GB2111840A

GB2111840A - 5x5x5 movable block device

Info

Publication number: GB2111840A
Application number: GB08232897A
Authority: GB
Inventors: David Rupert Collins; Daniel Smith
Original assignee: Individual
Current assignee: Individual
Priority date: 1981-11-24
Filing date: 1982-11-18
Publication date: 1983-07-13

Abstract

The centre of the device comprises a member (1) having six arms along three orthoganol axes. Central blocks (3) of each 5x5 outer array are resiliently attached to the ends of the arms and edge blocks (30) are held by blocks (40) which in turn are held by the central blocks (3). All the blocks are rotatable about the three axes. <IMAGE>

Description

SPECIFICATION A mechanism for modelling groups Field ofinvention The invention relates to a mechanism for modelling groups.

Background to the invention Cuboidal arrays of individually moveable elements are moveable in sets each of which includes a line of 4 facets in each of four adjoining faces of the cube, are well known as toys.

The present invention provides an improved mechanism primarily intended for use in devices capable of demonstrating combinations and permutations, and in devices that physically model some of the mathematics involved in the theory of groups and which is not limited to four facets in each line.

Devices embodying the mechanism may be brightly coloured and may of course also have some amusement value.

Summary ofthe invention According to the present invention there is provided a mechanism for modelling groups comprising a plurality of members captive to but moveable in sets in any of the three discrete rotational modes relative to a base structure, the choice of set determining the axis of rotation, the members presenting six groups of elements in a start position each of which have a characteristic or feature identifiable with a particular group, and the movement in sets re-distributing the elements to form variant groups, wherein each group comprises 25 elements in a 5 x 5 array.

Generally, the starting groups will all be different, although it is possible in a simplified version to have two or more the same, or matched pairs for example.

In the preferred form, there are 98 members forming a cube, each member having a block-like portion presenting one, two or three exposed square faces, totalling 150, on which said elements are provided. There can be variations on this, for example the sides may be made concave or convex, even to the extent of developing it into a sphere or cylinder. Further variations of the outer shape can be achieved by trimming down four parallel edges with a chamfer, to form a barrel with polygonal cross section, or by chamfering all twelve edges to form a diamond shape. Alternatively, the eight corners can be trimmed to form a polyhedronal cube.

The elements of each starting group may simply be distinguished by colour and/or pattern. The colours may be plain, so that each side of the cube in the starting position is completely red, blue, green and so on. However, aiternatives may be adopted, such as using flags as the elements, or simply patterns in monochrome. In other versions, the elements may be distinguished by projections or depressions relative to the base surfce. For example, the elements may be represented by the numbers 1 to 6 in "dot" form as on dice, with studs or dimples on the exposed faces arranged accordingly. In other variation, there may be projections of different lengths or shapes.

The base structure will generally be a six-armed spider with arms co-incident with the rotational axis mutually at right angles or aligned in opposite directions from a central boss.

Reference will hereafter be made exclusively to what we regard as the standard form, with blocks arranged to form a cube, and with each face of the cube consisting of a total of 25 faces, one from each of 25 blocks. The blocks that lie at the corner of the cube have three visible faces, the blocks that lie along the edge of the cube have two visible faces and, the rest of the blocks have one visible face.

Concealed within the cube is a logical mechanism that enables the blocks to be moved in relation to each other into a vast number of different combinations, yet at all times ensuring that all of the blocks are securely attached to each other.

The mechanism will allow any face layer of 25 blocks to be rotated about the axis perpendicular to that face through its centre. The mechanism will also any of the inner layers of 16 blocks, presenting 20 visible faces, to be rotated about the central axis perpendicular to that layer. Thus each individual block lies in three different planes of rotation, that is it forms part of three separate layers of blocks, each layer being at right angles to the other two.

By rotating different layers of blocks in different orders it is possible to move the blocks in almost any imaginable combination. There are some limitations, for example the blocks constituting the corners of the cube always move to a corner position, and blocks at the centre edge of the cube always move to a centre edge position. The same is true of the other types of blocks.

There are basically six different types of block; corner block, outside edge block, centre edge block, diagonal block, median block, and centre block.

These types are described more fully later.

An example of some of the combinations that can be realised with this mechanism is that it is possible to move any corner block to any other corner position and have it in any of the three possible orientations. It is then possible to move any one of the 7 remaining corner blocks to any of the 7 remaining corner positions, in any orientation, followed by any one of the 6 remaining corner blocks to any one of the 6 remaining corner positions, in any orientation and so on until the last corner where there is obviously no choice as to which position it can go in, and there is no choice of its orientation.

