1. Introduction
The solar sail is one of the efcient propulsion systems for
long duration exploration to deep space in the future, which
is accelerated continuously by sun's photons without propellant.
As the extended concept in Japan, the solar power
hybrid sail combined with ion engines has been developed.
As the solar sail consists of thin and large membrane to reduce
mass and to have enough propulsion-power, the membrane
must be retracted compactly on the ground and deployed
in the space. The deployment is actuated by the extendible
masts by NASA[1,2], the deployable boom in Europe[
3], and the centrifugal force in Japan[4]. Since the deployment
characteristics of all deployment system depend
on wrinkles and creases on the membrane, it is signicant
to investigate the folding and retraction properties.
The deployable membrane is required the simple manufacture
and the efcient retraction. Also, the membrane has to
be retracted again after the deployment test on the ground.
These requirements are not able to meet without mechanisms.
Therefore, the folding and retraction mechanisms
are necessary to be developed. Moreover, a large amplitude
of wrinkles between the fold lines decrease packaging
efciency and damage the solar cells on the solar power hybrid
sail. Hence, in the course of retraction, to reduce the
wrinkles is also the signicant requirement.
The rotationally skew fold[5] has been proposed by the authors
as wrapping fold pattern for spinning solar sail as
shown in Fig.1. This folding pattern is characterized by
double corrugation folding and is advantageous in the complete
folding and compact storage.
Fig.1 Rotationally skew fold[5]
Since the 1960's, it has been studied wrapping fold of a
at-thin membrane. Lanford[6] proposed the folding apparatus
for circular membrane to the simple spiral fold, as
shown in Fig.2 in 1961. The membrane is wrapped by rotating
the cylindrical center hub, and hill and valley folds
are achieved by tensile forces. The fold lines shown in the
gure are spiral trace. However, as shown in the gure,
since the fold lines are concentrating around the center hub,
the retraction system gives the low packaging efciency.
Also, larger size membrane becomes more difcult to retract
with the similar apparatus.
1
Fig.2 Lanford's folding apparatus[6]
Guest and Pellegrino[7] proposed another retraction concept.
The membrane of zero-thickness is wrapped around
the prismatic hub with the straight fold lines. The pattern
is able to be changed to account the thickness of the membrane.
In this paper, we propose the folding mechanisms for twodimensional
deployable membrane for spinning solar sail
by extending the concept of Lanford's folding apparatus.
The fold lines are generated by wrapping fold around the
center hub with tensile forces. The retraction experiments
are performed to examine the effects of the tensile forces,
the hinge mechanisms, and the center hub model on the
retraction properties. Finally, we discuss the packaging ef-
ciency of two types of center hub models.
2. Retraction mechanisms
2-1 Conceptual retraction mechanism
As a membrane has to be retracted efciently and folded
large-scale membrane, we propose a conceptual retraction
mechanism as shown in Fig.3.
Fig.3 Conceptual retraction mechanism
This novel concept uses a polygonal center hub, and the
membrane is retracted without concentrating fold lines
around the center hub. Also, hill and valley folds are generated
by adding tensile forces to the edge of the membrane
and rotating the polygonal center hub. Since the retraction
pattern depends on the tensile forces pattern, the tensile
forces pattern is requested to fold arbitrary target retraction
pattern.
2-2 Experimental retraction mechanism
Experimental retraction mechanism is illustrated in Fig.4.
As shown in the plane view, the membrane is set in the
broken line area, the center hub and membrane are polygon,
and the direction of the tensile forces is perpendicular
to the edge of membrane.
(a) Plane view (b) Side view
Fig.4 Experimental retraction mechanism
3. Target retraction patterns
As the membrane specimen, the 5mm-thickness and about
1;700mm-diameter octagonal membrane made from PET
is used for experiments, as shown in Fig.5.
(a) square center hub
(b) octagonal center hub
Fig.5 Plane view of membrane model
The rotationally skew fold is one of the retraction pattern
without concentrating creases around the polygonal center
hub, so we consider the rotationally skew fold to be the basic
target retraction pattern with the retraction mechanism.
At rst, the effects of the tensile pattern corresponding to
the target retraction pattern are investigated experimentally
to retract efciently. Also, two types of center hub model
are examined, the square center hub in Fig.5a, and the octagonal
one in Fig.5b.
