A concept for the one dimensional deployable truss structure is presented. The deployed configuration of the structure consists of the repetition of a longitudinal octahedral truss module. The principal mechanical feature of the truss is that the lateral members comprising the lateral triangular truss are telescoping beams. Contracting of the lateral members results in the deployment of the truss structure. The geometric transformation of this truss of variable geometry is presented. Both simultaneous and sequential modes of transformation are possible. The validity of the transformation applied to the deployment is verified through design of a conceptual model

Miura, K.

English

NASA Technical Reports Server

DESIGN AND OPERATION OF A DEPLOYABLE TRUSS STRUCTURE 
Xoryo Miura* 
ABSTRACT 
A new concept for the one-dimensional deployable truss structure is 
presented. The depioyed configuration of the structure consists of the 
repetition of an octahedral truss module longitudinally, and thus it is 
exactly the so-callctd "geodesic beam" structure. The principal me;hanical 
feature of the truss is that the lateral a~embers comprising the lateral 
triangular truss are telescoping beams. Contracting of th? lateral members 
results in the deploymen.; of the truss s t r ~ ~ x r c .  The geometric 
transformation of this truss of variable geometry is presented. It is 
shown that both simultaneous and sequential modes of transformation are 
possible. The validity of the transformation applied to the depl~yment is 
verified through design of a conceptual model. This concept of a deployable 
structure could be a potential candidate for future space applications. 
INTRODUCTION 
At present, the only established concept for the deployable m e -  
dimensional structure for space applications is the coilable longeron beam. 
However, a study (reference 1 )  has shown that the coilable longeron beam 
(Astromast )  i s  l i m i t e d  t o  beam dimensions of l e s s  than 1 meter because o f  
d i f f i c u l t i e s  i n  packaging the stowed energy i n  t h e  beam. For a p p l i c a t i o n s  
that  require large  beams, deployable beams with hinged longerons or  erectable 
beams must be developed. 
Recently, the Rockwell International Corporation and the Vought 
Corporation studied a number of existing structural concepts for fully 
deployable beams and platfornis (references 2, 3 ) .  In spite of these 
efforts, a satisfactory structural concept which has an advantage over others 
in every respect has not yet been found. This situation is not changed 
even if a different set of criteria for selection is used. Under these 
circumstances, the derivation of new concepts through various possible 
approaches seems to be beneficial. 
The present author has succeeded in devising a new concept for a one- 
dimensional deployable structure through a unique geometric approach. 
*The Institute of Space and Astronautical Science, Keguro, Tokyo, Japan 
https://ntrs.nasa.gov/search.jsp?R=19840017014 2020-03-22T09:03:32+00:00Z
The concept was v e r i f i e d  through a  conceptual  model. This  paper d e s c r i b e s  
b r i e f l y  t h e  t h e o r e t i c a l  foundat ion o f  t h e  concept ,  t h e  i n h e r e n t  mechanisms, 
and t h e  mode o f  t h e  deployment. 
DEPLOYABLE TRUSS CONCEPT 
The c o n c e p t  of t h e  deployable  t r u s s ,  which t h e  a u t h o r  proposes h e r e i n ,  
is e s s e n t i a l l y  a  t r u s s  of v a r i a b l e  geometry. Figure  1 i l l u s t r a t e s  a  t y p i c a l  
example  of t h e  p r o p o s e d  c o n c e p t  f o r  t h e  deployable t r u s s  s t r u c t u r e .  The 
fundamental module of t h e  t r u s s  is  an o c t a h e d r a l  t r u s s  composed of  a  p a i r  
of  l a t e r a l  t r i a n g u l a r  t r u s s e s  and s i x  d i a g o n a l  members. The two ad jacen t  
modules, which s h a r e  t h e  l a t e r a l  t r u s s ,  compase a  r e p e a t i n g  u n i t  of t h e  
t r u s s .  Thus ,  t h e  r e p e t i t i m  of t h e  u n i t  i n  t h e  l o n g i t u d i n a l  d i r e c t i o n  forms 
t h e  whole s t r u c t u r e  uf t h ~ l  deployable  t r u s s .  
A p a r t  of Figure  1 i s  en la rged  and shown i n  Figure  2 ,  which I l l u s t r a t e s  
t h e  v i c i n i t y  around a  l a t e r a l  t r i a n g u l a r  t r u s s .  The d e t a i l s  of  a  l a t e r a l  
member a r e  shown i n  Figure  3. Th i s  member, which is a  t e l e s c o p i n g  beam whose 
l e n g t h  c a n  v a r y ,  c o n t a i n s  i n s i d e  t h e  t u b u l a r  s e c t i o n  a n  e l a s t i c  t e n s i l e  
s p r i n g  t h a t  is  connected t o  b o t h  e n d s  of  t h e  beam. I n  a d d i t i o n ,  a  l a t c h  
