Modeling and simulation of the kinematic behavior of the deployment mechanism of solar array for a 1‐U CubeSat

Kinematics of deployable solar array mechanisms in CubeSat satellites have considerable influence on the stability and attitude control of a satellite, especially in low mass systems as CubeSats. One of the issues with the conventional solar panel deployment mechanisms in CubeSats is the speed of its deployment, especially when position‐lock to hold the panels back from oscillation is lacking. The generated oscillation becomes more pronounced in a system equipped with solar tracking unit and thus, reduces available projected area of the panels and causing fatigue at the yoke and panel hinges. This work aims at modeling and simulation of the 1‐U CubeSat solar panel deployment mechanism vibration control using fisher wire. Two‐fold panel deployment mechanism with a rolling sun‐tracking tilt mechanism was developed. The system performance from viewpoint of vibration analysis was evaluated using mass‐spring‐damper method and bond graph techniques. Numerical simulations and experiments were performed to validate the proposed method. The modeling and computational analysis were done with SOLIDWORKS software. The system was tested for vibration and stability using the seismic mass‐spring‐and‐damper arrangement to validate the model. A 3‐D printing was generated and tested to evaluate its vibration performance and its effects during deployment. The result was such that the two panels attached to a wing hinged at Y – and – Y directions deployed slowly and smoothly at approximately 2 s, giving room for the vibration to decay exponentially towards zero. This agrees with reported works where a DC motor was used to control speed of deployment by increasing time to 6.8 s. The simulated and experimental results of the printed model showed close agreement with the theoretical values with an error of 0.03% in energy supply reliability and up to 400% power generation potential when compared to body mounted solar panels with the same satellite specification without a significant impact on system strength and stability.


INTRODUCTION
Space technology is strategic to socio-economic development through industrial growth and ICT exploits. 1 The role of satellites in the global economy has diverse coverage, from precision agriculture, security, water management, environmental and weather monitoring, to disaster management. The recent trend in space technology is centered on design and development of lighter, smaller, and cheaper devices, namely: Micro, Nano and Pico satellites, with relatively the same functional capabilities and effectiveness as the conventional types. 2 This development was catalyzed with the advent of miniaturized electronic circuits, which helped to create small sized computers to run the activities of a satellite mission within host spacecraft. 3 CubeSat is a Nano satellite with an average mass of about 1.3 kg. The smallest satellite is Pico satellite with a mass range of 0.1 to 1 kg. 4 The advantages of Nano and Pico satellites over bigger satellites include: low cost and lesser handling 5 ; they are easy to launch/ multiple launch due to less weight and quick access to space due to their small nature, 6 thus allowing non-space faring nations and corporations to have access to space. Technically, CubeSats are self-dependent, fast to set up and versatile in applications. They have been used for researches, low earth orbit applications, like remote sensing, earth science, disaster response, climate monitoring and recently, in interplanetary missions. 7 An example of such missions was a pair of CubeSats, MarCo deployed to Mars in the mid-2018, to provide real-time landing coverage for National Aeronautics Space Administration's next mission to Mars and to Jupiter's icy moon Europa in the 2020 or 2030 as reported by Gretchen. 3 CubeSat power subsystem: CubeSat takes its power from the sun via the use of solar panels, which may be either body mounted (BM) or deployable solar array (DSA). The BM types have the panels mounted (fixed) on the side frames of the satellites. On the other hand, DSA have in addition to the fixed panels, deployable ones that give them more surface area to optimize power generation. 8 The payload operations of BM CubeSats were limited to basic low power image coverage due to inadequate power in earlier systems like the CUTE-I 1 U/BM for Armature Radio with 1.5 W launched in 2003 9 and CanX-2 3 U/BM as technology demonstrator for formation flying launched in 2008. 10 On the other hand, the use of DSA in the recent systems provides more power to achieve high precision images and other sophisticated operations as obtained in FLOCK-1 3 U/DSA with 20 W launched in 2014 as earth observer, 11 and Mars Cube One (MarCO) 6 U/DSA launched in 2018 for Telecom technology, 12 producing 8 to 12 times more power. The challenge faced with DSA type satellite is the solar array deployment mechanism. Solar array deployment mechanisms: There are two major mechanisms in solar array deployment: hold down and release mechanism (HDRM) and the deployment mechanism. HDRM controls the release of the panel from stowed position for final deployment. It holds separable parts, movable payload items, deployable appendages secured during flight and released in orbit. 13 HDRMs are comprised of two elements: (i) hold down preloading assembly -comprising of fasteners and cam/lever link to provide a preload system that will secure the structure during flight, and (ii) hold down release actuator -which releases preload upon a command of an electronic prompt/signal. Some of the mechanisms operate on low temperature range as in: shape memory alloy (SMA) triggered nuts and actuators (−60 /+70 • C), paraffin actuators -pin pullers/pushers (−60 /+80 • C), and electro-magnetic/solenoid pin pullers/ pushers (−60 /+80 • C). Others are electromagnets or magnetic clamps, thermal cutters or knife, pyrotechnic devices (release nuts/bolt cutter, separation nut, cutters, wire cutter, cable cutter), split spool devices (Fusible wire, SMA wires) and solenoid actuated nuts.
Deployment mechanism is the second part of the deployment. When the panels are released from the lock state, the actuation (deployment) process begins using the deployment mechanism designed for the system. This can be realized in several methods such as torsion spring-hinge lever, SMA, electric motor drive, ADELE hinge, and tape spring hinges. 14 One of the issues with the conventional solar panel deployment mechanisms in CubeSats is the speed of its deployment and excessive dynamic displacement due to launch loads, 15 especially when position-lock to hold the panels back in place after deployment is lacking. 16 The release speed generates high momentum that is enough to cause spring compression in the case of any re-bounce. This compression increases the stored potential energy in the spring until it is enough to completely overcome the momentum; which is a product of mass and velocity. It then pushes forth the panels by converting the stored potential energy once again into kinetic energy, thus setting in oscillation. This oscillation becomes more pronounced in system equipped with solar tracking as the responses to any base or rotor excitation on the panels could have frequencies in the neighborhood of the natural frequency of the panels in motion. This has two immediate problems: the oscillation amplifies the momentum and thus, reduces available projected area of the panels and could also cause fatigue at the yoke and panel hinges.
This work aims at the mathematical modeling and simulation of the kinematics behavior and development of a 1-U CubeSat solar panel deployment mechanism. Two-fold panel deployment mechanism with a rolling sun-tracking tilt mechanism is developed. The system performance from viewpoint of vibration analysis was evaluated by mass-spring-damper method and bond graph techniques. To minimize the vibration due to momentum and system excitation, panel weight and projected area optimization as well as deployment speed reduction were considered. Numerical simulations and experiments are performed to validate the proposed method. The modeling and computational analysis were done with SOLIDWORKS software. The system was tested for vibration and stability using the seismic mass-spring-and-damper arrangement to validate the model. A 3-D printing was generated and tested to evaluate its weight, solar area availability as well as vibration performance and its effects on energy supply during deployment.