2
3-1 Rotationally skew fold
By setting the target retraction pattern to the rotationally
skew fold, the possibility of efcient retraction is examined.
Figure 6 shows the rotationally skew fold pattern
whose pitch between each creases is 100mm. The square
hub model is illustrated in Fig.6a, and the octagonal model
is in Fig.6b. The direction of the tensile forces is perpendicular
to the edge of a membrane, as sketched in Fig.6.
(a) square center hub model
(b) octagonal center hub model
Fig.6 Rotationally skew fold
In the course of retraction, to reduce the large amplitude of
wrinkles between the fold lines, we propose a reinforcement
of hinge mechanisms. The stiffened elements attached
to the gray area in Fig.7 enable the hatched areas
to be retracted without a large amplitude of wrinkles between
the fold lines. Then, the hatched areas are expected
to become z-fold. Figure 7a shows for the square center
hub model, and gure 7b shows for the octagonal one.
(a) square center hub model
(b) octagonal center hub model
Fig.7 Rotationally skew fold with stiffened elements
3-2 Mixed spiral fold
We propose alternate fold pattern as sketched in Fig.8. The
fold pattern is called the mixed spiral fold, which is consisted
of z-fold and spiral fold. The spiral fold is generated
in the area except gray area and hatched areas in Fig.7. Figure
8a shows the square center hub model, and gure 8b
shows the octagonal one. This fold lines are generated by
adding tensile forces around the edge of membrane, and rotating
the polygonal center hub. The tensile point for edge
and direction are indicated in Fig.8.
(a) square center hub model
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(b) octagonal center hub model
Fig.8 Mixed spiral fold
4. Retraction properties
Retraction experiments were performed to examine the effects
of the reinforcement of hinge mechanisms, the tensile
forces pattern, and center hub shape on the retraction properties.
4-1 Simple wrapping fold with polygonal center hub
The effects of the hinge mechanisms on the retraction properties
are examined. The membrane is wrapped around the
polygonal center hub without hinge mechanisms. The tensile
forces pattern is for the rotationally skew fold.
(a) rotation angle = 2p=8 (b) rotation angle = 9p=8
(c) rotation angle = 21p=8 (d) rotation angle = 28p=8
Fig.9 Retraction process of simple fold
Figure 9 shows the retraction process with the square center
hub for rotation angle. In the rst stage of the retraction, the
membrane is wrapped with spiral fold lines as Lanford's
folding apparatus, see Fig.9a-b. When the retraction ends
in Fig.9d, the deformations around the edge are observed,
which is about 3 times as large as the pitch between each
tensile forces. In the case of octagon center hub, the similar
results are obtained. Therefore, the fold lines of the
rotationally skew fold are not generated without the hinge
mechanisms.
4-2 Retraction to rotationally skew fold
The possibility of the folding to the rotationally skew fold
is examined. The hinge mechanisms are attached around
the center hub. The tensile forces pattern is for rotationally
skew fold.
(a) rotation angle = p=8 (b) rotation angle = 3p=8
(c) rotation angle = 6p=8 (d) rotation angle = 25p=8
Fig.10 Retraction process of rotationally skew fold with
hinge mechanisms
Fig.11 Detail of z-fold area
The retraction process of the experiment is indicated in
Fig.10. Z-fold lines are generated by the effects of the
hinge mechanisms, see Fig.10a-b. Figure 11 shows the detail
of z-fold in Fig.10b. As shown in the gure, the areas
pointed by arrows are retracted without the large of wrinkles.
However, when the retraction ends in Fig.9d, the large
deformations around the edge are generated, and it is about
3 times as large as the pitch between each tensile forces.
Although z-fold is generated by applying the hinge mechanisms,
there is difculty to realize the efcient retraction.
Therefore, the tensile forces pattern has to be changed.
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4-3 Retraction to mixed spiral fold with square center hub
The retraction experiment is performed to investigate the
effects of changing the tensile forces pattern to the mixed
spiral fold. The membrane is wrapped around the square
center hub with the hinge mechanism.
