Date post: | 14-Jul-2015 |
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Symmetric Prismatic Tensegrity Structures
Jingyao ZhangSimon D. GuestMakoto Ohsaki
Objective
Prismatic Tensegrity Structure
Dihedral Symmetry
Self-equilibrated Configuration Stability Properties
Connectivity Configuration
D3
1, 1
D4
1, 1D
5
1, 1
D9
1, 1
Connectivity
2/13
Configuration
The simplest prismatic tensegrity structure
6 Nodes
3 Struts
6 Horizontal
3 Vertical
1,13D
Dnh,v
3/13
Dihedral Symmetry
D3 Symmetry
three-fold rotation 3 two-fold rotations
Dnh,v
n=3
C21, C22 , C23C , C1 23 3E (C )3
0
4/13
Connectivity – Horizontal Cables
h=1
h=2
Dnh,v
1
2
34
0
6
7 8
9
5
1
34
0
6
7 8
9
5
2
5/13
Connectivity – Vertical Cables
v=1
v=2
Dnh,v
1
34
0
6
7 8
9
5
2
1
34
0
6
78
9
5
2
6/13
Self-equilibrium
v sq q= −
0 =Ax 0 / 2(1 cos(2 / )) /(1 cos(2 / ))h vq q v n h nπ π= − −
0x 1 2 2 1, , , , ,i n−x x x xK K
A singular
symmetry
0xhx
n h−x
nx n v+x
7/13
infinite stiffness
Stability Criterion
0E G= + >K K K
T 0G= >Q M K M
Blo
ck
D
iago
nalis
atio
n
0>0>
0>0>
0>M – mechanism
=Q%
0 or E → ∞K
8/13
Stability
1h = Stable0G ≥K 0>Q
1h ≠ ??0GK ?0Q
1,18D
1,28D
1,38D
Stable Stable Stable
2,18D
2,28D
2,38D
Unstable Divisible Conditionally Stable
9/13
Divisible Structures
= +
D62,2
2,26D
1,13D
1,13D= +
10/13
Numerical Investigation
2,38D
2,18D
r
H
11/13
Catalogue
9
Please note in the paper that there are some mistakes on n, h and v.
12/13
Summary
Self-equilibrated Configuration
Stability
Connectivity Horizontal Cable
Vertical Cable
Configuration Height / Radius
Prismatic Tensegrity StructureS
ymm
etry
http:// tensegrity.AIStructure.com/prismatic
Divisibility
D 73,2
13/13