A Novel Space Large Deployable Paraboloid Structure with Power and Communication Integration

*e combination of a solar array and a communication antenna can reduce the entire mass, physical size, and cost in space applications. Currently, related studies mainly focus on the combination of the two structures on the one flat plate structure (FPS). Compared with the FPS, a paraboloid structure has a lower surface density and higher conversion efficiency. *erefore, a novel space large deployable paraboloid structure with power and communication integration (SSPCI) is proposed and designed in detail, for spacecraft on a sun synchronous earth orbit; it consists of a cable mesh membrane reflector (CMMR), an energy conversion device (ECD), and a three-extensible-rod (TER) pointing mechanism. To achieve the goal of integrating power and communication, the TER pointing mechanism drives the CMMR/ECD to track the sun in the sunshine region or to turn to face the ground station/other target in the Earth’s shadow region. *en, through simulation analyses of the deploying process, static force at a limit orientation, and sun tracking process of the SSPCI, it is proved that the SSPCI is feasible and has satisfactory performance. Finally, deploying experiments of the folded hoop of the CMMR and sun tracking experiments of the TER pointing mechanism on the ground were carried out successfully, which proves that the folded hoop can be deployed successfully with fairly high deploying dependability, and the TER pointing mechanism is feasible for the SSPCI from the mechanism principle and the control mode in space applications indirectly. Moreover, the tracking accuracy of the TER pointing mechanism is estimated to be within ±0.4° although the machining precision of its components is not high.


Introduction
As limitations of size of rockets carrying and cost of launching, it is a challenging issue to reduce the mass, physical size, and cost of major spacecraft components in space applications [1]. Generally, most spacecraft include at least one large-size solar array to provide power and one large-size communication antenna to establish a high gain and robust communication with the ground station. Both the two structures require a massive and large back support to maintain their surface tolerance. Moreover, they may interfere with each other in space. One solution to reduce the burden of these two large structures on the spacecraft is to combine them into one.
Currently, related research mainly focuses on the combination of a solar array and a communication antenna on the one flat plate structure (FPS). One technical scheme is patch antennas are directly integrated onto the solar cells of a small satellite to save valuable surface real estate that are proposed by Turpin and Baktur [4]. O'Conchubhair et al. studied the effect of a solar cell lattice on the performance of an IFA antenna [5]. An et al. designed, manufactured, and tested a Ka band reflectarray antenna integrated with solar cells, where solar cells are used as the reflectarray antenna substrate [6]. Because the communication antenna is on the front of the solar array, although the antenna has satisfactory radiation characteristics, an optical blockage for sunlight must exist in this structure. For the second idea, related research is less than the one of the first idea. Vaccaro et al. presented a new antenna which combines solar cells and printed patches. It is designed so as to accommodate the solar cells which provide power to a monolithic microwave integrated circuit amplifier [7]. Solar cells are on the top of this antenna. Similarly, solar cells may affect radiation characteristics of the antenna because the solar array is on the front of the communication antenna.
For the second technical scheme, it is easier to implement than the first one. Huang proposes the back of the microstrip reflectarray can be used for solar arrays [8]. Holland et al. proposed an origami style solar/antenna panel where the phased array is located on the opposite side of the solar array [9]. Compared with the first technical scheme, this scheme is applied in the case where sunlight and electromagnetic waves incident the spacecraft from both sides.
As mentioned above, although a solar array and a communication antenna could be integrated on one FPS, they will interact with each other when arranged on the same side of a FPS. Furthermore, the surface density of an integrated FPS is high, and its conversion efficiency is low. Compared with the FPS, a paraboloid structure has a lower surface density and higher conversion efficiency because it focuses sunlight or electromagnetic waves at the focal point. However, there are few studies on a paraboloid structure with power and communication integration. Only Lichodziejewski and Cassapakis have developed a power antenna concept, utilizing an inflatable membrane paraboloid reflector to concentrate solar energy for space electrical power generation, while concurrently or alternatively acting as an antenna with large aperture and high gain [10]. is power antenna is used for spacecraft on a deep space exploration orbit (DSEO), where sunlight and electromagnetic waves irradiate the spacecraft continuously from the same side. By adjusting the attitude of the spacecraft, this power antenna can concurrently receive sunlight and electromagnetic waves.
A sun synchronous earth orbit (SSEO), where the sun and earth are on both sides of a spacecraft, respectively, is different from a DSEO. erefore, sunlight and electromagnetic waves irradiate a spacecraft on a SSEO from different sides, respectively. Most spacecraft on the SSEO need more power and higher communication capacity than those on the DSEO. However, a paraboloid structure with power and communication integration for spacecraft on the SSEO has never been studied.
For this purpose, a novel space large deployable paraboloid structure with power and communication integration (SSPCI) for spacecraft on the SSEO is proposed in this paper, as shown in Figure 1. Section 2 of this paper presents a novel idea for integrating power and communication for the SSPCI, and then the overall structural design of the SSPCI is described, which consists of a cable mesh membrane reflector (CMMR), an energy conversion device (ECD), and a TER pointing mechanism for driving the CMMR/ECD to track the sun for power in the sunlight region or to turn to face the ground station for communication or achieving other targets in the earth shadow region. Following this, the key components of the SSPCI are structurally designed in Section 3. e tracking principle is deduced and elaborated for the SSPCI in Section 4. e simulation analyses of deploying process, static force, and sun tracking process of the SSPCI are addressed in Section 5. Deploying experiments of the CMMR and sun tracking experiments of the TER pointing mechanism on the ground were carried out successfully, as described in Section 6. Finally, Section 7 concludes the work with a summary.

