Acta Astronautica 139 (2017) 407–418

Contents lists available at ScienceDirect

Acta Astronautica
journal homepage: www.elsevier.com/locate/actaastro

Development of a solar array drive mechanism for micro-satellite platforms

Giorgos Galatis a, Jian Guo a, *, Jeroen Buursink b
a
Faculty of Aerospace Engineering, Delft University of Technology, Delft, 2629HS, The Netherlands
b
LuxSpace Sarl, Rue Pierre Werner, 6832, Betzdorf, Luxembourg

A R T I C L E I N F O A B S T R A C T

Keywords: Photovoltaic solar array (PVSA) systems are the most widely used method for spacecraft power generation.
SADM However, in many satellite missions, the optimum orientation of the PVSA system is not always compatible
Solar arrays with that of the payload orientation. Many methods, have been examined in the past to overcome this
LEO
problem. Up to date, the most widely used active method for large costly satellites is the Solar Array Drive
Micro-satellite
Mechanism (SADM). The SADM serves as the interface between the satellite body and the PVSA subsystem,
enabling the decoupling of their spatial orientation. Nonetheless, there exists a research and development gap
for such systems regarding low cost micro-satellites. During the literature study of this paper, individual
orbital parameters of various micro-satellites have been extracted and compared to the rotational freedom of
the corresponding SADMs used. The findings demonstrated that the implemented SADMs are over designed. It
is therefore concluded that these components are not tailored made for each spacecraft mission individually,
but rather, exhibit a generic design to full fill a majority of mission profiles and requirements. Motivated by the
above analysis, the cardinal objective of the current research is to develop a low cost mechanism that will be
precisely tailored for the use of a low Earth orbit (LEO) micro-satellite platform orbiting in altitudes of
500
1000 km. The design of the mechanism may vary from the existing miniaturized SADMs. For example,
the preliminary analysis of the current research suggests, that the conventional use of the slip ring system as
the electronic transfer unit can be replaced by a seMI Orientation Unit (MIOU). Systems engineering tools for
concept generation and selection have been used. In addition, simulation and mathematical modelling have
been implemented on component and system level, to accurately predict the behaviour of the system under
various modes of operation. The production and system testing of the prototype has taken place and it has
verified that the development of such a system, will aid the power generation of the solar arrays, while having
a positive impact on the cost reduction of such satellites.

1. Introduction solar arrays to configurations that have a steerable axis of rotation.

Thus fulfilling a ϕ ¼ 0∘ condition between the solar array plane normal
Solar energy, is the predominant source of power amongst the various and the incident light rays [2]. As a result it was found that steerable,
energy sources used for space exploration. The conversion of solar power or arrays with no sun angle effects experienced an increase of power
to electrical power on the spacecraft is initiated through the photovoltaic generation as high as 135%. Therefore, the implementation of a Solar
solar array subsystem. Several factors must be taken into consideration, Array Drive Mechanism (SADM) can provide savings in weight and
so as to ensure that optimal operating conditions of the photovoltaic solar costs, due to the increase of power production from a smaller
arrays are met [1]. solar array.
The optimal operating conditions of the photovoltaic solar array, Furthermore, losses in energy conversion or system efficiency occur
amongst others, is dependent on the angle of incident light to the normal for photovoltaic modules due to angular effects and are dependent on the
of photovoltaic solar array surface. With the increase of this angle, the system orientation, eclipse, and available radiation [3,4]. With the con-
irradiance on a tiled solar cell diminishes in proportion to the cosine of ventional photovoltaic subsystem used in space applications, the angle of
the angle. the incident solar light varies depending on the relative motion of the sun
An earlier study compared the efficiency and power output of fixed with respect to the orbital plane that changes over time [2,5]. Therefore

* Corresponding author.
E-mail address: j.guo@tudelft.nl (J. Guo).

http://dx.doi.org/10.1016/j.actaastro.2017.07.009
Received 17 February 2017; Received in revised form 29 May 2017; Accepted 8 July 2017
Available online 15 July 2017
0094-5765/© 2017 IAA. Published by Elsevier Ltd. All rights reserved.
G. Galatis et al. Acta Astronautica 139 (2017) 407–418

Abbreviations

AIT Assembly Integration Testing

COTS Components Of The Shelf
ETU Electronic Transfer Unit
FFC Flat Flexible Cable
LDR Light Dependent Resistor
LEO Low Earth Orbit
NEMA National Electrical Manufacturers Association
PVSA PhotoVoltaic Solar Array
SADM Solar Array Drive Mechanism