In addition to the above permutations it is possible to have at the same time any combination of permutations of the diagonal blocks, of the outer edge blocks, of the middle edge blocks, of the median blocks, and of the centre blocks.

Continuing the above example, we have the choice for every one of the corner block combinations, of being able to move any one of the 24 diagonal blocks to any one of the 24 diagonal positions and then have any one of the remaining 23 diagonal blocks moved to any one of the remaining 23 diagonal positions and so on until the last 2 diagonal blocks remain and there is no choice once on of them is positioned auto to which position the final one can go in. The process can be repeated with any one of the other types of blocks, the permutations available using any type of block being independent of the permutations available on any other type of block.

The sequence of moves necessary to achieve some of the permutations can be long and of much mathematical interest.

The invention will now be described by way of sample with reference to the accompanying drawings, which illustrate different views of one embodiment of the standard form of the invention.

Description ofthe drawings Figure 1 is an isometric view of a logic device, with some parts removed and others in ghost, Figure2 is a view of a centre layer array of blocks on the line ll-ll of Figure 1, Figure 3 is a view of a secnd layer or array of blocks on the line Ill-Ill of Figure 1.

Figure 4 is a view of an outer layer array of blocks on the line IV-IV of Figure 1, Figure 5 is three isometrics showing three axial rotation of some outer layer arrays, Figure 6 is th ree isometrics showing three axial rotation of some second layer arrays, Figure 7 is two isometric views of a corner block, Figure 8 is two isometric views of an outside edge block, Figure 9 is two isometric views of a centre edge block, Figure 70 is two isometric views of a diagonal block, and Figure 11 is two isometric views of a median block.

Detailed description of the Figures The device is in the form of a cube whose faces are formed by blocks in 5 x 5 arrays, the edge and corner blocks being common to two or three arrays.

In a start position each face of the cube will be individually and uniformly coloured, or otherwise distinguished from the other faces. The blocks have an interiocking engagement to be described below so that they are all captive to a central six armed spider.

1. The interlocking arrangement allows any layer of blocks to be rotated about the axis perpendicular and central to that layer relative to the other blocks of the cube: examples of this being shown in Figures 5 and 6.

The six arms 2 of the spider 1 are cylindrical and their axes correspond to the X, Y and Z axes of a three dimensional orthoganol system. These will be referred to as the main cube axes. At the end of each arm there is mounted a centre block and a centre block 3. This has a square head 4 with a central cylindrical stem 5 that normally abuts the end of the associated arm 2. It is held in position by a screw 6 whose head is recessed into the exposed face of the block, but between the screw head and the base of the recess there is a coil spring 7 so that the block 3 can be moved away slightly from the centre of the cube. This is necessary for ease of operation. The block 3 can also be rotated about its associated axis, with all the other blocks in its face layer. The underside of the head 4 is concave with curvature centred on the two main cube axes which do not pass through it.When finally assembled, the recess in the face is plugged or concealed so that to outward appearances it is uniform with the exposed faces of the other blocks.

In addition to these centre blocks 3 there are five other types of block. There are eight corner blokcs 10 (Figure 7), each having three exposed faces 11.

Adjacent them, along the cubes edges, there are twenty-four outside edge blocks 20 (Figure 8) each of which have two exposed faces 21. To complete the cube edges there are twelve centre edge blocks 30 (Figure 9), again each with two exposed faces 31.

Moving inwards, there are twenty-four diagonal blocks 40 (Figure 10) which present single faces 41 between the centre and corner blocks. Finally, there are twenty-four median blocks 50 (Figure 11) between the centre blocks and the centre edge blocks, showing single faces 51. These different block types will be described inturn.

The corner blocks 10 are themselves almost complete cubes. However, at the concealed inside corner there is a substantially hexahedronal lug 12 with symmetry about the diagonal axis. This lug has three faces 13 parallel to the faces 11 which meet and point towards the centre of the cube. Each of the other three faces 14 is an undercut step from a curved edge 15 centred on the cube axis normal to the associated face 13. It is by means of this lug that each corner block is held captive while still being enabled to turn in any plane with any of the three face layers of other blocks to which it is common.