1.1
Review of similar works NEE-01 PEGASUS is a 1-U CubeSat launched by EXA (Ecuadorian Civilian Space Agency) in 2013 to demonstrate technology capability. The solar array is released and deployed when activated by the heat of the sun using artificial muscle and memory metals respectively. It was placed in sun-synchronous orbit at an altitude of 630 × 657 km 2 , inclination of 98.04 and period of 97.45 min with adorable features 99.98% pure titanium and 1.5 mm thickness, but lacks holding-back mechanism to minimize vibration, 16 and thus exposed to high deployment induced vibration. Mirshams et al. 17 designed a deployable array using Torsion spring for deployment and paraffin actuator as deployment rate controller. A cam located on a bar moves in a helix path made on a cylindrical shell. This movement causes the shell to rotate and deploy the solar panel, which is connected to the cylindrical shell. A hold-down-and-release mechanism that employs commercial hook and loop technology "Velcro®", was used by Malavart and his team 18 to provide a structural path for the panels' release.
In operation, two bands of the hook and loop used as fasteners hold the deployable panel to the satellite's frame. A string pulled by a motor breaks the link between the two bands to release the panels. The introduction of the hook and loop arrangement makes the deploy mechanism to easily be re-engaged and facilitate complete resetting manually. Alireza 19 conducted analytical synthesis and analysis of function generation mechanisms, orange MATLAB function in the SIMULINK Model. The researcher demonstrated the process using a four-bar quick-return mechanism with a time ratio of 1.25 and a follower sweep angle of 50o with a variable torque motor operating on (1 + 2sin [1.5 t]) Nm torque. Lagrange's equations and Lagrange's multipliers method for constraint motion were applied to arrive at the positions, velocities, and accelerations of the links. The result showed that at the two extreme ranges of the follower motion, the mechanism is in toggle condition, with the crank in line with the coupler. Thus, two precision points of the mechanism were established as starting points to completely solve the equations for the desired links' dimensions and orientations. The angular velocity and acceleration were obtained using the orange MATLAB function in the SIMULINK Model. Lack of position system as a defect with the traditional deployment mechanisms for solar panels in CubeSats was investigated by Arturo et al. 16 The team observed that absence of such locks could generate spurious oscillations in the panel due to back-driving resulting to poor energy supply and hinge failures. They, therefore designed, analyzed, and manufactured a deployment mechanism for CubeSat solar panels with an integrated back-drive blocking system. Finite element analysis was carried out at the panel hinges and release spring. The result showed the anchor hinge and the used double-torsion spring provides a positive direction torque transfer thus minimizing oscillation potentials. The numerical analyses performed indicate reduction in weight and stress at the hinges thus indicating its feasibility and potential applications with further research development. Ronnie 20 presented deployable multi panel solar array for low cost 1-U CubeSat missions with capability of operating on solar power only without preset batteries. The electrical power supply has capability to manage 57 solar cells distributed on 8 panels and 32 battery cells distributed in 2 battery arrays for a total of 28.8 A or about 107 Watts. It has MCU-driven core and 8 solar input power channels each capable of supporting 6 V at 2 A and 25 ms switch arrangement. These outstanding features are considered to depend much on the deployment and stability mechanisms. The live result showed a clear occurrence of the release within few minutes after the satellite was being released into orbit, due to the use of active assembly in NEE-02 powered by an auxiliary battery and also passed the new solar array generation test for full Dnepr vibration and Long March 2D vibration profiles.
Eric 21 reported the development of a Self-Orienting CubeSat Solar Array by David in May 2018, using a two degree of freedom mechanism attached to the solar panels to turn them towards the sun. The uniqueness of the system is its ability not to draw direct power from its storage to perform the movement while lesser space and weight were achieved compared to other competing designs. The design has capability to orient four times more solar panel area towards the sun and potential of 3 to 4 times more energy generation, as compared to AFIT design. Alexis et al. 22 developed the main geometrical formulas based on Euler angles of an observatory system compared to the altazimuthal coordinate system required for motorized rotating mirrors in solar tracker based on two 45 mirrors in altazimuthal set-up with a light sensor on the spectrometer. The sets of equations were illustrated with a tracker developed for atmospheric research. The output showed a reduction in angular offset when placing the mirror due to the presence of feedback system from the mirror, which helps to correcting the tracker orientation as well as lesser dependency on the optical configuration as compared to active tracking systems. To control speed of deployment, Hossein 23 utilizes a brushed DC motor passive spring-driven deployment mechanism to reduce the deployment speed.
Shankar et al. 15 presented a new deployable solar panel module with over damped system that effectively protects the structure of the solar cells in the launch environment. The result showed the exited vibrations through the solar panels are quickly damped out using constrained layer dampers. The model was demonstrated with a three-pogo pin-based burn wire release mechanism fabricated and tested for application in the 6-U CubeSat "STEP Cube Lab-II" developed by Chosun University, South Korea. With the control system that utilizes longer launch time and rapid damping, the deployable panel was reported to have passed vibration test in both off and in-orbit deployment. This is said to ensure structural safety, and Better CubeSat operational stability. Long and Xinsheng 24 analysis studied the variation of angular velocities of center of solar panels having amplitude of about 25 rad/s and a frequency of 2 Hz for planer condition of deployment. To mitigate vibration while in space especially during tracking and stretching of the panels, the amplitude of the angular velocity was reduced to approximately 20 rad/s with an irregular frequency of about 0.5 Hz.
Apart from the issue of power reduction and mechanical fatigue, vibration also imparts the imagery and signal transfer to the earth's sub-system. The impact of the un-damped situation in satellite deployed at an altitude of 500 to 900 km was shown by Oda et al. 25 to have impact imagery from the satellite due to vibration of the solar array paddles in a thermal shock. The Japan Aerospace Exploration Agency -JAXA used an onboard camera mounted on the paddles with a reflective target marker of size 50 × 26 mm 2 at a distance of 6 m away from the camera to monitor the effect of vibration. The camera is designed with a 90 • field of view and limited pixels of SXGA-1280 × 1024, representing a camera pixel of 7 mm at markers position. Ode reports that a few mm offset (an average range of 6.5 to 8.5 mm) due to vibration, resulted to extremely low quality of image capture.
In all cases, system stiffness for frequency control and speed reduction are major ways of mitigating panel vibration and mechanical failures.