i s  i n s t a l l e d  i n  t h e  beam t o  f i x  i t s  l e n g t h  a t  t h e  s h o r t e s t  s t a t e .  Figures  
4a and 4b i l l u s t r a t e  t h e  p u r e l y  g e o m e t r i c  c o n f i g u r a t i o n  of  t h e  t r u s s  i n  
t h e  c o m p l e t e l y  fo lded  and deployed c o n d i t i o n s ,  r e s p e c t i v e l y .  Figure  5 shows 
t h e  almost  fo lded  s t a t c  of t h e  t r u s s .  
The ou tward  a p p e a r a n c e  of t h e  deployable  t r u s s  shown i n  t h e  preceding 
s e c t i o n  i s  known e l s e w h e r e  i f  i t  i s  a  r i g i d  s t a t i c  s t r u c t u r e  i n s t e a d  o f  
a  s t r u c t u r e  o f  v a r i a b l e  geometry .  For i n s t a n c e ,  i n  r e f e r e n c e  4 ,  t h a t  type  
of t r u s s  (geodesic  o r  i n v e r t e d  b a t t e n  beam) is  s t u d i e d  t o  v e r i f y  t h e  t h e o r y  
of  con t inuum a n a l o g y  f o r  l a r g e  s p a c e  s t r u c t u r e s .  Ac tua l ly ,  t h i s  t r u s s  i s  
one of the  most e f f i c i e n t  l ight-weight s t r u c t u r e s  u s i n g  t h e  minimum number 
of component members. I n  t h i s  s e c t i o n ,  t h e  au thor  shows t h e  geometric t r a n s -  
format ion by which t h e  t r u s s  can be t r a n s f e r r e d  t o  a  compact c o n E i g u r a t i o n .  
With mechanisms i n s t a l l e d  i n  t h e  t r u s s  a s  descr ibed i n  t h e  previous  s e c t i o n ,  
t h e  t r u s s  becomes deployable.  
The geometric t r ans fo rmat ion  expla ined i n  t h i s  s e c t i o n  is  t h e  mode where 
t h e  fo lding/deploying is c a r r i e d  o u t  s imul taneously  through t h e  whole 
s t r u c t u r e .  Let i t  be c a l l e d  t h e  s imul taneous  mode t r ans fo rmat ion .  
LATE RAl 
ORIGINAL PAGE R3 
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MODULE 
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MODULE 
- I - 
MODULE 
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MODULE 
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F i g u r e  1. Proposed Concept  o f  Deployable  T r u s s  S t r u c t u r e  
5 1 
. . , - .a&- d d m - -  .. . 
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ORlGiNAL PAGE 19 
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TUBE 
Figure 3 .  Detai ls  o f  Lateral Member 
MEMBER 
MEMBER 
ORIGINAL PAGE lg 
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( a )  Folded (b )  Deployed 
Figure 4. Geometric Configurations of Deployable Truss 
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Let  us  consider  a  s ing le  uni t  t h a t  i s  cocposed of a  pa i r  of octahedral 
t russes  a s  shown i n  F igu re  6. I t  i s  assumed t h a t  t h e  l a t e r a l  t r i a n g u l a r  
t r u s s  i s  r e g ~ l a r ,  t h e  l e n g t h  o f  a  d i a g o n a l  member i s  a , and t h e  l e n g t h  o f  
t h e  s i d e  o f  t h e  l a t e r a l  t r i a n g l e  is b . Then t h e  geometry o f  t h e  
o c t a h e d r a l  t r u s s  is comple tc iy  d e f i n e d  by t h e  magnitude o f  a and .? . 
If a is equa l  t o  b , t h e  t r u s s  becomes a  r e g u l a r  o c t a h e d r a l  t r u s s .  We 
s h a l l  s t a r t  wi th  t h i s  c a s e  and s t u d y  how t h e  t r u s s  is t r ans fo rmed ,  depending 
on t h e  r e l a t i v e  magnitude o f  b t o  a . 
A s  shown i n  Figl i re  6a, t h e  f a c e  a n g l e  between a  p a i r  o f  t r i a i g l e s  which 
compose a coccave diamond p a t t e r n  is  t aken  a s  20 . Then we have 
For  t h e  c o n f i g u r a t i o n  of F igu re  6a, a e q u a l s  b , and t h e r e f o x  
8 = cos-' (1 /3 j  = 70.53 (deg.). 
We a r e  immediately aware t h a t  Equat ion  1 has a n o n t r i v i a l  s o l u t i o n  f o r  
8 equal t o  zero. This i s  the fundamental f ac t  on which t h e  p r e s e n t  concept  
of dep loyab le  t r u s s  depends. Thak is 
The v a n i s h i n g  or' t i le f a c e  a n g l e  8 means t h a t  :he h e i g h t  o f  each  o c t a h e d r a l  
module v a n i s h e s ,  t oo .  I n  o t l ~ e r  words, t h e  complete  t r u s s  is t r ans fo rmed  t o  
a  f l a t  c o n r i g u r a t i o n  a s  shown i n  F igu ro  6b. 
The proposed concept  o f  d e p l ~ ~ y a b l e  t r u s s  uses  t h i s  f a c t .  I f  we are 
able  t o  design the l a t e r a l  member with variable  length ( i . e . ,  a t e l e s c o p i n g  
beam), we a r e  c l o s e  t o  t h e  so lu t ion .  Let the length of the l a t e r a l  member 
vary a s  follows: 
a r b  - < = &a, 
t h e n ,  t h e  h e i g h t  of a  module h v a r i e s  between t h e  l i m i t = :  
ORIGINAL PAGE 19 
OF POOR QUALrrY 
Deplo 
(b )  Folded c , I  
