in FIG. 7b. The members forming the structure 292 are all equal in length.
[0231] It is to be noted that the orientation of the sixth members in both the assemblies 294a, 294b is reversed to that in the structure 202 of FIG. 7a. This results in the structure assuming an opposite configuration when in the extended position, as shown by a comparison of FIGS. 7a and 7f.
[0232] As shown in FIG. 7f, the structure is in an extended position, with the structure extended through an angle of β, where β=2.arccos(ϕ/2), that is an angle of 100°.
[0233] The structures shown in FIGS. 7a to 7f are examples of structures obtainable using the basic assembly of FIG. 3 with a value of ϕ=1.285. The principles underlying the structures of FIGS. 7a to 7f and their behaviour and configuration can be applied using different values of ϕ. Examples of alternative structures obtained when the value of ϕ is varied with the range 1<ϕ≤2 are shown in FIGS. 8 to 11 and discussed below.
[0234] Turning to FIG. 8a, there is shown a diagrammatic representation of a structure comprising a plurality of interconnected assemblies. The structure of FIG. 8a is formed from a plurality of assemblies in which ϕ is equal to the square root of 2, that is ϕ=1.414.
[0235] The structure, generally indicated as 302, comprises two assemblies 304a, 304b of the general configuration shown in FIG. 4 and described above. The assemblies 304a, 304b are interconnected in an analogous manner to that of the assembly of FIG. 7a, that is first by having the point P on the fifth member of the assembly 304a pivotally connected to the point P on the fifth member of the assembly 304b. Further, the sixth member of each assembly 304a, 304b is extended beyond the fifth member, with the ends of the sixth members pivotally connected to each other.
[0236] The members required to form the structure of FIG. 8a are shown in FIG. 8b. The members of the structure 302 are all equal in length, with the difference in the members being the number of pivot connections provided. More particularly, the structure 302 is formed from eight members 306 and four members 308. The members 306 are characterised by having means for forming a pivot connection provided at three positions on the member, in particular a first position at one end, a second position at a second end and a third position a distance A/(1+ϕ) from the first position, where A is the distance between the first and second positions, as indicated in FIG. 8b. The members 308 are characterised by having means for forming a pivot connection provided at two positions on the member, in particular a first position at one end and a second position at a second end.
[0237] As shown in FIG. 8a, the structure is in an extended position, with the structure extended through an angle of β, where β=2.arccos(ϕ/2), that is an angle of 90°. The angle α between the first and third members of the assembly 304b is provided by the relationship α=arccos(ϕ/2), that is an angle of 45°.
[0238] FIGS. 8c to 8f show assemblies directly analogous to the assemblies of FIGS. 7c to 7f and described above, but in which ϕ=1.414.
[0239] As indicated in FIG. 8c, with the structure 332 in the extended position shown, a straight line is defined by the ends of members of the structure. The straight line extends at an angle γ=arccos(ϕ/2)/2, that is 22.5°, to the line extending perpendicular to the first member of the assembly 334.
[0240] The assembly is shown in FIG. 8d in an extended position, in which the ends of the members define a straight line extending at 90° to the line joining the first and second fixed pivots, as indicated in FIG. 8d. It is to be noted that the fourth member of each assembly 354 and 356 extends perpendicular to the line joining the first and second fixed pivots. This is an advantage of forming the assemblies with ϕ=1.414.
[0241] Turning to FIG. 9a, there is shown a diagrammatic representation of a structure comprising a plurality of interconnected assemblies. The structure of FIG. 9a is formed from a plurality of assemblies in which ϕ=1.532.
[0242] The structure, generally indicated as 402, comprises two assemblies 404a, 404b of the general configuration shown in FIG. 4 and described above. The assemblies 404a, 404b are interconnected in an analogous manner to that of the assembly of FIG. 7a, that is first by having the point P on the fifth member of the assembly 404a pivotally connected to the point P on the fifth member of the assembly 404b. Further, the sixth member of each assembly 404a, 404b is extended beyond the fifth member, with the ends of the sixth members pivotally connected to each other.
[0243] The members required to form the structure of FIG. 9a are shown in FIG. 9b. The members of the structure 402 are all equal in length, with the difference in the members being the number of pivot connections provided. More particularly, the structure 402 is formed from eight members 406 and four members 408. The members 406 are characterised by having means for forming a pivot connection provided at three positions on the member, in particular a first position at one end, a second position at a second end and a third position a distance A/(1+ϕ) from the first position, where A is the distance between the first and second positions, as indicated in FIG. 9b. The members 408 are characterised by having means for forming a pivot connection provided at two positions on the member, in particular a first position at one end and a second position at a second end.
[0244] As shown in FIG. 9a, the structure is in an extended position, with the structure extended through an angle of β, where β=2.arccos(ϕ/2), that is an angle of 80°. The angle α between the first and third members of the assembly 404b is provided by the relationship α=arccos(ϕ/2), that is an angle of 40°.
[0245] FIGS. 9c to 9f show assemblies directly analogous to the assemblies of FIGS. 7c to 7f and described above, but in which 1=1.532.
[0246] As indicated in FIG. 9c, with the structure 432 in the extended position shown, a straight line is defined by the ends of members of the structure. The straight line extends at an angle γ=arccos(ϕ/2)/2, that is 20°, to the line extending perpendicular to the first member of the assembly 434.
[0247] FIGS. 10a to 10f and 11a to 11f show assemblies formed in an analogous manner to those of FIGS. 7a to 7f, 8a to 8f and 9a to 9f as described above, but with different values of ϕ. These figures are included to show the variation in the arrangement and function of the assemblies available from varying the value of ϕ. In the case of the assemblies of FIGS. 10a to 10f, ϕ is equal to one plus the square root of 5, all divided by 2, that is ϕ=1.618. In the case of the assemblies of FIGS. 11a to 11f, ϕ is equal to the square root of 3, that is ϕ=1.732.