The outside edge blocks 20 each have an almost complete square face 22 adjacent a corner block 10, but it is stepped inwardly at the inner corner. This step 23 has a curvature centred on the main cube axis normal to the plane of the face 22 and accom modates the guiders part of the lug 12 of the adjacent corner block (and other formations described below) as it is rotated about that axis. The opposite face 24, adjacent a centre edge block 30 is planar. A double-stepped formation extends towards the cube centre from the two faces 25 opposite the exposed faces 21 and adjacent diagonal blocks 40.This formation has a first portion 26 with curved steps 27 centred on the main cube axes normal to the faces 25 and sides coplanar with two of the faces 13 of the adjacent corner block 12, and a second portion 28 extending beyond the inner corner of the portion 26 towards the centre of the cube. This is also proud of the face 24 and is of poly-hedronal block form but with a cylindrical surface 29 centred on the main cube axis normal to the plane of the faces 25. Where the block 28 protrudes beyond the face 24 there is a curved step 28a centred on the main cube axis normal to that face, and a 45O clearance chamfer 29a is provided along the innermost edge of the block parallel to the main cube axis. The blocks 20 in any cube edge are not identical but are mirror images of each other with respect to the intervening plane through the centre of the associated centre block 30. The portions 26 and 28 hold the outside edge block 20 captive and provide guidance on rotational movement.

Each centre edge block 30 is a cube with a narrower but generally square-form extension 32 on the edge opposite the fully exposed one, sandwiched between projecting portions 28 of adjacent blocks 20. The two narrow sides 33 of this extension facing away from the block are in tangential contact with the two adjacent arms 2. The other narrow sides are both stepped into two cylindrically curved surfaces 34 and 34a centred on the axex of the adjacent arms 2 to form bridges between pairs of surfaces 29.

They do not meet the block 30 directly, there being a shallow shoulder formation 35 across each face 36 opposite the exposed face 31, terminating in a curved step 37 co-axial with the adjacent surfaces 34 and 34a. The depth of each shoulder formation 35 is the same as that of the lugs 12 and steps 27, and it effectively bridges those on either side. At the intercepts of formations 35 on each side of extension 32 there is a concave recess 38 centred on the cube axis parallel to sides 31. These recesses 38 cooperate closely with steps 28a on blocks 28.

The diagonal blocks 40 each have two adjacent faces 42 remote from the cube centre formed with curved recesses 43 to receive the projecting portions 26 of the outer edge blocks 20. When a cube face layer is rotated, the lugs 12 of its corner blocks 10 and the shoulders 35 of its centre edge blocks 30 also co-operate with these recesses. The other two faces 44 adjacent the exposed face 41 have projections 45 which are segments of a cylinder and which meets at right angles at the corner nearest the cube centre.

These have cubed steps 46 centred on respective cubes axes inn the plane parallel to the face 41. The sixth face 47 of a diagonal block, opposite the exposed face 41, is flat apart from a square step 48 inn one corner which is an extension of projections 45. The edges 49 of this step and the edges 49a of the face 47 nearest the cube centre will slide over the surfaces 34 and 34a.

The median blocks 50 have a face 52 adjacent the exposed face 51 and remote fromm the cube centre which is inwardly stepped at 53 across its whole width with a curve to accomodate the shoulder 35 of a centre edge block 30, and, on rotation, the projecting portions 26 and lugs 12. The face 54 opposite the exposed face 51 is concave with a cylindrical curvature centred on the main cube axis parallel to faces 51 and 52 but with a centre lug 55 which projects beyond the face 56 opposite the face 52.

The projections 45 of the adjacent diagonal blocks 40 snugly fit the spaces at each side of the lug 55, whose projecting and extends under the adjacent centre block 3, to be trapped thereby.

Claims

1. A mechanism for modelling groups consisting a plurality of members captive to but moveable in sets in any of three discrete rotational modes relative to a base structure, the choice of set determining the axis of rotation, wherein: (a) the members present six groups of elements in a start position each of which has a characteristic or feature identifiable with a particular group, (b) movement in sets re-distributes the elements to form variant groups, and (c) each group comprises 25 elements in a 5 x 5 array.

2. A mechanism according to claim 1 wherein the starting groups are all different.

3. A mechanism according to claim 1 wherein there are 98 members forming a cube, each member having a block-like portion presenting one, two or three exposed square faces, totalling 150, on which said elements are provided.

4. A mechanism according to claim 3 wherein the sides are concave or convex or curved to form a spherical or cylindrical shape or four parallel edges of the overall shape are chamfered to form a barrel with polygonal crop section, or all twelve edges are chamfered to form a diamond shape, or, the eight corners are trimmed to form a polyhedronal cube.

5. A mechanism according to claim 1 wherein the elements of each starting group are distinguished by colour and/or pattern.

6. A mechanism according to claim 1 wherein a base structure comprises a six-armed spider, with arms coincident with the rotational axis mutually at right angles or aligned in opposite directions from a central boss.