System description and components:
The main components of the solar array deployable system as shown in Figure 1, are: main body 1 (CubeSat sidewall), yokes 2, panel frames 3, torsion spring and hinge 4, and DC servo motor 5. The main body houses and anchors all other components. The yoke is pivotally mounted on the main body for holding the panel arms in place and rotating series of foldable solar array arms. The array consists of two symmetrical wings, each having two arms hinged together and attached to the arm holder with a torsion spring hinge to release the panel array from a stowed position to the deployed position. Each arm is attached to a servo motor shaft with a bearing, which Components of a CubeSat with two solar arrays in assembled and exploded views F I G U R E 2 A monocrystalline solar cell. 29 (Reproduced with permission) rotates the yoke up to 90 • to track the sun's rays. The DC servomotor is the primary actuator used to drive the movable parts. Other components include DC battery to store and supply required power for system operations and system circuit board to provide connections, signals, and controls. The wings of the solar panels are stowed against the sidewalls of the CubeSat in folded form, using a hold-down and release mechanism. At the prompt of the remote control, the hold-down pin is released and the tensioned spring unwinds to deploy the wings in horizontal position. Materials: One of the underlying concepts of this study is to utilize as much as possible, locally available materials to produce the solar array components. All materials used were chosen based on local availability, minimal cost, lightweight, and durability. The materials used are classified into two -soft and solid materials. The soft materials are the computer software and the mathematical formulation used, while the solid ones involved the physical materials.
i. The Model Design Software -the design and modeling of the solar array structures and its substrate was done with SOLIDWORKS 2016, 64 bits editions. SOLIDWORKS is a computer-aided design (CAD) software widely used in the space industry due to its robust 3-D capabilities of creating, editing, assembling and updating of models, performance in the area of conceptual design with applications of motors and forces to evaluate the operations of mechanisms, and ease-to-use. 26 The software was used to create a visual representation of the CubeSat.
ii. Physical Component Development -the entire structural system of the deployable solar array was developed through printing on DELTA WASP 2040 TURBO 3-D printer, which creates a three-dimensional object from a CAD model. DELTA WASP 2040 TURBO is a fused deposition Modeling (FDM) machine with a wide range of available materials ranging from Commodity thermoplastic (such as PLA and ABS) to engineering materials and high-performance thermoplastics (such as PA, TPU, PETG, PEEK, and PEI). 27 For this work, a PLA was used for the CubeSat structure, while liquid-resin was used for the arms, gears, and holders. PLA and resin are biodegradable thermoplastics that give a good visual quality. In addition, liquid-resin is lighter in weight and has outstanding thermal insulation, smoother finishing, and lower friction on mating parts.
iii. The Solar Panels: the panels are made from thick compressed paper sheets with solar cells mounted on it. The panels are mounted on the solar arm with arm to yoke ratio of 4 (35.64 mm: 145.41 mm). The solar panels were sized based on the dimensions of the CubeSat. Each panel's sheet is 70 × 110 × 3 mm 3 in size.
iv. The Solar Cells: A mono-crystalline solar cell shown in Figure 2, with an efficiency of 20.4% was used. The solar cell specifications are usually chosen based on the satellite's power requirements, such as satellite mission, type of orbit, power level, mission life and operating temperatures; Vidyanandan 28 but since this CubeSat is designed for demonstration, the solar cells were chosen based on availability. The dimensions of the solar cells are 125 × 125 × 0.5 mm 3 . The electrical ratings are: 0.5 V, 5.8 A, cell with efficiency of 20.4% and maximum power output of 2.9 W per cell.
For all the panel geometries, the HDRM holes' locations are at equal distance from the edges. The pins are fixed at the center of two adjacent solar cells on each side to provide enough space for the assembly of panels and their holddown pins.
v. The Electrical System: This comprises of: (i) two servomotors; arm motor and the tilt motor, (ii) two gears connected to each of the servo motor gears and (iii) a circuit board connecting all the electrical wiring.
The arm motor controls the speed of deployment of the panels. It ensures the panels are released slowly in approximately 2 s to complete deployment. The arm motor is attached with 3 mm screw to the arm holder and is linked to the two wings with a 0.3 mm fishing wire. The tilt motor gradually swings the arm left and right up to 45 • towards the rays of the sun. Both servo motors are SG-90 model, which are shown in Figure 3 with a weight of 9 g and spatial dimension of The parts are divided into three: the structural system, the deployment mechanism, and the electrical system.
i. The structural system: The standard dimensions of a CubeSat was established in 1999 based on the research work of Bob Twiggs from Stanford University Space Development Laboratory (SSDL) on functional satellite space optimization in which 10 cm cubic units with a mass of no more than 1.33 kg 30 was adopted. There are, currently, five types of CubeSats: 0.5, 1, 2, 3, and 6 U. The number corresponds to the (approximate) length of the CubeSat in decimeters and the widths limited to 1decimeter, NASA 31 and Arturo. 16 The design of the structural system includes the main body (Cube-Sats frame), the arms, and the solar panels. The CubeSat structural size is approximately 105 × 101 × 101 mm 3 , 3.5 mm frame thickness, and a total weight of 110.4 g. The modeled features of the body frame are shown in isometric view in Figure 4A. To reduce weight, void spaces are created on the sidewall with linking webs to preserve required strength. The working drawings for frame construction are given in Figure 4B.
ii. The Solar panel Arms and Sheets: The panels are mounted on the solar arm with arm to yoke ratio of 4 in Figure 5. Their sizes are based on the dimensions of the CubeSat. There are holes of dimension 2 mm to screw the panel sheets to the arms. To stop the forward motion of the second arm, a back-heel step out base is made on it to rest on the hinge F I G U R E 5 Solar array arm mount F I G U R E 6 Solar array panels joint at the end of the first arm. This development does not lock the panel in place; it only stops its forward motion. The panel sheets are rectangular and equal in size as shown in Figure 6. The width is 110 mm and the length is 70 mm each.