Fig. 1. Main subsystems of a Solar Array Drive mechanism.

the total photovoltaic solar array performance and system efficiency have
a high dependency on the overall history of the solar light. Consequently continuous solar orientation of the photovoltaic solar array system can
the incident angle is a critical parameter affecting the photovoltaic be achieved.
output performance of a fixed solar array subsystem. This paper, attempts to lay the research foundations for the devel-
Several design solutions for reducing the aforementioned angle have opment of a low cost tailored SADM for LEO micro-satellites with the use
been proposed, and developed. Such designs are categorised as passive, of Commercial Off The Shelf (COTS), and aims to answer the main
semi passive, or active methods. Regarding the active design, a widely research question, through analysis and testing of the produced proto-
accepted method, which is also proposed as a solution within this paper, type. The main research question is:
is the implementation of the solar array drive mechanism (SADM). The
SADM is an active hinged joint that is located between the solar panel “Could a low cost Solar Array Drive Mechanism (SADM) be developed,
and the satellite chassis. Because of the SADM's location, it is considered and tailored as such to be exclusively used by LEO micro-satellite
to be a critical hardware component of the spacecraft, and it is designated platforms?”
to be a single point failure [6]. Overall it has been shown that 32% of all Amongst the other derived requirements, the mechanism must fullfill
spacecraft mission failures are attributed to the failure of the spacecraft an initial high level pointing requirement of 1∘ .1
power subsystem [7]. In the following sections, the total design process, from concept
The SADM provides the optimal alignment of a satellites solar panels generation to manufacturing and testing of a system prototype, is
towards the Sun. In addition, the SADM allows electrical power and data described. Specifically, the first section describes the systems engineering
transfer between the PVSA and the spacecraft during their relative framework that is required for the development of the initial conceptual
movement. As a result, the SADM decouples the relative orientation of design of the mechanism. Next, the detailed design of the generated
the two systems. The SADM consists of (i) an actuator, the purpose of concept is presented. This section also includes a detailed design of each
which is to rotate the solar array in the required direction; (ii) an elec- subsystem as well as a brief analysis of the selected position sensor. The
trical transfer unit, where it serves to convey signals and power through a lifetime behaviour of each of the mechanism subsystems is simulated in
rotational joint; and (iii) a system of sensors, which provides position the proceeding section. All leading to a final system simulation leading to
control [8]. the verification of the system. In the final section the Assembly Integra-
There are several existing examples of implemented SADMs in LEO tion and Testing (AIT) of the system is presented. The end purpose of this
satellites. To start with, the Sentinel-1 is located in a near polar sun chapter is to validate that the end developed mechanism complies to the
synchronous (dawn- dusk) orbit at an altitude of 693 km. Due to its orbit, set of requirements, and functions as intended to. In the conclusion to this
the Setinel-1 uses the Karma-4 SADM produced by Kongsberg [9]. The paper, a brief summary of the findings is presented, and various obser-
Karma-4 implements a twist capsule, for the Electronic Transfer Unit vations and results are discussed.
(ETU), to provide the limited angle range, needed by the satellite solar
arrays. Another example satellite that implemented a SADM is the 2. Front-end systems engineering & concept selection
EarthCare satellite located in a 393 km altitude [10]. This satellite also
encapsulates a twist capsule to allow for the required partial rotation of The main subsystems of a SADM are the ETU, the rotary actuator, the
the solar arrays. What is more, the SPOT satellite, orbiting at 832 km in a angular positioning sensor, and the mechanism housing subsystem
Sun synchronous orbit, utilizes the SEPTA 14 SADM [11]. Additional (Fig. 1). The functionality of the mechanism housing is to support, and
examples of current implemented SADM are the NUSTAR and the Proteus provide hinging points of the mechanism subsystems. During our design
satellites orbiting at 650 km and 1336 km respectively. Both these sat- review process, we concluded that the mechanism housing would not (at
ellites use the SEPTA 31 SADM [12,13]. this phase of the project) be designed to sustain any loads, other than the
Emerging designs are also being developed for nano-satellites. One component gravity loads.
example is the orientable deployed solar array system for a nano-
spacecraft, which amplifies the achievable performance of these, typi- 2.1. Solar array rotational requirements
cally, power-limited systems. The final mechanism design refers to the
use of a miniaturized stepper motor that leads a simpler motor driving The system operates under two modes: (i) Sun observation mode,
circuit providing an accurate PSVA position measurement [5]. where the system orientates the solar arrays to intercept light during the
However, mission and market analysis that we conducted, high- Sun illuminated part of the orbit; and, (ii) the Eclipse mode, where the
lighted the minimal emphasis that has been given for the development of solar arrays rotate into position, and meet the sun rays once the satellite
a SADM, tailored to the needs of the orbital requirements of micro- has exited from the eclipse.
satellites in LEO [14]. Therefore, a need for further research regarding
the use of a SADM on micro satellite platforms has been identified. The
proposed solution allows the spatial de-coupling of the solar array and 1
This requirement is subjected to change depending on the maximum accuracy that can
the satellite chassis. Through this method, we aim to show that be achieved with the prototype.