F igwe 6. Repoatin2 Unit of Truss 
T h i s  means t h a t ,  by e x t e n d i n g  t h e  l a t e r a l  members by a f a c t o r  of h 8 t he  
height of the  t r u s s  should v a ~ i s h .  
See  F igu re  3 f o r  a n  example of  t h e  l a t e r a l  t e lescoping  member. This 
member cons i s t s  of an ex t e rna l  tube, an inner  tube, a t e n s i l e  e l a s t i c  sp r ing  
i n s i d e  t h e  t u b e ,  and a l a t c h  mechanism t h a t  i s  ac tua t ed  when t h e  member 
is shortened t o  a de f ined  l e n g t h .  The d f  agonal  members a r e  f i x e d  l e n g t h  
members. Although the  hinge mechanism is  not shown i n  d e t a i l ,  i t  is designed 
t o  follow the movement of t he  t russ .  Figure 5 shows t h e  shape  of  t h e  t r u s s  
a t  a lmos t  f u l l y  f o l d e d  s t a t e .  T h i s  r a t h e r  s t r a n g e  ro id ing  mechanism may 
be somewhat beyond one's ins igh t .  It i s  e a s i e r  f o r  one  t o  unde r s t and  t h e  
mechanism through a three-dimensional k i n e t i c  model. 
GEOMETRIC TRlLYSFORMATION OF THE TRUSS (SEQUENTIAL MODE) 
Theoret ical ly  speaking ,  a geome t r i c  t r a n s f o r m a t i o n  i n  a s e q u e n t i a l  
mode is  p o s s i b l e  i n  which each  module i s  deployed successively and o the r  
modules remain fixed. Because t h e  s e q u e n t i a l  mode i s  i m p ~ r t a n t  from t h e  
point of view of deployment cont ro l ,  we w i l l  s tudy t h a t  mode i n  t h i s  section. 
Figure 7 shows the  zone of t he  t r u s s  where t h e  s e q u e n t i a l  deployment 
i s  underway. For c l a r i t y  of  explanat ion,  it is b e t t e r  t o  d iv ide  t h e  whole 
t r u s s  i n t o  the following three  zones: t he  deployed zone, the  t r a n s i e n t  zone, 
and t h e  folded zone. It is assumed t h a t  the  trcss comprises n l a t e r a l  t r i an -  
glilar t r u s se s  and n-1 nodules .  The p r e v i o u s l y  mentioned t h r e e  zones a r e  
explaine2 3s follows: 
Deployed Zone - Trans t en t  Zono Folded Zone 
Latera l  t r u s s  1,2,3,..... i-1 i i+l,..... 
Module 1,2,3,......1-2 i-1, i i , i + l ,  . . . 
The important f a c t  i s  t h a t  t h e r e  e x i z t s  a geome t r i c  t r a a s f o r m a t i o n  
which a l l o w s  t h e  c o n t r a c t i o n  o f  the  i - th  l a t e r a l  t r i a n g u l a r  t r u s s  and the  
following deployment of the  (i-1)-th and i - t h  modules w i thou t  i n t e r f e r i n g  
with o ther  zonen of the t russ .  
The sequence of motions of t he  t r u s s ,  which c o n s t i t u t e s  t he  cont rac t ion  
of the  i-th l a t e r a l  t r u s s ,  is explained as f o l i ~ w s :  When the  i - th  t r i angu la r  
t r u s s  s t a r t s  c o n t r a c t i n g ,  i t  is r a i s e d  from the  base and t h e  i - t h  module 
s t a r t s  t o  deploy. Before t h a t ,  the  (i-1)-th module is  p a r t i a l l y  dep loyed ,  
ORIGINAL PBGE 19 
OF POOR QUALm 
Figure 7. Sequential Mode Deployment 
and is continuing to deploy. When the i-th lateral truss finishes its contrac- 
tion and is latched, the (i-1)-th module completes the deployment. The se- 
quence of this process is illustrated in the series of figures in Figure 8. 
The relation between the length of the diagonal membx a , the lenqth 
of the lateral member b , and the height of the morhle h is obtained 
easily by using Figure 7. If a and b are conrected with the variable 
parameter .Ic , 
b = k-a, where J ? I k l l ,  - 
then, the heights of the modules are 
h , = / ( 2 + k - k 2 )  1 3 - a ,  ( (i-1)-th module ) (6) 
= m- k2/3 0. ( i-th module ) (7) 
From a practical standpoint, the sequential mode transformation 
possesses a great ~dvantage over the simultaneous one. This is because in 
the former case the c!eploying/folding takes place near the base and thus 
design of the mechanism is simpler. The outer truss is then al~ays extending 
from the base as a rigid structure. 
C0NCEPTUF.L MODEL 
Although 'here is no doubt of the validity of the geometric transtcrma- 
tions, a model i . 3 ~  been constructed to demonstrate the concept. This model, 
made of acrylic glass tubes and aluminum hinges, is shown in Figure 9. The 
deployment of the modtl in a sequential mode is shown in the series of photos 
in Figure 10. The model ;*arks as expected and demonstrates the validity 
of the geometric ttansCorrnatfon. 
CONCLUDING REMARKS 
A new concept for the one-dimensional deployable truss structure is 
presented. The deployed configuration of the structure cmsists of the 
repetitlon of an octahedral truss module longitudinally, arid thus is exactly 
the so-called "geodesic beam" structure. The principal mechanical feature 
ORIGINAL PAGE 19 
OF POOR QUALlTY 