2.1
The deployment and operation drive system of the solar panels Gears Mesh Arrangements: Two gears are involved, one is used to control the speed at which the motor deploys the arms using a fisher wire to hold the arms against the spring while the second gear is used for solar tracking up to an angle of 45 • to each side of the yoke. The pictorial and orthographic views of the tilt gears as well as their attachment points to the servo motor are shown in Figures 7 and 8.

The Modeling of the Kinematic Features of Deployment Mechanism:
The modeling of the kinematic features of the solar array deployment mechanism was considered for displacement, speed and acceleration required to ensure smooth deployment of the arms. These kinematic parameters are eventual tools used for proper sizing of the torsional spring and damping for use at joint intersection of the solar array. They are based on principles of energy flow in bond graph method (discussed in another paper for the dynamics part of the model) and principles of vibration in mechatronics.
The solar array represents such a system of interacting appendages, which gradually unfolds into stretch out sheets when fully deployed as shown in Figure 9.
The deploying systems of the array can thus, be represented with a planer link mechanism with three-link members; the yoke, panel-1 and panel-2.
Kinematic Analyses of the Deployment Mechanism: the kinematic analyses are divided into two parts namely, the arms and spring mechanism for deployment of the solar arrays and the axial rotor unit for solar tracking.
The Arms and Spring-Link Mechanism for the panels Deployment: consider the end view configuration shown in Figure 10 and note the following two categories of assumptions. 1. The link mechanism is planer with 2-D operation fixtures and binary joints turning pair. The panels were in folded state just before launching commenced and were displaced through: Angular displacement -for Panel-1: −90 • < <0 • , and for panel-2: -270 • < <−180 • . The panels are rectangular, symmetrical and homogeneous with centers at c = L 2 , while the yoke, is approximated to a trapezoidal shape with center 33 2. Links OA and AB arrangement were approximated to double compound pendulum configuration with the following adjustments: The length of link OA = the length of link AB, and link OA is configured to only perform one-fourth of a revolution, that is: ≤ 90 o .
• Link CO rotates laterally with the panels to track solar radiation, and may cause vibration in OA and AB through rotor excitation causing them to vibrate vertically and horizontally.
From Figure 10, the geometric horizontal and vertical positions of the joint 1 and end point 2 are approximated to that of a double pendulum whose motion and analysis are similar to the works of Elbori and Abdasamd. 33 The kinematic equations of motion as the driver link is displaced through an angle 1 , and the driven link displaced through 2 , are given in Equations (1)-(4), as: The corresponding horizontal and vertical velocities are obtained by differentiating Equations (1)-(4), with respects to 1 , and 2 to give Equations (5)-(8), as: Similarly, the corresponding horizontal and vertical accelerations are obtained by differentiating Equations (5)- (8), to give Equations (9)-(12), as:

Solar tracking rotor excitation
The tracking mechanism was based on Single-Axis Orientation System. Such design was reported by Andrew et al. 34 to have been used on the launch of MarCO (Mars Cube One) in 2018, and on the development of HaWK (High Watts per Kilogram) solar arrays manufactured by MMA Design LLC unit in Colorado. In operation, the solar arrays are able to rotate about their common center through the yoke, while the orthogonal axis is compensated for with the rotation of the CubeSats along its axis using attitude control systems. However, the design may not provide adequate solutions to sun tracking when compared to other developments. This work focused only on the impact the tracking operation of the single axis orientation models may have on the panel vibrations through rotor excitation via gear mesh arrangement.
The tracking system is an active type that uses electrical drives and mechanical gear arrangements to continually position the panels normal to the sun's radiation. 35 Only the mechanical aspect was considered for angular displacement and angular velocity, which are the parameters involved in exiting adjoined members.
The driver motor gear in mesh with tilt gear for solar tracking are shown in Figure 11A. Two separate movements are involved, the linear spread out of the panels with horizontal and vertical components, and the rotation of the tilt (yoke). The output rotation of the shaft x for solar tracking will cause an excitation on the deploying panel as shown in Figure 11B.
As the driver rotates at an angular speed of 1 , increase in the angular displacement of the panel gear 2 (driven tilt gear) with respect to the displacement of motor gear 1 (driving gear) is given by the gear ratio in Equation (13) and the angular and linear velocities are given Equations (14) and (15), Prikhodko and Smelyagin: 36 F I G U R E 11 Model and body diagram for rotor excitation on panels by the tracking system Thus, for the driven gear, and v m = 1 * r Considering the panels' arrangement in Figure 11A, as a lump rigid cantilever with the free body diagram shown in Figure 11B, the vibration of the lump body in the horizontal direction, H, due to the excitation from changes in speed and hence momentum of the rotor. Since the rotor's shaft is centrally held in a bearing, vertical movement at the bearing joint is zero (restricted). For any presence of imbalance mass, m o , away from the longitudinal axis of the rotor, changes in speed will result to changes in momentum due to centripetal force. Thus, applying Newton's second law to the panels and the motor respectively gives, Kelly: 37 But, Since the presence of the induced vertical forces produces zero vertical displacement at the bearing point, then, F v at the bearing is zero. Thus, merging Equations (16) and (17), factorizing, and dividing through by parameter k, gives: In standard from, the vibration parameters (natural frequency n , frequency ratio , and the stiffness k) from Equation (18); are given as: Hence, the kinematic characteristic Equation (18), can be expressed as: The control of the spring properties to reduce the magnification of this input vibration was done with a tension string (fisher wire) which holds the second panel against the spring, thus allowing it to gradually deploy to its final position.
The steady state response is of interest as it is independent of initial position and velocity of the oscillating mass (panels), and it is given as: Where X o , is the amplitude of the response and is the phase difference from the input, whose values are given as: and Maximum amplitude occurs at a frequency given by [xx]: To avoid resonance therefore, the natural frequency must be very high by increasing the stiffness of the spring through its mass content as indicated in Equations (19) and (20). So that the condition for attaining stability is: 37

Panels vibration and stability
In the vertical direction, vibration due to momentum transfer was considered to be equivalent to base excitation. The arrangement is as shown in Figure 12A,B. Figure 12A shows the schematic diagram of the accelerometer commonly used to measure such small vibrations, and Figure 12B shows the vibration pattern. At any instantaneous angle i of panel-1 to the lateral axis of the yoke, the joint point of panel-1 and panel-2 as shown in Figure 12B, vibrates up and down about its instantaneous position by amplitude Δy i and the end point also moves horizontally forth and back in oscillation by amplitude Δx i . Restraining the vertical vibration of the joint will significantly restrain that of the end. Thus, only the vertical vibration was considered.
The support base is the panel arm whose vibratory motion is required as it swings outwards -indicated in Figure 12B as upward motion, represented by displacement y b , and the corresponding displacement of the seismic mass by y m . Using newton's second law of motion, the differences in force of displacement that causes the vibration can be expressed using the mass-spring and damper system as: As vibration sets in, the arm motion can be approximated to a compound-pendulum undergoing sinusoidal displacement, with y b = Ysin( t); where Y is the amplitude, and the frequency. Setting displacement: y m − y b = z. The resultant force in z-direction (vertical) is:

F I G U R E 12 Solar array arm vibrations profile during deployment
For steady state solution, the instantaneous displacement is given as: 37 Where Where is the shift phase angle and Z is the amplitude. The solution of these equations was considered for three scenarios: underdamped, critically damped, and over-damped situation. At the end, the design worked with critically damped situation.