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Fig. 2. Graphical representation of the solar array rotation during the sun observation mode for an altitude, inclination and NAAN of H ¼ 900, I ¼ 98, N ¼ 90 (H900I9N90). The data sets
have been obtained from STK™ simulation.

To create the simulations, the Satellite Tool Kit™(STK) has been used. sign convention of the software program the angle undergoes a sine
During the orbital simulations, the satellite is modelled as a Nadir wave function.
pointing satellite, while rotation is prohibited around its roll and pitch The Sun is intercepted at approximately 15∘ below the velocity vector
axis (x,y-axis). Furthermore, to achieve optimum lighting conditions, the (x-axis) of the satellite (Figs. 2 and 3). As the solar array-sun vector
PVSAs where modelled to rotate in order for the perpendicular light changes quadrants, it rotates a total of 180∘ up until the -x-axis (Figs. 2
conditions to be achieved. and 5), where undergoing this -x axis the sun is lost at approximately 115∘
The simulations investigated the mechanisms angular ranges for a (Figs. 2 and 6).
combination of LEO orbital profiles. These are (i) altitude The solar array requires a maximum angular rotation equal to
(H ¼ 500–1000 km); (ii) angle of inclination ði ¼ 0∘
98∘ ); and (iii) θ ¼ 310∘ . By implementing a safety margin of SF ¼ 1:1 it is concluded
longitude of the ascending node ðN ¼ 0∘ ; 30∘ ; 45∘ ; 60∘ ; 90∘ ; 120∘ Þ. The that the maximum rotation angle that the mechanism must be able to
longitude of ascending node is considered to be zero when the sun is in provide, in order to fullfill the angular ranges of all nadir pointing
the orbital plane. microsatellites in low Earth orbit's, is θ ¼ 340∘ Further on, through the
Amongst all LEO orbits simulated, the plot in Fig. 2, illustrates the same analysis it has been found that for an orbit with altitude of
maximum angle of rotation that is required by the mechanism during its H ¼ 500 km, the system will experience the least amount of eclipse time,
Sun observation mode. This plot is better understood in conjunction with that is equal to teclipse ¼ 23 min. Finally, it has been found that the orbit
the simulation snapshots found in Figures from Figs. 3 to 6. Due to the

Fig. 4. Once the sun vector has changed quadrants the angle of rotation begins to in-
Fig. 3. The sun vector first intercepts the sun at approximately 40∘ bellow the x-axis. crease again.

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that is characterized by altitude of H ¼ 500 km, an inclination of i ¼ 80∘ ,

and a longitude of the ascending node of N ¼ 0∘ , will impose the
maximum mean angular velocity of the system, equal to
ω ¼ 4:34 deg=min. Further analysis of the simulation process can be
found in Ref. [14] (see Fig. 4).

2.2. Finalised system concept

The final concept generation has been derived by utilizing a systems

engineering trade-off process. The trade-off process has quantified all
relevant options for each subsystem. As a result of the trade-off scheme,
the system architecture is derived and depicted in Fig. 7.
The blue boarder in Fig. 7, indicates the structural housing of the
mechanism. Within the housing, the mechanism encapsulates the stepper
motor, a goose-neck configuration for partial rotation of the ETU, and the
angular sensor selected to be a potentiometer. Its mode of operation is
based on existing SADMs, such as [15,16].

3. System detailed design

Fig. 5. The sun vector over goes a 180∘ rotation.
The following section presents the detailed design of the SADM. The
dynamic equation of the rotary actuator is presented in the first subsec-
tion. Following, parameters of the dynamic equation are derived, leading
to the sizing of the rotary actuator. A gear system is introduced to the
mechanism to establish inertia matching of the mechanism and the load.
In the final two subsections, the gear layout is presented along with the
mechanisms ETU design.