of the truss is that the lateral members comprising the lateral triangular 
truss are telescoping beams. Contraction of the lateral members results 
in deployment of the truss. The geometric transformation of this truss of 
variable geometry is presented. It is shown that both simultaneous and 
sequential modes of deployment are possible. The validity of the concept 
is verified by means of a conceptual model. Though the study is in its 
initial phase, this concept for the deployable truss structure seems to have 
qualities suitable for space applications. 
ACKNOWLEDGEMENT 
The author wishes to thank to Mr. Kenichi Suzuki of Godo Seisakusho for 
his contribution in designing the conceptual model. 
REFERENCES 
1. Mikulas, Martin M., Jr., and Harold G. Bush, "Advances in Structural 
Concepts, Large Space Antenna Systems Technology - 1982," NASA CP-2269, 
November 1982, pp. 258-283. 
2. Greenberg, H. S., "Development of Deployable Structures for Large Space 
Platforms," NASA CR-170689, December 1982. 
3. Cox, R. L., and R. A. Nelson, "Development of Deployable Structures for 
Large Space Platforms," NASA CR-170690, December !982. 
4. Noor, A. K., M. S. Anderson and W. H. Greene, "Continuum Models for Beam- 
and Plate-Like Lattice Structures," AAZA J., - 16 (12), December 1978. 


Design and operation of a deployable truss structure

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