Minimizing vibration using fishing Wire (line)
Vibration in deployable Panels could impart dynamic instability in the operation of CubeSats resulting to poor power supply and mechanical failures [Peters]. To avoid these consequences, fisher wire is utilized to hold the panels against the torsion springs. The fisher wire is a flexible and high-tension cord 38 made from a crosslinking low-density polyethylene with a tensile strength of 24 MPa. The fishing wire is tightened firmly to the free end of the outer panel (panel 2) and kept intention with the aid of a motor via four free rolling pulleys.
a. Initial angular velocity of the panels The initial angular velocity of the panels is provided by the spring at point of release when = 90 • , and varies gradually to zero = 0 • . The typical release spring selected has two extended arms at 90 • to each other (one is fixed against a frame and the other depress-able) as shown in Figure 13.

F I G U R E 13 Torsion release spring for the CubeSat panels
As the free leg is deflected fully through = 90 o , and the maximum potential energy stored in the spring is given by: 39 Thus, the torsion spring is compressed by 90 • when in stow position (when the panels are folded in). At the instance of release, when the restraining force is taken away, the spring sprung out, converting the stored potential energy into kinetic energy to push panel-1 outwards from = 90 o through i , … 2 , 1 , … to 0 = 0 o . The maximum value of the kinetic energy is equal to maximum potential energy at = 90, and is expressed as: 40 Thus, equating Equations (1) and (2), and rearranging gives the maximum angular velocity as: Where, max = maximum angular velocity, P.E = potential energy, K.E = kinetic energy and I = moment of inertia, k is the spring rate and is the angular displacement.

Deployment time
Time for deployment of panel with respect to the angular displacement can be expressed in terms of angular velocity as: 32 Where, is the instantaneous angular position or displacement, is the angular velocity and t = time.

Determination of thickness and strength of the fisher wire
The torque exerted by the springs on the panels is a function of the panel weight and the spring arm length. The panel weight is made of components; mass of the solar cells, mass of the panels and mass of the arms that hold them together. Thus, the total load is calculated from: Where m s is the mass of Solar cells, m p is the mass of the Panels, m a is the mass of the arms, g is the acceleration due to gravity at the height of deployment, and r is the total length of panels (L 1 + L 2 ). Fisher wire comes in two forms.

Design and selection of tension fisher wire
The tension string was modeled to have the same stiffness as the spring. This assumes that the vibration of the panels will be transferred directly to the string. Thus, to damp out the vibration, the force exerted by the spring must be countered by the tension in the string. With the assumption that both the string will vibrate with the same frequency as the panels, then, the first fundamental frequency is given as: Lynch and Jim. 41 The associated stress in the string due to the tension as given expressed by Oldrich: 42 From Equation (39), the required diameter d, for the string that is stiff enough to hold the panels firmly against the spring is determined. The tensile strength of the material for the string is used as the basis while the length of the string is determined from the sum of the panel lengths plus 1 / 4 (number of the pulleys employed) and small addition to anchor the string to panel-2 and the driving motor-shaft. Selection of Fisher Wire: the selection of fisher thread is characterized by its twine numeration indicated by numbers, N g (length per gram of the thread), and the number of strands, n s composing the thread. It is commercially quoted as a fraction, N g /n and referred to as the structural number of the thread. In selecting the thread, the length L is first measured in meters and the weight measured in gram. The number of strands, n is quoted by the manufacturers. To improve strength against fatigue, a multi twine thread is used. The number of twine N t required is obtained from the relation Baranov: 43 Where u, is the correction coefficient for degree of shortness for twined threads, (u = 1.05 for nylon 41 ). The number, n, is commercially quoted for number of strands and m is the weight of the string in gram. The diameter of the string is dependent on the quantity of material that is used for the tread. For strength, the ratio of the bulkiness of the material known as spool capacity to its length is commercially used to quote the diameter as, 38 Thus, the stiffness of the thread can be varied until the first fundamental frequency is obtained, and the standard number corresponding to that is chosen for the damping of the panels. These are used to select a commercially quoted that is in the neighborhood of the designed value.

Projected area of panels for solar rays
The energy generated in a solar panel depends largely on its surface area available to receive the solar energy from the sun. With a panel of length L and width W, the maximum available area for solar panels will be L × W. However, this assumes the plane of the panels will be at right angle to the sunrays. This is quite impossible in the case of solar arrays due to two main angular displacements that are associated with its deployments and operations.
1. Unfolding of the panels: the panels are normally folded and stowed on the opposite sides of the CubeSat's frame until it is released. During deployment, the folded panels gradually open up from 0 • inclination angle up to about 90 • , when it is fully opened. During this period, the surface of the panel area will not be fully available for the sun's exposure. 2. Secondly, as the CubeSat floats, it continually changes the panel surface areas away from the sun's rays. With tracking system in place, the photoelectric cell is being turned back to the sun's rays. Again, during this period, the panels are not directly facing the sun. When the rays are parallel to the plane of the panels, the rays' reception is assumed to be minimum and gets maximum when directly facing it.
In the two conditions discussed, the quantity of energy generated is dependent on the projected area of panels for the reception of the sun's rays. Projected area in this term implies percentage equivalent area at any angular position of the panels that will provide the same quantity of energy when the panel is at 90 • . With this definition, the power generated is obtained from Ehren: 44 Where is the solar cell efficiency given as 20.4% from the manufacturer, SI is the solar intensity constant whose value is taken to be 1361 W/m 2 , is the area of the panels obtained from L × W and, the angular displacements and represents the incident ray angles respectively the tilt angle of tracking and half of the angle of inclination between the folded panels during unfolding and vibration.

