Design and Evaluation of a Parallel Manipulator for Interconnected Transmission Tracking

The joint connections found within the RSSR-SS platform are characterized by bound interactions, which provide the joint flexibility often seen in Rotary and Universal joints. This flexibility enables the plate to move in a manner that accommodates its specific requirements. The text delineates the procedural aspects including the fabrication of diverse components, assembly of the model, and establishment of the experimental framework. Multiple techniques are used in the manufacturing process of each unique item. The SolidWorks software is used to create models of various components of the RSSR-SS platform and assemble the final product. The modal analysis further demonstrated the dynamic behaviour of the spring. The determination of the optimal Universal joint profile for the RSSR-SS platform involves the construction of an assembly and complete model using the Solid Works application, using specific assembly processes. The Solid Works software has many connections to facilitate the visualization of the top plate's functionality. In order to provide an appropriate range of motion for the plate on the RSSR-SS platform, all joint connections are established using bonded connections and universal joints. Every component is meticulously crafted using a variety of techniques.

Minimizing the dimensions, physical volume, and financial expenditure associated with the extendable road tracker’s pivotal elements constitutes a critical undertaking in the realm of design. In general. Any application needs at the very least a database in the form of a large array that is used in the transmission antenna [1, 2]. Large apertures allow the tracker with combined array, achieving the primary goals of decreasing the tracker's bulk, storage capacity, cost etc. It also deployed surface area without compromising on performance too. The integration of Jacobian Matrix in single planar device called a Flat Plate Structure (FPS) is now the primary topic of research work [3]. A concentrator in the shape of a Flat receiver mounted on RSSR-SS plat, it outperforms the FPS in terms of conversion efficiency while having a lower surface density [4]. Space applications have utilised large-aperture receiver antennas and concentrators. The receiver surface, like the solar disc concentrator, reflects electromagnetic waves and sunlight [5]. On the other hand, the combination of these two technologies has only been the subject of a limited number of research paper published by researchers. The parabolic reflector antenna developed by Sukri et al. [6] presented a novel approach for improving robotic arm precision through numerical code recognition, enabling efficient and automated object handling in industrial and manufacturing applications. Singh et al. [7] described a design for a power antenna that makes use of a paraboloid reflector made from an inflated membrane. Rigid structure of the platform is composed of a two RS Dyads and one SS Dyad [8], which are interconnected by flexible wires. This surface serves as a substrate for the deposition of aluminized membrane facets.

The manipulator can focus both electromagnetic radiation and sunlight. The tracker plate is attached to the central cylinder at the focal plane of the Consortium for Marine Robotics (CMR), allowing for the switching between collecting electromagnetic radiation and capturing solar rays [9].

The coordinate system spirals when a tracker is in a Sun-Synchronous Equatorial Orbit (SSEO). This spiral path can be approximated as a circular track for one orbit [10]. The Solar Power Photovoltaic Conversion Interface lies in the middle of the tracker's orbital plane and sun-facing plane due to solar wings and the sun's location relative to the earth [11]. Besides the above parameters, the tracker must meet the following. The requirements for a solar panel tracking system in space can be summarized as follows: (1) the system should possess an ample workspace that enables a broad range of motion, facilitating the tracking of the sun and orientation towards the ground station; (2) the structure of the system should be uncomplicated yet dependable, catering to the specific demands of space missions; and (3) the system should exhibit a high level of precision in pointing, ensuring efficient power generation or communication capabilities [12].

In space applications, the most prevalent multifaceted rotation tracking systems, known as RSSR-SS, employ a serial mechanism featuring azimuth and elevation components [13]. Parallel mechanisms provide benefits over serial mechanisms, including a simple and lightweight design, better structural rigidity, decreased inertia, increased dependability [14], and superior platform positioning and pointing [15, 16]. Despite various parallel techniques with two-dimensional rotation, few have been implemented in space applications. This study introduces a rotating parallel mechanism that has two degrees of freedom (2-DOF) and incorporates a redundant drive system, specifically designed for the purpose of antenna targeting [17, 18]. The use of a parallel mechanism with redundancy has the potential to enhance both the precision of targeting and the capacity and reliability of the payload, as compared to a non-redundant counterpart. The redundancy drive is used to improve system efficiency, but this comes at the cost of increased system size, volume, cost, and energy consumption. Inefficient use of linear drive results in wasteful energy usage, even after the extra drive rod has been eliminated. Accordingly, the RSSR SS would benefit from a different methodology.