3.1. Dynamic model of rotary actuator

Fig. 8 shows, the free body diagram of the system. The rotary actuator
is meshed with a gear. All moments and forces acting upon the system
are displayed.
The dynamic equation (Equation (1)), is found through the torque
equilibrium of the free body diagram.
"  2 # "  2 #
Nm Nm
Tm ¼ Jm þ Jl θ€m þ Bm þ Bl θ_m (1)
Nl Nl

By following the methodology found in Ref. [14], and implementing

Fig. 6. The satellite goes into eclipse once the sun vector is located approximately 114∘ the results found in Section 3.1.1, the torque output of the actuator is
bellow the -x-axis. calculated to be Tm ¼ 0:14 Nm.

Fig. 7. System architecture of the solar array drive mechanism.

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Table 1
Parameters of compound gear sizing.

PCD [mm] Number of Teeth

Gear 1 (G1) 13.50 15

Compound Gear 2.1 (CG2.1) 27.00 30
Compound Gear 2.2 (CG2.2) 10.80 11
Compound Gear 3.1 (CG3.1) 29.70 33
Compound Gear 3.2 (CG3.2) 17.10 19
Gear 4 (G4) 51.30 57

Fig. 8. Generic free body diagram of an actuator-gear system. 3.2.1. Gear system
A system of compound gears, and a set of external gears are used to
mechanically couple the rotary actuator to the main shaft of the mech-
anism. According to our analysis found in Ref. [14], the highest gear
3.1.1. Gear ratio sizing
reduction that could be achieved is Gr ¼ 18 : 1. Table 1 contains the final
Assuming an ideal system where no friction exists, equation (1) is
system of gears, the correlating pitch circle diameter (PCD), and number
manipulated to express the inertia matching requirement between the
of teeth of each gear.
rotor and the load (Where Nm =Nl has been substituted with Gr):
The necessary gear reduction to be implemented into the system is
rffiffiffiffiffi Grtotal ¼ 210 : 1. A gear reduction system of Gr ¼ 18 : 1 is used to me-
Jl
Gr ¼ (2) chanically couple the actuator with the main shaft. Hence, the remaining
Jm
Gr ¼ 12 : 1 gear reduction is implemented as a planetary gear system.
By substitution of the inertia values of the load and the gear in The planetary gear system is determined to be a COTS, and is pre-
Equation (2), it has been calculated that an intermediate gear system installed onto the actuator by the manufacturer of the actuator.
with a ratio of Gr ¼ 210 : 1 is required for inertia matching. This gear
ratio is to be fitted between the load and the actuator. 3.3. Gear layout
Through the method of iteration among the motor inertia, load
inertia, and market available gear ratios. It is concluded that the standard The final configuration of the gear system is illustrated in Fig. 10. The
NEMA 11 bipolar stepper motor is to be selected. The NEMA notation layout of the gear system is divided into two segments. The first segment
refers to the selected stepper motor, which is dimensionally standardized (green, red, and orange gears), consists of a compound gear system, which
by the “US National Electrical Manufacturers Association (NEMA)”. The is connected to the rotor via the main shaft with a gear ratio of
purpose of NEMA is to standardize various aspects of stepper motors. Gr ¼ 18 : 1. While the second planetary gear system (gray cylinder) is
directly installed on the actuator, and has a gear ratio of 12:1.
3.2. Implementation of the gear system
3.4. Actuator micro stepping
Based on our calculations (Fig. 9), the distance between the actuator
and the main mechanism shaft is d ¼ 33:25mm. Therefore, the gear ratio, In Section 2.1 it was found that the maximum angular velocity
or part of the gear ratio is used to mechanically connect the actuator, and required by the mechanism is ω ¼ 4:34 deg=min. The NEMA 11 stepper
the main shaft. motor has a step size of 1:8∘ , implying that with this step size the
The layout of the gear system is divided into two segments. The first mechanism will be operating in a “stop-go” fashion. The implementation
segment, consists of a compound gear system, which connects the rotor of a driver capable of further subdividing the actuator step size is
with the main shaft. The second gear system is a planetary gear system, necessary. This ensures that the actuator will have a smoother step
that is directly installed onto the actuator. transition, while resonant phenomena are avoided.

Fig. 9. The dimensional distance between the shaft of the rotor, and the mechanism shaft. Fig. 10. Final gear system configuration of the SADM-MIOU.