RESULT AND DISCUSSION
The kinematic analysis of a CubeSat's solar panel arrays with passive deploying mechanism and an integrated tension fisher-wire to control speed of deployment was modeled, simulated, and fabricated. To keep weight and spatial dimension within the standard values, 30,31 heavier electromechanical deploying drivers are replaced with a lesser weight strings as a proposed option for future possible implementation. The absence of holdback locks to prevent panels from bouncing back to compress the torsion spring that could set in vibration causes lower power generation and fatigue at the hinges Arturo et al. 16 The proposed modification in this article aims at the component sizing and kinematic parameters for space and weight optimization, system stability during panel array deployment and operation, and photovoltaic surface projection /orientation towards solar rays for maximum power generation. Table 1 presents the final dimensions and operating parameters of the solar array deployment components: spring and panel design parameters using 1-U CubeSat's geometric specifications and design; Equations (1) through (25). Highlighted in blue in Table 1 are core parameters of the spring design. An overall spring stiffness of 0.0157 Nm/rad is required to move the solar panels with a resultant torque of 0.0247 Nm from 0 to 90 • .The complete panel deployment is done in 0.0777 s with an angular velocity of 20.2084 rad/s. Because the time taken to complete the deployment is extremely small (0.0777 s), the velocity is high, and thus the momentum. As the panels reach the final positions they hit the hinges and re-bounce back with not the same but relatively higher velocity. This returning momentum is enough to push back the spring slightly and thus set in some potential energy, which increases gradually until it completely counters the reverse motion. At this point, the spring pushes the panels forth again to repeat the cycle. One of the intents of this work is to identify the time that is enough for the vibration to die out so that the panels can be planned to deploy over the time and hence taking away the excessive momentum that causes vibration. This idea is based on the fact that velocity is displacement over time. Thus, with the same displacement over a longer period, momentum as a product of velocity and mass will also be reduced.

Design dimensions and operating parameters
Based on the standard size presented by NASA 31 and reported by Theoharis et al. 30 16 have a dimension of 10 × 10 × 10 cm 3 (in launch configuration) and a mass of ∼1.26 kg having two solar panel wings with three panels on each side for a total of six panels per wing. The deployed dimensions are 10 × 10 × 75 cm 3 and 1.5 mm panel thickness. The weight of the 3-D print of the housing frame has a thickness of approximately 3.5 mm with about 37.9% void area to arrive at a net weight of 110.4 g. There are two servomotors of 36 g each and gear train assembly of 27.8 g combined weight for the speed control line and 43.5 g combined weight for the solar tracking gear train. The arms and the yoke were printed from a PLA -high performance thermoplastic material of density 1240 kg/m 3 and have a weight of 139.3 g. The panels are built from a compressed paper bonded together with resin adhesive having a density of 1201 kg/m 3 and a net weight of 188.58 g. The overall weight of the CubeSat with the two opposite wings is 0.8375 kg from simulation and 0.942 kg from physical measurement. The difference represents about 11% coming from plastic welding materials; joining links and inaccurate measurement of had to reach void areas. However, the two values are well within the standard weigh of a CubeSat with the physical measurement leaving about 29% of its standard weight for the communication systems. This is an indication that the CubeSats will satisfy the maximum space and weight optimum criteria for its proper operation. The solar array assembly accounts for about 49.2% of the CubeSat weight and thus, imbalance in its operations will result to low power output and fatigue at the hinges, as reported in Reference 16.

3.2
Simulation results of the kinematic profile of the solar array When the panels are in folded position shortly before it was released, the horizontal displacement of panel-1 is zero as well as the horizontal and vertical positions of the end point of panel-2. Only the vertical displacement of the tip of panel-1 is in vertical position of 70 mm downward, as shown the graph of panel-1(V). The tip of panel-2 travels at the same rate as the tip of panel-1 but its maximum distance with reference to the yoke joint is 140 mm at maximum angular displacement of 90 • . On the other hand, the vertical distance of the tip of panel-1 from the yoke axis reduces to zero while F I G U R E 14 Linear kinematic characteristics of the panels at various angular displacements that of panel-2 remains constant at zero. The sinusoidal profile of the curves at starting and ending points as indicated helps to reduce or eliminate speeds at each end that could cause oscillation.
In Figure 14B, the horizontal velocities are at highest values for panel-2(H) and Panel-1(H) while the vertical velocity of the tip of panel-1 is zero but increases gradually to about −1.35 m/s. thus, with this high velocity at the joint, this is likely to be a re-bounce back. Since the tip of the panel-2 does not move vertically, its vertical velocity is zero and so also its vertical acceleration as shown in Figure 14C. The horizontal acceleration of the tips is approximately equal, thus they both have the same speed at any instance. The maximum vertical acceleration of the tips of panel-1 m is about 28.6 m/s 2 when the panels are released, and reduces to zero at about 55 • angular displacement where the acceleration of the horizontal motion is highest. This indicates that the kinematic amplitudes of the acceleration require check at this turning point. The angular velocity also varies according to the relation = v r , where r in this case is the length of the panels. Thus, for a length of 0.07 m, 1 = 2.8 0.07 = 40 rads∕s, representing approximately 382 revolutions per minute or 6.37 Hz. This is too high and indicates uncontrolled speed that could result to severe launch vibration loads as reported by Shankar et al. 15 To reduce the frequency, especially with tracking systems, Long and Xinsheng, 24 suggested that the speed of deployment is required to be lower, and the amplitude controlled to avoid resonance. Structurally, the force and hence, momentum at the hinge is dependent on the landing acceleration of the panels. From Newton's second law of motion; F = ma or T = I , the higher the acceleration the higher the torque and hence generated stress at the hinges. The maximum acceleration of 35.7 m/s 2 at 55 • angular displacement and reduces to 28.6 m/s 2 at landing point. When compared to the solar panel deployment test results of Long and Xinsheng, the acceleration of vibration response for a deployment time of 1.58 s was reported to have a maximum value of 8 m/s 2 , which is far below and safer than our value. This is also an indication that speed control and hence, damping is required.