Description of Space Large Deployable Paraboloid Structure with Power and Communication Integration
As is known, spacecraft on the SSEO always spend part of their time in the sunshine region and part of their time in the earth shadow region in a flight cycle. Based on this, a novel idea for integrating power and communication is proposed: when spacecraft are in the sunshine region, the SSPCI loaded on it tracks the sun for power; when spacecraft are in the earth shadow region, the SSPCI turns to face the ground station for communication or achieving other targets.

Energy conversion device
Cable mesh membrane reflector TER pointing mechanism Spacecra Figure 1: Schematic of the SSPCI.

International Journal of Antennas and Propagation
Based on this idea and our research on space large deployable antennas [11][12][13], the overall structure of the SSPCI is proposed, as shown in Figure 2. e SSPCI consists of a CMMR, a TER pointing mechanism, and an ECD. From the perspective of the whole system structure, the SSPCI has a simple and efficient structure, and each component is itself a mature structure. erefore, the system has high stability and reliability.

Consideration of Cable Mesh Membrane Reflector and
Energy Conversion Device. For the reflector of the SSPCI, an ultralight CMMR is proposed, as shown in Figure 2. It uses a folded hoop and a central cylinder as its rigid backbone; flexible cables are used with them to form a mesh surface on which the aluminized membrane is assembled. e aluminized membrane can reflect both sunlight and electromagnetic waves. Meanwhile, a preliminary physical model of the CMMR is shown in Figure 3.
e ECD is fixed to the focal point of the CMMR by the central cylinder. A beam splitter or metallic grid is mounted in front of a solar cell array or lightweight thermoelectric conversion device [14] and is used to reflect electromagnetic waves onto a feed, as shown in Figure 2 [10]. In this way, sunlight and electromagnetic waves can be separated and utilized for power or communication.