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3.5. Electronic transfer unit

The mechanism layout to house the goose neck configuration is dis-

played in Fig. 11. The telemetry, data, and power cables are introduced
from the solar array to the mechanism through the hollow shaft (label
①). The wiring in turn is connected to the Flat Flexible Cable (FFC)
connection pins that are housed on the shaft (label ③). The space be-
tween the mechanism structure and the shaft is used to house the FFC
geometry for the ETU design. Furthermore, the resulting signals, telem-
etry and power exits the mechanism from the small opening (label ④).
The main shaft is designed as such that the diameter is larger at the
section where the flat flexible cable is located. This allows the shaft to be
clamped between the two ball bearings, located at the opposite ends of
the mechanism (label ⑤). In turn, the ball bearings are clamped by the
mechanism caps, where they are attached to the mechanism housing
(label ⑥). The clamping of the shaft is designed to constrain its motion to
1-Degree of Freedom (DoF) around its central axis.

3.5.1. Flat flexible cable

Fig. 12. The loop displacement and cable length with respect to the ratio of the inner and
The FFC is pre-located within the confinement created by the inner
outer diameter is depicted.
casing of the housing and the outer diameter of the main mechanism
shaft. One end of the FFC is rigidly attached to the drum, while the other
end is attached to the housing (Fig. 11). As the main shaft rotates
clockwise, the centre bend of the FFC moves in the same direction. The 3.7. SADM geometric envelope
FFC goose neck configuration's maximum angular range is related to the
outer diameter of the shaft and the inner diameter of the casing, as: Fig. 13, depicts the sketch and section cut of the mechanism. The
mechanism is located within the satellite, and is mechanically attached,
θshaft with the use of bolts to the satellites inner surface. The hollow shaft is
θcable ¼   (3)
rO
þ1 initiated from the mechanism and protrudes the satellite body leading to
rI
the PVSA.
Fig. 12 shows the plot of Equation (3) and the appropriate length of Table 2 presents the mechanical properties of the mechanism. On the
the FFC with respect to the ratio of diameters can be selected according to first column, the mechanical subsystems are tabulated. In the proceeding
it (Fig. 12). columns the relevant dimensions of each subsystem are shown. In case
that the dimension is not available, the corresponding value has been
3.6. Angular sensor replaced with “[
]”. The diameter entry for the shaft is 20:00=24:00.
This is due to the varying cross section of the shaft. It is further calculated
The angular sensor, has been calculated to have a resistance value of that the mechanism will have a total weight of 1.87 Kg.
Ω ¼ 1K Ohm. The analysis of the potentiometer is accomplished through
the use of the Thevenin equivalent circuit methods, and the Analogue to 4. System simulation
Digital Converter (ADC) circuit interface of the micro controller.
The micro-controller of the test bench has been determined to be an The system simulation of the SADM has been divided into two sec-
Arduino-UNO with a 10 bit ADC port. Next, the potentiometer value was tions. The first section is the simulation of the electrical system, while the
compared with the micro-controller load resistance, and has been found second section is the simulation of the reverse kinematics of the me-
that the sensor behaves linearly throughout its operation. chanical system.

4.1. Rotary actuator

The simulation of the rotary actuator is based on the “power_ step-

permotor” example provided by the SimMechanics® library. The pa-
rameters of the simulation are found in Table 3.
Our simulations indicated that the rotatory actuator requires an
output torque of about Tm ¼ 0:15 Nm (Fig. 14). Nontheless, small de-
viations from a constant torque value occur. The oscillations are attrib-
uted to torques that originate from the interaction between the phase
currents and the magnetic flux created by the magnets, as also the detent
torque of the step motor, which has not been taken under consideration
during the simulation.

4.2. Mechanical simulation

The mechanical system has been modelled through Simulink's™ sub

package of SimMechanics™. The mechanical simulation consists of the
gear reduction system along with the mechanical properties of the load.
The system is illustrated in Fig. 15.
The mechanical sketch consists of two basic sections, namely, the
Fig. 11. Mechanical design of the ETU housing. controller and the mechanical section. The function of the controller is to

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Fig. 13. Mechanical sketch and cross section of the mechanism.