With the goal of regulating the position of RSSR SS tracking parallel manipulator, a three-degree-of-freedom (3-DOF) parallel pointing system has been created. The construction of this mechanism has resemblance to the ones described in references [19, 20]. However, its limb chain is made up of four rotary joints and tow spherical joint in extendable connecting rods. The system is thus not as stiff or accurate in its tracking as it could be. It's important to mention that each branch in the chain consists of five rotary joints, and this configuration has been observed to decrease the reliability of the mechanism [21]. It can be proved mathematically that this approach is inappropriate for implementation in the RSSR SS since the number of unknowns exceeds the number of equations. A compliant 2-degree-of-freedom (DOF) pointing mechanism for spacecraft thrusters, antennas, and Jacobian array systems was proposed by Li and Wang [22]. However, it's important to note that the rotation range of this pointing mechanism is limited to just 15°, which does not meet the wide-ranging rotation requirements specified for RSSR SS. RSSR-SS parallel mechanisms with more than three degrees of freedom have found applications in various areas, including pointing for space remote sensors, active vibration isolation for precise space payloads, and the end effector of space station transposition mechanisms. However, it's crucial to emphasize that RSSR SS only necessitates rotation in two dimensions, rendering none of the aforementioned options suitable for use as the RSSR SS tracker. To fulfill the requirements of the RSSR SS tracker, there's a need to develop a TER parallel tracker, specifically the 3-RPS parallel manipulator [23-25]. This choice has the potential to enable the RSSR SS to accurately track the sun or reposition itself toward the ground station, addressing the limitations mentioned earlier. The 3-RPS mechanism is characterized by its simplicity and lightweight nature, offering structural stability, durability, and improved positioning and orientation capabilities for the mobile platform when compared to sequential mechanisms. The linear extendable rods in the TER tracker contribute to energy efficiency and eliminate the need for bulky speed reducers, which are typically required for monitoring the relatively modest movement speed of RSSR SS. However, it's worth noting that there is limited literature available on 3-RPS parallel manipulators in the context of spaceship appendages. This study aims to examine, formulate, and empirically verify the RSSR SS model of the TER tracker, as detailed in the following section. The kinematic model is converted to a dynamic model using the Newton-Euler formulation [26]. The TER tracker's motion trajectory is specifically designed either for sun tracking or reorientation toward the ground station, as outlined in reference [27]. In the upcoming section, this research configures parameters to assess the TER tracker's workspace and pointing accuracy and conducts simulations to evaluate its performance. Additionally, MATLAB is used to calculate the TER tracker's drive power. Initial ground-based testing for sun monitoring with the TER tracker has yielded positive results. The subsequent section will delve into the findings of this work.

This work introduces an innovative Three-Extendable-Rod (TER) tracker incorporated into a 3-RPS parallel manipulator for the RSSR-SS platform, intended for dual-purpose space applications related to solar energy harvesting and terrestrial communication. This design provides a lightweight, compact, and energy-efficient alternative to conventional serial or bulky redundant mechanisms, with improved pointing precision and structural rigidity.

When designing a function-generating mechanism, it's vital to correlate incoming and outgoing connections' rotational movement; this leads to a predictable output from a known input. Connecting a system's input and output. When x changes, y=f(x) travels over an interval. When input and output are rotated in the same direction, x and y coordinates match. Function generator connection movement. The link connects to and is driven by the Actuator link's movement as shown in Figures 4-6.

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Figure 4. R-S link and rigid body points

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Figure 5. RSSR-SS mechanism with passive

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Figure 6. Generation of trajectory DOF to ground link

As illustrated, vectors may be used to depict mechanisms' connections. Multiple vector combinations show dimensional synthesis resolutions. One technique uses vector pairs to do dimensional synthesis. Figure 6 shows four-bar relationship is represented by dyads.