Design of ree-Extensible-Rod (TER) Pointing Mechanism.
e TER pointing mechanism is the most key component of the SSPCI which is used to drive the CMMR/ ECD to track the sun or to turn to face the ground station/ other target. Before proceeding with design, the mounting position of the SSPCI on the spacecraft should be determined firstly.
Most spacecraft on the SSEO adopt three-axis attitude stabilization, and their body coordinate system (BCS) and orbital coordinate system (OCS) coincide to implement ground orientation easily. e sun's path on the OCS is a spiral shape when a spacecraft is travelling on the SSEO. It can be treated as a circle in one cycle. According to the mounting position of solar arrays on a spacecraft and the position relationship between the sun and the earth's center relative to a spacecraft, a mounting position for the SSPCI is determined. For example, for a hexahedron spacecraft, the SSPCI is mounted at the center of the plane of the spacecraft that is parallel to the orbital plane and faces towards the sun, as shown in Figure 4. Not only can the SSPCI satisfy the requirements of sun tracking but also it can easily turn to face the ground station for communication or achieving other targets at this position.
After the mounting position has been determined for the SSPCI, a TER pointing mechanism is proposed, as shown in Figure 5. e TER pointing mechanism includes a base platform, a mobile platform, and three extensible rods. ree extensible rods, all with the same structure, are arranged between the two platforms in an equilateral triangle. e lower end of each extensible rod is connected to the base platform by a rotary joint, and the upper end is connected to the mobile platform by a compound joint. Huang and Zeng point out that the TER pointing mechanism has three degrees of freedom, two rotational motions, and an independent vertical translational motion [15]. e two rotational motions can satisfy the requirement of the SSPCI, while the independent vertical translational motion can be used to pull the mobile platform down to the base platform to reduce the carrying size of the TER pointing mechanism in the rocket fairing. e TER pointing mechanism is simple and lightweight in structure. It has high tracking accuracy, low inertia, and a fast response speed [16].

Achievement of Integrating Power and Communication.
As shown in Figure 2, the SSPCI is connected to the spacecraft by a supporting rod; a rotary joint is at the lower end of the supporting rod where a motor is equipped for the deployment of the SSCPI, and the upper end of the supporting rod is fixed to the base platform of the TER pointing mechanism. e mobile platform is connected to the lower end of the central cylinder of the CMMR by a rotary joint on which a motor is equipped for the deployment of the SSPCI. When the SSPCI is tracking the sun for power, the length of three extensible rods are controlled to allow the mobile platform to rotate along axis When the SSPCI needs to turn to face the ground station, the TER pointing mechanism keeps the elevation angle in the process of tracking the sun unchanged and rotates along axis Y b back to the direction of axis Z b , while the SSPCI rotates around the rotary joint at the lower end of the supporting rod until the central cylinder points towards the center of the earth, as shown in Figure 6.

Deployable Joint of CMMR.
e deployable joint, which is used to connect and drive the folded hoop to deploy in place, is the most key structure of the CMMR. e joint with a pair of synchronize gears, which is driven by torsion springs, is a fair satisfactory selection for a space large deployable structure [17]. Figure 7 shows the physical model of the deployable joint. Simplified taper gears are used to drive rods of the hoop from the horizontal position to vertical position. When the folded hoop is folded, the stretch energy is stored in torsion springs. Clamps and pins are used to connect the parts of the joint together. e deployable joint is simple and lightweight in structure, which has a fairly high deploying dependability.

Compound Joint of TER Pointing Mechanism.
For tracking the sun, the TER pointing mechanism needs to implement a large range motion. Instead of a spherical joint, a smart compound joint with a hook joint and rotary joint is used to connect each extensible rod with the mobile platform, whose axes converge at one point, as shown in   Figure 10 presents the kinematic model of the TER pointing mechanism. First, a static coordinate system, O − XYZ, is established at center O of the base platform where axis Z is vertically upward along the base platform, axis X points towards the center point of rotary joint (R) R 1 at the lower end of extensible rod 1, and axis Y is formed as the crossproduct of the two previous axes (right-hand rule is applied). A mobile coordinate system, o − xyz, is established at center o of the mobile platform; axis z is vertically upward along the

Sun
Centre of earth mobile platform, axis x points towards the center of the compound joint, S 1 , at the upper end of extensible rod 1, and axis y is formed as the cross-product of the two previous axes (right-hand rule is applied). r is the radius of the mobile platform, and R is the radius of the base platform. In addition, the mobile platform is connected to the lower end of the central cylinder of the CMMR by a rotary joint (R) at its center point R 4 , which rotates along axis y. e position and orientation of the TER pointing mechanism can be expressed as where c and s denote cos and sin, respectively. According to the structure constraint of the TER pointing mechanism, x, y, and z can be represented by other parameters as follows: Substituting equation (3) in equation (4), L i is described as Carrying out a modular operation to two ends of equation (5) yields

