symmetric prismatic tensegrity structures by zhang, guest, ohsaki

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