Both C_aand C_b originate at the ground pivot and end at the mobile pivot, whereas D_a and D_b originate at the mobile pivot and terminate at the tracer point:

$C_a e^{\left(\theta_j+\theta_1\right)}+D_a e^{\left(\alpha_j+\alpha_1\right)}-C_a e^{\theta_1}-D_1 e^{\alpha_1}-P_j+P_1=0$

Following are some design equations that may be derived by using the identity of Euler and distinguishing between the real and imaginary parts of a function:

$\begin{gathered}C_a \cos \left(\theta_j+\theta_1\right)+D_a \cos \left(\alpha_j+\alpha_1\right)-C_a \cos \left(\theta_1\right)-D_a \cos \left(\alpha_1\right)-P_{j x}-P_{1 x}=0\end{gathered}$

$\begin{gathered}C_a \sin \left(\theta_j+\theta_1\right)+D_a \sin \left(\alpha_j+\alpha_1\right)-C_a \sin \left(\theta_1\right)-D_a \sin \left(\alpha_1\right)-P_{j y}-P_{1 y}=0\end{gathered}$

C_b and D_b are a right dyad of the mechanism, as illustrated in Figure 7. A terrestrial pivot serves as the starting point for the C_b, which then returns there at its conclusion. C_d  stops at the tracer's endpoint.

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Figure 7. Right-hand movement of a RSSR-SS mechanism (RS Dyad)

The corresponding equation for a complete circuit in the correct dyad is

$C_a e^{\left(\phi_j+\phi_1\right)}+D_a e^{\left(\alpha_j+\alpha_1\right)}-C_a e^{\phi_1}-D_1 e^{\alpha_1}-P_j+P_1=0$

The real component of the imaginary and the following design equations are derived by considering the left RS dyad and the right RS dyad, respectively:

$\begin{gathered}C_a \cos \left(\phi_j+\phi_1\right)+D_a \cos \left(\alpha_j+\alpha_1\right)-C_a \cos \left(\phi_1\right)-D_a \cos \left(\alpha_1\right)-P_{j x}-P_{1 x}=0\end{gathered}$

$\begin{gathered}C_a \sin \left(\phi_j+\phi_1\right)+D_a \sin \left(\alpha_j+\alpha_1\right)-C_a \sin \left(\phi_1\right)-D_a \sin \left(\alpha_1\right)-P_{j y}-P_{1 y}=0\end{gathered}$

The following equation for a Trajectory may be solved in MATLAB, yielding a very precise position.

Kinematic synthesis is constructing a task-capable machine. Kinematic synthesis includes function, trajectory, and movement creation. As stated in Section 3, only the RSSR-SS mechanism will be synthesised here. The mechanism has five links, one permanent and four movables. RSSR is crucial for function creation and has been examined extensively. RSSR-SS topology must overcome the mechanism's floating link issue. It recommends constructing a trajectory and linking a rigid body.

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Figure 9. Analogy between linear displacement and angle of rotation

Dimensional synthesis is a subset of kinematic synthesis that involves determining the lengths (dimensions) of a mechanism's connections [30]. Figure 9 shows how a random point p travels between 1 and j. It is shown by p1 and pj, which are called precision points to studied mechanism to meet these goals.

The composite rotation matrix converts vector coordinates to xyz. It represents the matrix's composite rotation matrix. Multi-loop spatial links are desirable since they can transport more weights. Multi-Loop spatial links have more joints than single-loop links. In synthesis scenarios with several points or locations, they are preferred. Here three operating conditions for a multi-loop spatial connection used to calculate the cylinder's displacement and angle (RS and SS Dyads). And Angular Position 1, and 3 for Cylinder 1, 2, and 3 correspondingly. Table 1 shows the total time needed to inflate a cylinder based on length.

Table 1. Extendable-rod position vs. angle $\theta$₁, $\theta$₂ and $\theta$₃ position for Only One Cylinder X1

MATLAB was utilized to solve all nonlinear equations obtained by thesis synthesis. Changing the program's convergence tolerance refines the result. Here exponential rotation matrix formulae apply. The loop closure equations and motion generation synthesis can synthesis all spatial linkages with reduced kinematic pairings. When generic motion equations are expressed systematically, they may be implemented in computers. Using the algebra of exponential rotation matrices, the thesis loop closure equations were reduced. These properties make dealing with matrix problems simpler.

For the purpose of reducing matrix equations arising in kinematic analysis and synthesis, the algebra of Jacobian matrices is a powerful and beautiful mathematical tool. There is little research on its use for analysing or synthesising spatial processes, although it has been used to the study of robot manipulators. Other mechanism designers may be enticed to adopt this algebra if it proves useful in solving further challenges of spatial mechanism analysis and synthesis as shown in Figures 10-12.

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Figure 10. RSSR-SS mechanism rotate about angle a-up

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Figure 11. RSSR-SS mechanism rotate about angle w

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Figure 12. RSSR-SS mechanism rotate about angle w rigid body rotation