For Sun Tracking. As mentioned above, the BCS
of the spacecraft on the SSEO coincide to implement ground orientation easily. According to VSOP (variation seculaires des orbits planetaires) 87 theory [18,19], the unit direction vector of the sun in the second equatorial coordinate system O s − X s Y s Z s , S s , is given by where χ and ε denote the apparent right ascension and declination of the sun, respectively.  Figure 9: An exploded diagram of the smart compound joint. Figure 10: Geometry of the TER pointing mechanism. 6 International Journal of Antennas and Propagation where ω is the latitude angle, i is the orbital inclination, and Ω is the right ascension of the ascending node; R x , R y , and R z denote the unit rotation matrix around axis x, y, and z, respectively. e TER pointing mechanism is mounted on the spacecraft, as shown in Figure 11. e unit direction vector of the sun in O − XYZ can be computed as en, the azimuth angle of the sun ϕ and elevation angle φ in O − XYZ is given by As aforementioned, there are three degrees of freedom in the TER pointing mechanism: two-dimensional rotations, and a translation motion along direction Z. For sun tracking, only the orientation of the mobile platform is required to be determined, which can be done by α and β. e third parameter z is adjustable, which can be used in interesting ways or be optimized as a useful objective function.
Hence, α and β can be given by where if S d (y) ≥ 0 and α � − α.
Substituting equation (11) to equation (6), the length of each extensible rod in the process of sun tracking can be given by

For Ground Station Communication or Achieving Other
Targets. When the TER pointing mechanism drives the CMMR/ECD to face the ground station or achieving other targets, α, β, and δ are can be given as en, l i and δ can be given by  [20]. e orbital parameters are listed in Table 1 [21]. Structural parameters of the CMMR are listed in Table 2, and those of the TER pointing mechanism are shown in Table 3. e energy conversion device is replaced by a cylinder with dimensions of 0.2 m × 0.2 m, and the mass is 3 kg. In the finite element analysis, the rigid structures of the SSPCI use the material of the carbon fiber, the cables use the material of Kevlar, and the reflective membrane uses the material of the aluminized membrane. e properties of the related materials are listed in Table 4. e mass of the CMMR and the ECD is 7.129 kg, the mass of the TER pointing mechanism is 4.3678 kg, and the overall mass of the SSPCI is 11.4968 kg.

Interference Detection of SSPCI.
e relevant dimensions of the system have been given in Section 5.1. However, it should be judged that whether the moving scope of the TER pointing mechanism can satisfy the requirement of the mission, and the SSPCI will interfere with the satellite body in the tracking process. Figure 11: Position of the TER pointing mechanism mounting on the spacecraft.

International Journal of Antennas and Propagation
According to the parameters of the orbit listed in Table 1, through the commercial simulation software, the angle between the sun vector and the orbital plane during one year is plotted in Figure 12. e minimum value of the angle is 18.504°, the maximum value is 29.884°, and the sun vector is always on the one side of the orbital plane. e moving scope of the TER pointing mechanism is mainly limited by the length of each extensible rod and the rotation angles of each compound joint and rotary joint. As listed in Table 3, the minimum length of the extensible rod is 492 mm, and the maximum length is 908 mm. As shown in Figure 8, the maximum rotation angle of the compound joint is 85°. According to engineering experience, the maximum rotation angle of the rotary joint is 57°. According to literature [22], the moving scope of the TER pointing mechanism is obtained, as shown in Figure 13. e blue part is the workspace of the TER pointing mechanism under the limiting condition, and the orange part is the required workspace for the SSPCI. It can be observed that the moving scope of the TER pointing mechanism can satisfy the requirement of the SSPCI.
In the process of tracking the sun, the most likely time for interference is when the SSPCI turns the diagonal section of the satellite body at the minimum pitch angle, as shown in Figure 14(a). e minimum working height of the supporting structure is calculated as 1393 mm. Because the working height of the TER pointing mechanism is 700 mm, the length of the supporting rod is 693 mm. Figure 14(b) shows the limit position of the SSPCI for communication. It can be observed that the SSPCI will not interfere with the satellite body in the tracking process, thus verifying the correctness of the relevant dimensions.

Simulation of Deploying Process.
e deploying probability is the key performance for a deployable structure. e SSPCI can be deployed by two steps: the deployment of the support structure and the deployment of the folded hoop. e deploying process is simulated by multibody dynamic simulation software.