7. A mechanism according to claim 1 wherein 98 blocks are arranged to form a cube, with each face of the cube consisting of a total of 25 faces, one from each of 25 blocks, and the blocks that lie at each of the corners of the cube have three visible faces whilst the blocks that lie along the edges of the cube have two visible faces and concealed within the cube is a logic mechanism by which the blocks can be moved in relation to each other into a plurality of different combinations, whilst at all times securely attaching the blocks to each other, the mechanism allowing any face layer of 25 blocks to be rotated about an axis perpendicular to that face through its centre, and any of the inner layers of 16 blocks, presenting 20 visible faces, to be rotated about a central axis perpendicular to that layer so that each individual block lies in three different planes of rotation, that is it forms part of these separate layers of blocks, each layer being at right angles to the other two.

8. A mechanism according to claim 6 wherein: a) the six arms of the spider are cylindrical and the axes thereof correspond to the X Y and Z axes of a three dimensional orthogonal system and comprise the main cube axes; b) at the end of each arm there is mounted a centre block which is held in position by a screw the head of which is recessed into the outer exposed face of the block; c) between the screw head and the base of the recess there is a coil spring so that the block can be pulled slightly away from the centre of the cube, to facilitate operation; d) the centre block can also be rotated about its associated axis, with all the other blocks in its face layer; e) the underside of the head is concave with the concave curvatures centred on the two main cube axes which do not pass through it.

9. A mechanism according to claim 8 wherein there are eight corner blocks, each having three exposed faces, twenty-four outside edge blocks each of which have two exposed faces, twelve centre edge blocks each with two exposed faces; twenty four diagonal blocks which present single faces between the centre and corner blocks; and twenty % four median blocks between the centre blocks and the centre edge blocks, showing single faces; wherein: a) the corner blocks are almost complete cubes, but at the concealed inside corner of each there is a substantially hexahedronal lug with symmetry about the diagonal axis, the lug having three faces parallel to the faces which meet and point towards the centre of the cube, each of the other three faces being an undercut step from a curved edge centred on the cube axis normal to the associated face, each corner block being held captive by means of the said lug while still being enabled to turn in any plane with any of the three face layers of other blocks to which it is common;; b) the outside edge blocks each have an almost complete square face (to lie adjacent a corner block) which face is stepped inwardly at the outer corner, this step having a curvature centred on the main cube axis normal to the plane of the said square face thereof and accommodating and guiding part of the diagonaliy extending lug of an adjacent corner block as it is rotated about the main cube axis, the opposite face of the edge block (to lie adjacent a centre edge block) being planar, a double-stepped formation for extending towards the cube centre from the two other faces of the edge block (which other faces are opposite the exposed faces and will lie adjacent blocks in the array), this double-stepped formation having a first portion with curved steps centred on the main cube axes normal to the said two other faces and with sides coplanar with two of the faces of an adjacent corner block, and a second portion extending beyond the inner corner of the said first portion for extending towards the centre of the cube, which is also proud of the said opposite face and is of polyhedronal block form but with a cylindrical surface centred on the main cube axis normal to the plane of the said two other faces, and where the block protrudes beyond the said opposite face there is a curved step centred on the main cube axis normal to that face, and a 45 clearance chamfer which is provided along the innermost edge of the block parallel to a main cube axis, and wherein outside edge blocks in any cube edge are not identical but are mirror images of each other with respect to the intervening plane through the centre of the associated centre edge block, and the said first and second portions hold each outside edge block captive and provide guidance on rotational movement;; c) each centre edge block is a cube with a narrower but generally square-form extension on the edge one which will be fully exposed on assembly and adapted to be sandwiched between said second portions projecting from adjacent extrude edge blocks, each said extension being two narrow sides facing away from the block which will be in tangential contact with the two adjacent arms of the central spider, whilst the other narrow sides are both stepped into two cylindrically curved surfaces which will be centred on the axes of the said adjacent arms of the spider on assembly to form bridges between pairs of said cylindrical surfaces;; d) the diagonal blocks each have two adjacent faces remote from the cube centre formed with curved recesses to receive the said first projecting portions of outer edge blocks when assembled, and two other faces adjacent the exposed face of the diagonal block have projections which are segments of a cylinder and which meet at right angles at the corner of the block which when assembled will be nearest the cube centre, these projecting having curved steps which when assembled will be centred on respective cube axes in a plane parallel to the exposed face of the block whilst the sixth face of the block, opposite the face which is exposed on assembly is flat apart from a square step in one corner which is an extension of the said projections; and e) the median blocks have a face adjacent the face which will be exposed on assembly, which face is remote from the cube centre, and is inwardly stepped with a curve across its whole width, whilst the face opposite the said exposed face thereof is concave with a cylindrical curvature centred on the main cube axis parallel to the first mentioned face and the said exposed face with a central lug which projects beyond the face of the block opposite the said first mentioned face.