Table 2 l ¼ 3 mm and a diameter equal to the actual gear PCD diameter (section
Geometric design envelope, and subcomponent weight. 3.2.1). The revolute joint represents the first compound gear system
Length (mm) Thickness (mm) Diameter (mm) Weight (Kg) encountered by the rotary actuator (smallest gear in Fig. 15). The
simulated joint has been assigned a density value of 7859 Kg=m3 . The
Cassing 92.00 3.00 62.00 0.14
Caps [
] 3.00 76.00 0.15 signal from the PID is fed into the first revolute joint of the simulation.
Actuator 104.00 [
] 42.85 0.40 The revolute joint has been tuned such that the inverse kinematics of the
Gears [
] [
] [
] 0.20 joint are sensed.
Bearings 12.00 22.00 42.00 0.20 The first revolute joint is constrained to the next revolute joint (third
Shaft 247.83 3.00 20.00/24.00 0.78
Total: 1.87 Kg
largest gear in Fig. 15). The gear constraint has been parametrized with a
gear reduction ratio of Gr ¼ 2 : 1. The second revolute joint has been
modelled to have identical mechanical properties as the first gear. The
two remaining revolute joints are coupled with a gear reduction of
Table 3
Gr ¼ 3 : 1. In conclusion, the total gear reduction of the mechanical
Input parameters to the stepper motor Simulink® schematic.
system is Gr ¼ 18 : 1.
Parameters Value Units
The final revolute joint has been modelled to provide the system with
Winding Inductance 7:2⋅10
3 H a damping rate of 0:3 Nm=ðdeg=secÞ. While the joint has been parame-
Winding Resistance 9.2 Ohm trized in such a way that the required angle, velocity, acceleration, and
Step Angle 1.8 Degrees
the torque are tabulated. Lastly, the output signals of the final revolute
Maximum Flux Leakage 0.005 Vs
Maximum Detent Torque 4:5⋅10
3 Nm joint are further reduced by a 12:1 gear ratio.
Total Inertia 0.135 Kgm2 The reverse kinematics simulation is subjected to follow the sine
Initial angular velocity 0 rad=sec wave input signal (Fig. 16). The torque to be provided by the rotary
Initial Position 0 Degrees actuator is shown in Fig. 17. It is observed that the torque demand of the
driver (Fig. 17) increases in accordance to the input signal (Fig. 16). The
maximum torque required is found at the point where the signal changes
monotonicity.
serve as an input signal to the mechanical section of the simulation. The
What is more, Fig. 17 shows that the maximum torque to be provided
input signal has been determined to be a sine wave function with an
by the rotary actuator has a value of Tm ¼ 0:14 Nm. This has been
amplitude of magnitude A ¼ 300½
 and a period equal to T ¼ 1380 sec,
numerically predicted, and verified by the electrical simulation (section
which is equivalent to one solar observation mode. The significance of
4.1). Nontheless, during the direction change of the angular vector, small
this input signal is to simulate the lighting angles of the sun that the solar
oscillations occur in the system. These oscillations are linked to the load
array will encounter during its orbit.
inertia (inertia matching).
The input signal is compared with the current orientation of the solar
array. This, in turn, will stimulate the output of the Proportional Integral
5. Assembly, integration & testing
Derivative (PID) controller, which then will control the rotary actuator
accordingly, so as to reach the desired position.
The end purpose of this section is to validate that the end system
The second part of the schematic is the mechanical section. This
complies to the set of requirements, and functions as intended to. The
section simulates the various mechanical constraints, and physical
integration is divided into two main branches: the mechanical and the
characteristics of all members that constitute the system. A revolute joint
electrical/software integration.
has been implemented and modelled as a cylinder with a length of

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Fig. 14. Dynamic torque output of the rotary actuator.

Quarter, Eight, Sixteenth Step mode). Resonance phenomena have been

found at the quarter step mode. Results are presented in Table 4.
The potentiometer measures in a non-linear manner. The divergence
of the potentiometer values are calculated to be within a 1% divergence
from the linear prediction.