System stability during panel deployment
The graph of distance covered against time is plotted in Figure 15 to give the inertia and frictional resistances offered at the initiation of the solar array unfolding. Situation is not always as smooth as presented in the simulation of the kinematic characteristic in Figure 14. In Figure 15, the intercept at the origin represents the initial point of release at point (0,0), but motion was initially resisted due to inertia and presence of friction in the system. The release only starts (panel commence opening) at about 42 ms, at the break-off point. After the break-off point, the solar array opens quickly to about 4 mm in 5.16 ms. The solar array then exhibits a draw-back for another 4.2 ms before it finally picks as a result of the flip-flop kinetic-potential energy within the spring system. This situation sets in oscillation with amplitude of about 4 mm. Though this seems to be very minute, its impact could be 10 times escalated. The magnitude of this vibration at any angular displacement is obtained using Equation (29), while its amplitude and phase shift are calculated from Equations (30) and (31). Similar work was conducted by Husein, 29 who presented an innovative approach to the rotational speed control of a solar panel in deployment. A brushed DC motor was utilized as a passive spring driven mechanism to reduce the deployment speed. The connector's

Undamped vibration of the solar array during deployment
The result of a simulated scenario in which the frequency of the set-in vibration matches that of the natural frequency of the mechanism was considered. The process covered a period of 5 s and the amplitude is as high as 4 mm and repetitive all through the period with a constant frequency of 3 cycles per second. The graph therefore shows that it is important to damp the system in order to prevent resonance from taking place as shown in Figure 16, for undamped situation. From the graph of Figure 16, it is evident that the steady state response of the system exhibits a harmonic feature with a frequency of 3 Hz and an amplitude of 4 mm. This displacement out-of-plane could be amplified to a resonance threshold if the natural frequency of the spring is somewhere around 3 Hz and causes the panels to dangle alternately to opposite sides with very high amplitude that could result to a very low projected area for the solar ray. From Equations (19) and (21), with the panels' weight fixed; the vibration of the panels can be amplified if the spring constant is too low. To avoid this scenario, the amplitude must be reduced using the spring design parameters. The natural frequency of the spring material must be very high so that an assured condition of stability is attained. This is true from Equation (27); in which w w n ≪ 1. With w n ≫ 3, say 10 Hz, the frequency ratio is about 0.33, thus pushing away the possibility of occurrence of resonance.
Since the amplitude is dependent on the spring properties and damping factors in addition to both natural and excitation frequencies, one way of making w n to be large is by increasing the stiffness of the spring, which was done by selecting spring with about 6 times the diameter of the designed value. Similar vibration of deployable CubeSat solar panels with an amplitude of 4 mm can result to resonance and drastically reduce projected surface area of the solar cells and hence, energy generation.

3.5
Impact of solar tracking on the panel deployment Figure 17 shows the impact of tracking on the deployment of the solar arrays. The tracking systems that majorly impact vibration on the other parts are mainly clearance on bearings when it is relatively too loose and bearing friction when it is relatively too tight. The servomotor has a speed of 100 rpm (about 10.47 rad/s). With a gear ratio of about 2.39, the rack gear angular velocity is 3.92 rad/s using Equation (14). With a possible maximum bearing clearance of 0.8 mm, the response to the rotor excitation has amplitude of 1.28 mm with a frequency of 0.6 per second. In addition, it was observed that the bearing clearance causes increase in the frequency of the oscillation of the panels and the kinematics parameters of the panels. This position was also reported in Reference 17 who presented that the higher the size of clearance at the hinge (bearing point) of solar panels the higher the frequency and amplitude of oscillation.

F I G U R E 17 Simulated undamped vibration due to tracking rotor transfer (base excitation)
The effects of the two vibrations, horizontal and vertical on the panels can set in flip-flop chaos like that of compound pendulum. To control this, it is important to reduce both speed of tracking and deployment and for this, a fisher wire (string) was used. It was tied to the end of the second panel and wound in the reverse direction over the middle joint (hinge) to the tilt motor and stretched out against the springs. By this, the panels gradually land at their extreme position and reduced tendencies for high reverse momentum. However, the limitation is that with string made from polyethylene, being in tension for a 2-3 years period could lead to plasticity and break with shocks [plasticity].

Deployment time
From the design calculations, the panels are to be deployed in approximately 0.0777 s, which is too fast and can affect the stability of the satellite. Deployment of these solar panels has considerable influence on dynamic and altitude control of the satellite and may make disturbances in altitude control of the satellite as reported by Reference 17. Hence, to minimize these disturbances, the solar panels should be slowly deployed. There are two options to adjusting the timing, and invariably to control the speed of deployment. First, is to vary parameters related to time using Equation (36). Since time is indirectly proportional to the angular velocity, increasing angular velocity decreases the time and vice versa. Now iterating the two parameters varying time from 0.5 to 5 s, and keeping angular displacement constant, the angular velocity versus time graph in Figure 18 is obtained. At t = 0, just before the release of the panels, the stored potential energy in the spring is maximum and when released, it is converted to kinetic energy which is also maximum at the instance of release. It then reduced exponentially to F I G U R E 18 Exponential decay of angular velocity with time