(a) rotation angle = 2p=8 (b) rotation angle = 9p=8
(c) rotation angle = 14p=8 (d) rotation angle = 30p=8
Fig.12 Retraction process of mixed spiral fold with square
center hub
Fig.13 Detail of spiral fold areas
The retraction process of the mixed spiral fold with the
square center hub is shown in Fig.12. As shown in Fig.12b,
except for the z-fold area, the spiral fold lines are generated
in the rst stage of the retraction. Figure 13 indicates
the detail of the spiral fold areas in Fig.12a. In the spiral
fold area, few large amplitude of winkles are generated, see
Fig.13. In the end of the retraction, the retraction height is
almost uniform, see Fig.12d. Therefore, it is possible to
retract efciently by applying the reinforcement of hinge
mechanisms and the tensile forces for mixed spiral fold as
Fig.8a.
The causes of the large deformation around edge generated
in the experiment for the rotationally skew fold with
the hinge mechanisms are due to the tensile forces pattern.
Figure 14 indicates the tensile patterns for square center
hub, for rotationally skew fold in the left hand side, and for
mixed spiral fold in the right hand side. As shown in the
left hand side, since hill and hill folds are adjoined, Also,
in the areas except for z-fold area, the pitch between each
tensile forces is 141mm, which is about 1.4 times as wide
Fig.14 Tensile patterns for square center hub
as the pitch of z-fold. Thus, it is anticipated that these details
generate the large deformations around the edge, and
its pitch becomes about 3 times larger than that of the pitch
of target fold lines.
4-4 Retraction to mixed spiral fold with octagonal center hub
The effects of the center hub shape on the retraction properties
are investigated. The membrane is wrapped around
the octagonal center hub to the mixed spiral fold with the
hinge mechanisms and the corresponding tensile forces.
(a) rotation angle = p=8 (b) rotation angle = 5p=8
(c) rotation angle = 15p=8 (d) rotation angle = 30p=8
Fig.15 Retraction process of mixed spiral fold with
octagonal center hub
(a) z-fold area (b) spiral fold area
Fig.16 Detail of areas
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Figure 15 shows the retraction process of the experiment.
In the rst stage of retraction, the z-fold lines and the spiral
fold lines are generated, see Fig.Fig.15b. The z-fold area
and the spiral fold area in the Fig.15b are detailed in Fig.16.
As shown in the gure, in the case of using the octagonal
center hub, the membrane is retracted with fewer wrinkles
than the case of using the square center hub. As the cause
of the results, in the case of using the octagonal center hub,
the membrane has 2 times as many spiral fold areas as the
square hub model has. Hence, the concentration of fold
lines is avoided, and fewer wrinkles are generated.
Table 1: Retraction conguration
square hub octagonal hub
max. retraction height 128mm 128mm
max. retraction thickness 4:2mm 2:3mm
retraction thickness for layer 37mm 21mm
rotation angle 31p=8 31p=8
Table.1 indicates the retraction conguration for the mixed
spiral fold. Both of the maximum retraction height is 1.28
times as high as the pitch of the ideal retraction hight,
100mm. In the case of the square hub model, the maximum
retraction thickness is 4:2mm, and in the case of the octagonal
center hub, it is 2:3mm. Also, the retraction thickness
for layer of the square hub is 1.76 times as thick as the
value of the octagonal hub. As the cause of the different
results, in the case of square hub, the pitch between each
tensile forces in the spiral fold area is 0.81 times as wide
as that pitch of the case of octagonal hub. Also, in the case
of octagonal hub, the concentration of fold lines is avoided
because the membrane has 2 times as many spiral fold areas
as the square hub model has. Therefore, the different
results indicate that the wrapping around the square center
hub is able to give more efcient retraction than the wrapping
around the octagonal center hub.
On the other hand, when the membrane is retracted, the
retraction thickness of layer is 4 s 7 times as thick as the
membrane thickness, 5mm. Hence, it is quite possible that
larger membrane is able to be retracted efciently.
5. Conclusions
Folding and retraction mechanisms of deployable membrane
for spinning solar sail were proposed experimentally.
The fold lines are generated by wrapping the membrane
around the polygonal center hub with tensile forces. In the
course of retraction, to avoid a large amplitude of wrinkles
between the fold lines and to improve the packaging ef-
ciency, the center area of the membrane was reinforced
with hinge mechanisms. The retraction experiments were
demonstrated to investigate the effects of the tensile forces,
the hinge mechanism, and the center hub model on the retraction
properties. The mixed spiral fold consisted of zfold
and simple spiral fold indicated better performance as
the target retraction pattern for packaging efciency.
Acknowledgment
The authors wish to express their gratitude to JAXA/ISAS
solar sail working group for valuable suggestions rendered
during the course of this research.
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