5.2. Mechanical integration

The purpose of this section is twofold. Initially, all dimensions and

tolerances are evaluated and checked, in order for the assembly of the
components to be feasible. Secondly, this section provides an initial
testing of the goose-neck ETU functionality and its motion dynamics.
The initial stage of the mechanical integration is to assess that the
printed components are manufactured within the specified tolerances.
The first step is to assemble the back and front caps of the housing, and
check if the components fit together. Furthermore, a test shaft has been
placed through the two caps, so as the alignment of the main shaft with
the housing is to be verified. Moreover, the gear pins are installed and
mounted on the housing (Fig. 20).
Fig. 15. Mechanics Explorer of the mechanism simulation. SimMechanics has been used. The main shaft is fitted through the cap and the goose neck config-
uration is installed. The cable is installed, in a preset geometrical manner
in order for the desired goose neck geometry to be achieved. The
5.1. Electrical integration configuration has been tested manually for potential abnormalities dur-
ing its operation. It is observed that bulging of the FFC from the axis is
The electrical subsystem, shown in Fig. 18, demonstrates the present, as seen in Fig. 21. Optical inspection of the area, lead us to the
Arduino-UNO micro controller, and its interconnections amongst the conclusion that the bulging is a result of compressive forces acting upon
other electrical components. The rotary actuator (right of image) is the cable. The cause of this phenomenon is considered to be derived from
connected through a H-bridge (labelled “Easy Driver”) to the micro the high bending stiffens of the cable.
controller (labelled “Arduino Uno”).
Two Light Dependent Resistors (LDRs) are noticed (bottom left), the 5.3. System testing
LDR have been implemented into the schematic such that the integration
of the closed loop control system can be tested. The LDRs act as sun The SADM is assembled and integrated into the test rig (Fig. 22). The
sensors that monitor the movement of the light source, therefore leading systems test setup, constitutes of the mechanism placed on a Plexiglass
to the rotation or stoppage of the actuator. The electrical system inte- surface with its
Z axis pointing toward the ground. The orientation of
gration is shown in Fig. 19. the mechanism is chosen, such that only gravitational forces are applied
Stepwise component testing and integration have been implemented to the mechanisms 3D printed structure The transparency of the Plex-
to verify that all systems are healthy. The variance in the step size is iglass allows to measure the angular deflection of the solar array.
calculated to be 4% between the actual and manufacturer specifications. In extension to the mechanism, a piece of ply wood is fitted. The di-
The driver has been tested for five micro-stepping modes (Full, Half, mensions the ply wood has dimensions of 50  50 cm and a mass

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Fig. 16. Reverse kinematics. Actuator torque required to rotate the mechanical system. Consisting of the solar array and compound gear system.

moment of inertia similar to that of the load. The ply wood is fitted to loosely set, and may be subjected to change. Looking at Fig. 24, the
represent the solar array that the mechanism will rotate. On the surface of reader will observe the cosine value for a range of angle from 0∘
10∘ . It
the solar array, the two LDRs are placed to sense the direction of the is therefore concluded that a deviation on the pointing accuracy up to 10∘
incoming light, produced by a laboratory light source. Both LDRs are will have minimum impact on the efficiency of the PVSA system.
separated with the use of a cardboard fitting. The fitting constrains the The rotary actuator is supplied with a constant voltage source of 5 V.
LDRs field of view, and limits them to a 90∘ viewing angle per LDR. A multi meter has been placed, between the step driver and one of the
The solar array has been illuminated with the light source from three electric poles of the step motor, such that the current draw from the
different positions (90∘ ; 45∘ ; 0∘ ), measured from the normal of the solar motor is tabulated. Through the defined test procedure it has been
array surface. The SADM is then let to rotate toward the incoming light calculated that the maximum current draw of the step motor is 13:9 mA.
until it comes to a full rest. The measurement of the pointing accuracy of For a power supply of 5 V the average power the system consumes
the mechanism is derived by measuring the length of the cast shadow and is 69.5 mW.
by using trigonometry (Fig. 23).
Through the above described test procedure, and based on the out- 6. Results & discussion
comes of the test results, the mechanism's pointing accuracy is found to
lie within the margin of a 3∘ accuracy. The simulation of the system validated the torque value, which has
The pointing accuracy found does not satisfy the initial 1∘ degree been numerically calculated in section 3. In both simulations the torque
pointing accuracy. Though as mentioned, this requirement has been requirement of Tm ¼ 0:14 Nm is found to coincide with the numerical
results obtained through the analysis.
A closer inspection of the simulation results reveals the existence of
oscillations caused by the actuator. The oscillation frequency is not
adequate to produce resonance phenomena within the system. Following
the simulation results, the observed torque variations are attributed to
the torques that originate from the interaction between the phase cur-
rents, and the magnetic fluxes created by the bipolar magnets of the
stepper motor.
Furthermore, the simulation of the mechanical system is completed,
indicating the existence of oscillations within the mechanical system
caused by the loads momentum change. The gear system that couples the
actuator to the main shaft shows after simulations, that the compound
gear system produce a Gr ¼ 210 : 1 gear reduction. Finally, through the
use of inverse kinematics, it is also shown that Tm ¼ 0:14 Nm of torque is
required to rotate the solar array under the simulated conditions.
Structural components, such as the housing and caps of the mecha-
nism, have been produced in house through 3D-printing. Moreover,
preferential components, such as ball bearings and the compound gear
system, have been for manufacture. The rotary actuator is a COTS
component [17]. System integration followed a bottom-up approach. The
design consists of two aspects, namely, the electronic system constituted
by all the electrical components and the interconnections that allow the
Fig. 17. Oscillations observed during the mechanical simulation.