F I G U R E 19
Damped and undamped set-in vibration with normalized amplitude as low as 0.5 rad/s at the stoppage time. Theoretically, the maximum potential and kinetic energy were obtained from Equations (33) and (34). The combination of the two equations is calculated from Equation (35).
From simulated result, a combined angular velocity of 20.2084 rad/s was obtained as indicated in Table 1. Practically, with the spring constant, k 1 and moment of inertia, I 1 of 0.0157 Nm/rad and 0.000095 kg m 2 respectively for panel-1, the angular velocity, 1 is 16.11 rad/s using Equation (35), representing a difference of 20.3%. This reduction suggests that the kinetic energy at the commencement of opening is lesser than the expected value (20.2084 rad/s), which may be due to presence of friction and inertia as indicated in Figure 15, thus, possibly resulting to the late take off at the break-off time (4.2 ms). On the other hand, with the spring constant, k 2 and moment of inertia of 0.0079 Nm/rad and 0.000026 kg m 2 respectively for panel-2, (see Table 1), the angular velocity is 21.85 rad/s using same Equation (35). The value of this time is higher by 8.1%. Since panel-1 is expected to open first before panel-2, the angular motion of panel-1 may have aided that of panel-2 and thus reduces the effect of friction and inertia on its motion, hence the increase in its value. The two results also tend to agree with the first law of motion as the panels tend to resist motion when release from rest and panel-2 tends to move faster due to the inertial motion imparted by the movement of panel-1. The significant of these differences could result to horizontal vibration; the faster panel-2 tends to pull panel-1 at some instance while the slower panel-1 will respond by jacking back panel-2 by equal and opposite force horizontally and thus, causing sliding oscillation. Therefore, to mitigate or reduce this to the barest minimum, an elastic-fisher string is proposed to continually arrest and damp out the vibration. This damping effect was also suggested by Shankar, 15 who made use of multilayered stiffener with viscoelastic acrylic tapes to attenuate launch loads resulting from vibrations, which was tested through free vibration against various layers of the stiffener and demonstrated on 3 U CubeSat. Figure 19 presents the normalized amplitude as ratio of amplitude at each point to the maximum value of deflection obtained.
The graph in blue shows the underdamped scenario while the one in orange gives the normalized amplitude for the critically damped condition. The red arrow pointing upward close to the origin shows the position of the designed release time, 0.078 s. Within that zone, the amplitude ratio is 0.45 on average. Though, the vibration continues to die down, but it is not significant until about 2 s, when it eventually calmed down completely. For the critically damped situation, the vibration decays exponentially and approaches zero at about 2 s. Thus, the deployment time should be greater than or equal to 2 s to avoid sustaining any set-in vibration.
A brushed DC motor was utilized in a passive spring driven deployment mechanism by Hossein 23 to reduce the panels' deployment speed. The motor terminals were connected to an external resistance in a closed circuit. The back EMF of a motor connected to an external torque produced by the torsional springs is coupled to the DC motor's shaft. The generated current produced an opposite torque that is used to slow down the deployment speed of the panels. The solar panel angular velocity increases as the external resistance and peaked in all cases at about 0.9 s after which it decayed exponentially. For an external resistance of 50 Ω, the maximum angular velocity is 17.2 deg/s and the solar panel reaches its full F I G U R E 20 Power generation at different tilt angles over selected inclination deployed position in 6.8 s. When compared to the results of similar vibration control by Shankar et al. 15 in which a response displacement magnitude of 0.12 mm was attained after damping, the current work approaches zero asymptotically after 2 s with a magnitude of about 0.05 mm.
Impact of vibration on Power Supply: the total area of panels exposed directly to the sun's rays is a function of both the tracking tilt angle and panels' ray incident angle as shown in Equation (42). With the tilt angles normalized using ratio of perpendicularity (PPD ratio), the graph of simulated power generation at different angles of tilts and incidents are shown in Figure 20.
Perpendicularity is here defined as the ratio of the instantaneous tilt angle required to attain perpendicular rays from the sun to maximum possible tilt required to keep incident ray at 90 • . For tracking, the maximum possible tilt angle is 45 • to each side of the normal to the panel surface. When the sun's rays have incident angle of 90 • to the panel surface, the PPD has a ratio of 1 and reduces to 0 as the rays to the panel meets it at 45 • . This is indicated on the horizontal axis of the graph as a scale of measurement from 0 for 45 • to 1 for 90 • . For the panel opening and vibration, half of the angle between the two panels is used as a measure of the incident rays. For example, when the panels are fully opened, the angle between the two panels is 180 • and thus 90 • is the incident ray angle (IRA), and when the inclusive angle is 60 • , the IRA is 30 • , since the normal ray will bisect the inclusive angles.
At all IRA; 90 • , 60 • and so forth, the graphs show that power generation increases with increase in perpendicularity ratio. In all cases, maximum power output is obtained at perpendicularity of 1. The importance of this result is that at PPD ratio of 1, the panels require no tracking as the sun's rays are already directly on it and thus vibration due to rotor excitation will be minimum and become maximum at a ratio of 1, when the sun's rays meet the panels at 90 • in tracking operation. The maximum power produced is 2.14 W when the sun incidents on the panel at 1 and 1.51 W when the incident is at an angle of 45 • in tracking. The spacing between the graphs reduces as IRA increases. For example, at PPD ratio of 1, the power difference between 30 • and 60 • IRA is approximately 0.78 W while the difference reduces to 0.29 W between 60 • and 90 • IRA. When the IRA tends to zero -panels almost folded, the power production tends to zero and remains almost flattened irrespective of tilt angle of tracking (or PPD ratio). For any given IRA, the range of power generation (maximum -minimum values) decreases from 0.63 W at 90 • IRA to 0.31 W at 30 • and further to 0.05 W at 5 • IRA.
The importance of this result is that vibration due to tracking could cause a rotor excitation in the opening of the panels. The response vibration of the panels to these excitations can further cause the panels to move forth and back in horizontal direction, as well as, up and down in vertical direction as in Figure 12. These oscillatory motions may be amplified if the frequency is close or equal to the natural frequency of the panels (that is, resonance sets in) as shown in Equation (27), which can have serious impact on power production system failure due to induced stress from fatigue.
To minimize these consequences, the model makes provision for the panels to be constantly held in tension against the deploying spring with a fisher wire as a damper to vibration responses and thus, keeping the panels safe, as well as, providing more projected area for solar power generation.
Panels that oscillate have reduced projected areas for solar reception and hence, lower energy generation as reported in Reference 16. Body solar panels can only have one side fully available for solar reception. The current work has arms each with two foldable panels -that is four of them in the CubeSat. With the aid of solar tracking arrangement, the four panels will be fully available for solar reception, thus, having available potential of generating up to 400% of that of body mounted panels. The need for effective damping was also advocated by Shankar et al. 15 who fabricated and tested a CubeSat with the aim of ensuring structural safety of a deployable solar panel under a severe launch vibration environment using a multilayered stiffener with viscoelastic acrylic tapes to achieve a superior damping characteristic. The effectiveness of the proposed design for launch vibration attenuation was demonstrated through qualification level sine and random vibration tests.

CONCLUSION
The design of this work was done with much focus on the main aim of the project, which is, to develop a solar array deployment mechanism for a 1-U CubeSat using locally sourced materials. The design of the work and parameters generated from the design calculations were used for the construction of the parts of this project with few substitutions in choice of material. The designed torsion spring due to its unavailability locally was replaced with an elastic band of same stiffness. This work was successfully tested with minimal variance and adjustments from the calculated parameters and design materials respectively. The solar panels are held in stowed position (vertical position) from the tension of the elastic band and deployed in approximately 2 s with a speed of 47.1 rpm. Also, with the help of the tilt capability of the panels towards the sun, the panels can generate enough energy to sustain the CubeSat than when they are fixed or body-mounted. This work serves as an educational tool for satellite development especially in the area of deployable solar array. It also brings to light areas that require more research and improvement in space technology development in Nigeria.

CONFLICT OF INTEREST
Authors have no conflict of interest relevant to this article.

DATA AVAILABILITY STATEMENT
Data sharing not applicable to this article as no datasets were generated or analyzed during the current study ORCID Benjamin Iyenagbe Ugheoke https://orcid.org/0000-0002-7579-9297