Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
ATAKE's structure - new variations of the
scissors technique
K. Atake
ATAKE Space Design Laboratory Co., Ltd. Japan
Abstract
This presentation proposes a new kind of a scissors technique, which is a
framework structure comprising three or more primary constituent units, each
including two rigid diagonal members constituting the diagonals of a
quadrangular lateral face of a solid and coupled together for relative rotation
about a first rotation axis passing through the intersection of the diagonals. The
primary constituent units are coupled to one another via second and third rotation
axes into a ring-like form. A more complicated framework structure can be
obtained by using a plurality of these framework structures as secondary
constituent units which are coupled to one another with a coupler or a primary
constituent unit (scissors) used in common between adjacent ones of the
secondary constituent units. Using complete pin joints composed by three axes in
between scissors makes the system more flexible and it makes almost all kinds of
3D shapes folding into a bundle. Adding tension components like wires or
membranes to its developed form, it becomes a 3D truss and gets effective
strength. We think this method is useful for the rapid construction of towers,
bridges, domes and space structures.
Figure 1: The dome and the bridge in Park Hanamizuki in Japan.
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
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1 The principle - simple ring
The minimum component of this system is the so-called scissors which define
two diagonal lines of a quadrilateral and which are pivotally connected to each
other at a point of intersection. At least three minimum components are
connected to one another to form a ring through complete pin joints which has
three axes (ordinary door hinge could use for it), and provide a secondary unit of
this frame structure. And in order to make 3D variable structures, at least the
quadrilaterals from which diagonal frames are taken out must be trapeziums in
mathematics.
1.1 Application to frustum of pyramid
These simple rings can be divided mainly into two types. One is based on a
frustum of pyramid type. We call this type of secondary unit simply a pyramid
type. Only the triangular pyramid is stable when tension components are added.
Figure 2: Triangular pyramid unit.
Figure 3: Square pyramid unit.
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
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Figure 4: Pentagonal pyramid unit.
1.2 Application to sliced skew prism
When the number of scissors in one ring is even, there is another type of ring
which is almost a stable solution. It is based on the sliced skew prism. We call
this type simply the skew type. When the number is 4, the skew will be
tetrahedron. And when the number is 6, the triangular skew prism will be a
octahedron. To combine these two types of unit can provide more complicate
foldable structures.
Figure 5: Minimum skew type based on sliced tetrahedron.
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
Mobile and Rapidly Assembled Structures III
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Figure 6: Skew type based on sliced octahedron.
2 Vertical connections of ring units
2.1 Application to towers
Piling up these pyramid-type structural units vertically it becomes an foldable
tower. If the reduction ratio of units are geometrical, this tower can transform
into completely plane. To use this method we can make high tower without
working in high place.
2.2 Application to bridges
Applying this vertical connection to horizontal like a balancing toy, it becomes
foldable bridge easy to construct. It will be useful for rapid construction of a fly
over or a bridge for pedestrians. The Bridge of Hanamizuki Park (Fig. 1) is
designed for this method. But actually it was not constructed by this method.
Figure 8 shows another project applied to the suspension type of bridge and the
developing. The bridge is designed that to pull the suspension wire make it
develop.
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
Mobile and Rapidly Assembled Structures HI
Figure 7: Tower Model the maximum height is about 2600mm.
147
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
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Figure 8: A suspension bridge project: the span is 50m.
3 Horizontal connection of secondary units
To connect secondary unit horizontally by scissors in common compose various
3D foldable shapes.
3.1 Application to double layer polyhedron
To connect only pyramid type unit horizontally compose double layer
polyhedron. All kind of regular and semi regular polyhedron can obtain by this
method. But most of them are not stable.
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
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Figure 9: Double-layer cube - this is not stable itself.
3.2 Application to chairs
Horizontal connection of only skew type unit compose complex shapes like
chairs. The liner connection compose simple arch and most of them are stable.
Figure 10: Foldable chair - this is almost stable.
Figure 11: Foldable arch.
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
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3.3 Application to double layer plates
In case of the number of components in one unit is four, two type of shape the
pyramids and the sliced skew prism are complemented to each other. It is
according to a space packing pattern of octahedral and tetrahedral.
So it is considerable to apply this system to the octet truss (space truss) system
double layer truss plate based on square.
Figure 12: Square plate.
Octet truss based on triangular or hexagonal plate structure is also realize to use
this system. Here are frustum of triangular pyramid and sliced octahedral
complementary.
Figure 13: Hexagonal plate.
3.4 Application to vaults
Lateral connection of arches by inverted scissors or pyramid units provide
foldable double layer vault. These vault can get more complex curve to change
the dividing ratio of each scissors.
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
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Fig. 14 Double-layer vault
3.5 Application to domes
The horizontal connection of sliced octahedron unit applied to the hexagon of
upper half of semi regular 32 polyhedron (soccer ball) provide foldable double
layer domes. It is a kind of fuller domes. This is composed by all same 48
scissors and almost stable itself.
Photos below show the development of the dome in Park Hanamizuki
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
Mobile and Rapidly Assembled Structures III
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Figure 15: Double- layer dome.
3.6 Application to boats
Two inverted triangular pyramid connected skew composed boat shape. This
structure can provide foldable boat.
Figure 16: Folding boat.
4 Plan diagram
It is difficult to express and to understand these structures through real 3D
graphics, but when the structure is fold up, the shape is almost same except the
end (the top view),so only the symbolic diagram of top view could express hole
structure, figure 3 shows the relation the diagram and 3D shape. The length of
the line shows the length of bottoms of the trapezoid .
To construct the units as the fold up shape by this diagram is not so hard. And the
final shape can be obtained to expand the unit.
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
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Figure 17: Plan diagram of inverted pyramid (left) and skew (right).
Tetrahedron
Cube
Cubeoctahedron
/\
Octahedron
icosahedron
Dodecahedron
Figure 18: Plan diagram of polyhedron -all units are pyramid type.
Quadrangular plate
Hexagonal plate
Dome
chair
Boat
Arch
Vault
Figure 19: Plan diagram of various shapes -units are combined.
Mobile and Rapidly Assembled Structures III, C.A. Brebbia & F.P. Escrig (Editors)
© 2000 WIT Press, www.witpress.com, ISBN 1-85312-817-1
Mobile and Rapidly Assembled Structures HI
References
[1] ATAKE Katsuhito Diagonal and Variable Frame Structures Katachi U
Symmetry Extended Abstract university of Tukuba pp345-348 1994
[2] ATAKE Katsuhito Diagonal and Variable Frame Structures Symmetry Culture
and Science Extended Abstracts 1 ISIS Symmetry 1995