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G. Galatis et al. Acta Astronautica 139 (2017) 407–418

Fig. 18. Schematic of the electrical subsystem of the SADM.

Fig. 19. Integration of all the electrical components that constitute the SADM prototype. Fig. 21. The above figure depicts the bulging of the FFC during back rotation of the goose-
neck configuration.

Table 4
Stepper motor, step mode characteristics actual versus theoretical values.

Resolution Result Comments Specs. Measured

Full Step Pass [
] 1:800∘ =stp 1:88∘ =stp

Half Step Pass [
] 0:900∘ =stp 0:789∘ =stp
Quarter Step Fail Step Skipping, Resonance 0:450∘ =stp N/A
Eighth Step Pass [
] 0:225∘ =stp 0:238∘ =stp
Sixteenth Step Pass [
] 0:113∘ =stp 0:125∘ =stp

Fig. 20. Mechanical integration of gear system to the housing. Fig. 22. Total system integration.

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G. Galatis et al. Acta Astronautica 139 (2017) 407–418

Table 5
Identification of factors that influence the pointing accuracy of the mechanism.

Source of error ΔΘmin [deg] ΔΘmax [deg]

Misalignment of axis
0.01 0.01

Readout delay 0 2
Manufacturing/assembly 0 0.7
Step size
1.8 1.8
Gear backlash
0.1 0.1

pointing error of θ ¼ ±2:69∘ (tabulated in Table 5). In addition it was

found that the average peak power and average power consumption per
orbit lies within acceptable margins (P ¼ 13:9 mW). The rotary actuator
has also been tested for its holding torque, verifying the maintenance of
the orientation of the solar array by the rotary actuator. Lastly, conduc-
Fig. 23. Test set-up, for the measurement of the angle between the incoming light rays
tive testing confirmed that the ETU conveys electrical signals and power
and the mechanisms pointing accuracy. The shadow that is cast, is measured with the use
of a millimetre scale. from the solar array to the satellite bus.

7. Conclusions & limitations

The current paper lays the foundations for of the development of a

system, capable of decoupling the spatial orientation of the PVSA with
that of the satellite chassis. A conceptual design of a SADM that will be
capable to support future microsatellite missions located in LEO, has
been described.
Based on the findings presented in this paper, a SADM can be tailor-
made to fit the majority of LEO orbits that range within 400
1000 Km
altitude. Most importantly, It has been shown that the use of a slip ring
system is not a necessity. This is, due to the partial rotation required by
the solar arrays during orbit. Overall, the advantage of implementing the
SADM is that it leads to a solar array constantly solar pointing, where in
return will lead to a reduced solar array panel area Further research
should proceed with the development of the SADM. There is a market
need for such a system, and hence a rapid development of the SADM will
provide a market advantage.
Nontheless, like every study, this conceptual design has its limita-
tions. Initially, the COTS that have been used are not space graded and
future studies are advised to replace these components. Furthermore, it is
strongly recommended that the 3D printed members be replaced by
Fig. 24. Cosine plot, for the range of angles: 0∘
10∘ . space graded material that will be capable to undertake all loads that this
mechanism may encounter. The ETU showed that FFC bulging is present
when the solar array rotates back too its position. The source of this
functionality of the system. In addition, the system should have the bulging, has been found to be a cause of compressive stresses applied
software integrated within the micro controller. onto the FFC. To overcome such stresses, a placement of less rigid FFC or
Stepwise component testing and integration has been implemented multiple smaller FFCs is recommended to be implemented in the future
to assure that all systems are healthy. The variance in the step size, is development of the mechanism. Lastly, tribology aspects for friction
calculated to be 4% between the actual and manufacturers specifica- reduction between moving members have not been studied in the scope
tions. During the integration testing of the rotary actuator non-linear of this project. Subsequent studies should also explore such
measurement has been observed. The potentiometer values are calcu- tribology aspects.
lated to be within a 1% divergence from the linear prediction. The
function of the potentiometer, is to provide an indication signal to the Acknowledgements
micro controller signifying that the mechanism has reached one of the
two end states (0∘
340∘ ). Therefore it is concluded that the repeat- This work would not have been possible without support of both the
ability of the measurement is acceptable for the current phase of Delft University of Technology, and LuxSpace Sarl.
the project.
It has been noted that the implemented software during the inte- References
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