Support Structure Deployment.
e satellite platform is unconstrained in this process. e acceleration of gravity is set to zero. As shown in Figure 15, two rotary drives are applied at the position of motor 1 and motor 2, respectively. e rotation angles of two motors are planned by a cubic polynomial in the deploying process. e relevant settings are made as follows: the deployment time is 200 s; both the angles of the two rotary drives are 90°; both the initial and terminal angular velocities of the two rotary drives are 0°/s. Simulation results show that the support structure can be deployed from status 1 to status 2 successfully, as shown in Figure 15. Dynamic curves of the spacecraft's center of mass with time are shown in Figure 16. e maximum displacement is no more than 15 mm. e maximum velocity and acceleration is no more than 0.35 mm/s and 0.01 mm/s, respectively; the results illustrate that the deployment of the support structure has little effect on the spacecraft. Figure 17 displays the dynamic curves of driving torques of the two motors with time. e maximum of them is not more than 25 Nmm, which indicates that two small and lightweight motors can implement the target.

Folded Hoop Deployment.
e deployment of the folded hoop is the second and most important step for the deployment of the SSPCI. e folded hoop is unconstrained in this process. e acceleration of gravity is set to zero. Every two rods are connected by two rotary pairs driven by a torsion spring, which is used to simulate the deployable joint   Figure 18. Figure 19 shows that the displacement, velocity, and acceleration of the mass center of one of the rotary pairs with time, respectively.

Static Force Analysis.
e SSPCI has to keep a satisfactory mechanical property in space environment. Meanwhile, the CMMR requires a high surface precision for power or communication. us, static force analysis of the SSPCI at a limit orientation in zero gravity was carried out.
A simplified Φ5 m finite element method (FEM) model of the SSPCI was constructed. Parameters of the SSPCI are set based on Section 5.1. BEAM4 is used for the folded hoop, the central cylinder, the TER pointing mechanism, and the supporting rod. LINK10 is used for flexible cables. SHELL41 is used for the aluminized membrane. SOLID45 is used for the ECD and the satellite. e upper end node of each extensible rod and the corresponding position node of the mobile platform are coupled to constrain their three translational degrees of freedom (DOF) to simulate the compound joint. Meanwhile, the lower end node of each extensible rod and the one of the base platform are coupled to constrain their three translation DOF and two rotational DOF to simulate the rotary joint. e bottom of the ECD and the upper end of the central cylinder are rigidly fastened. e Solid45 of the ECD and the spacecraft is generated by mapping mesh into tetrahedron elements, while the other element types are generated by nodes directly. e lower surface of the satellite is fully constrained. e acceleration of gravity is set to zero. Because the main external load of the SSPCI is the temperature load in space, the temperature loads of 20°C, − 100°C, and 100°C are applied to the SSPCI, respectively. e large deformation and automatic time step are opened, and the finite element model is analyzed by static force analysis and modal analysis.
Simulation results are shown in Figures 20-23. e maximum displacement of the SSPCI at the temperature load of 20°C is 44 mm, as shown in Figure 20; the RMS of the CMMR is 3.6 mm to the best fit paraboloid after posttreatment, which is small enough to satisfy the requirements of concentrating both sunlight and electromagnetic waves. e fundamental frequency of the SSPCI is 0.9282 Hz, as shown in Figure 21.
e fundamental frequency can be increased by further system-level optimization. e maximum displacement of the SSPCI at the temperature load of − 100°C is 39 mm, as shown in Figure 22; the RMS of the CMMR is 12 mm. e maximum displacement of the SSPCI at the temperature load of 100°C is 35 mm, as shown in Figure 23; the RMS of the CMMR is 24 mm. Currently, the RMS of the CMMR at the temperature of 100°C is not satisfactory, which can be solved by necessary temperature control measures and further system-level optimization.

Sun Tracking Process Analysis.
As aforementioned, the sun's path can be treated as a circle relative to the spacecraft in one orbital cycle. erefore, the CMMR/ECD of the SSPCI has to rotate in a circle to follow the sun, which is driven by the TER pointing mechanism. e simulation process in one orbital cycle starting from 0 : 00 on July 7,    2017, is built up. Figure 24 shows the simulation model of the SSPCI. e reflector remains the pitch angle of 18.504°r elative to the mounting plane. e velocity of the attitude angle is planned, as shown in Figure 25. Figure 26 displays the dynamic curves of the spacecraft's center of mass with time.
e maximum value of displacement, velocity, and acceleration is no more than 20 mm, 0.015 mm/s, and 0.0015 mm/s 2 , respectively; the results illustrates that the motion of the SSPCI has little effect on the spacecraft. Figure 27 displays the dynamic curves of driving forces of three extensible rods with time. e maximum force of each extensible rod is no more than 0.015 N at start up time, which indicates three low power and lightweight motors can implement the target. Figure 28 displays the dynamic curves of the consumed power of each extensible rod with time from 13 s to 6075 s. Furthermore, the consumed power of three extensible rods in a flying cycle is 2.4186 × 10 − 4 J. e spacecraft flies 14.2 orbits around the earth in one day. e consumed power of the TER pointing mechanism in one day is 2.9 × 10 − 3 J, and the consumed power of the TER pointing mechanism in one year with 365 days is 1.06 J. Figure 29 displays the dynamic curves of the distance between the upper and lower U plates of each compound joint with time. It can be observed that the distance of each compound joint is always greater than zero; the results illustrate that there is no interference between the upper and lower U plates, and the design of the compound joint is feasible, stability, and reliability for the SSPCI. e folded hoop is constructed with 36 aluminum bars, whose outer diameter is Φ1 mm and thickness is 0.2 mm. e stowed size of the folded hoop is Φ17 mm × 19 mm. e actual model is hung to compensate the gravity influence, as shown in Figure 30(a). After releasing the rubber hand, the model can be deployed successfully as similar as the simulation analysis. Figure 30(b) shows the deployed status of the actual model.

Key Experiments for SSPCI on the Ground
Due to the parallel driving manner of the torsion spring, although the actual model is not precisely manufactured and assembled, it can still be deployed successfully. is illustrates that the structure has a fairly high deploying dependability.

Sun Tracking Experiments of TER Pointing
Mechanism on the Ground. Although theoretical and simulation analysis of the TER pointing mechanism have been made, it is still doubtful for its feasibility without an actual test. us, we have carried out sun tracking experiments of the TER pointing mechanism on the ground successfully. Although  the environment on the ground is different from the one in space, and the mechanism principle and control mode of the TER pointing mechanism are identical. erefore, it can be indirectly predicted that the TER pointing mechanism is feasible for the SSPCI in a space environment. Figure 31 shows three moments of the sun tracking process in a day. Although the precision of manufacture is not high, it can still be observed that the central cylinder has no projection on the mobile platform at the three moments (morning moment in Figure 31(a), noon moment in Figure 31(b), and afternoon moment in Figure 31(c)). e shadow region on the mounting sleeve on the morning moment is shown in Figure 31(d). e wall thickness of the mounting sleeve is 6 mm, and the length of the central cylinder is 895 mm. is illustrates that the tracking precision of the TER pointing mechanism is within 0.4°(i.e., arctan (6/895)), which is sufficient for the SSPCI.

Conclusions
A novel SSPCI is designed in this paper. e theoretical analysis, simulation analysis, and preliminary experiments on the ground are conducted for the SSPCI. Analytical deduction and experiments show that the SSPCI has several remarkable advantages, which can be summarized as follows: (1) Due to integrating two functions (for power and communication) on one paraboloid structure, a large-size solar array and a large-size communication antenna can be combined into one. (2) e SSPCI is an ultralight paraboloid structure. Compared with the solar panel [23], the surface density of SSPCI is lower, while its power density is higher, as listed in Table 5. (3) Although only the SSPCI with an aperture of Φ5 m is simulated and analyzed, its aperture may be further expanded to Φ20 m to meet the requirements of a higher power spacecraft because of its low surface density. (4) e novel TER pointing mechanism with simple structure, lightweight, and high pointing accuracy can be used for many other applications in space environment.
One of the major area of focus for future works would be the optimal design of the size and shape of the SSPCI in a specific orbit for a given power supply and communication rate required by a specific satellite. In addition, the stability and reliability of the SSPCI should be analyzed in more detail according to the space environment.

Data Availability
e data used to support the finding the study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.