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\title{Geometric Parameter Optimization of Soft Pneumatic Actuators for Adaptive and Damage-Free Loading and Unloading Grippers}

\author[1]{Basem Akl}
\author[1,*]{Mostafa Orban}
\author[1]{Mustafa Mahmoud Elsayed}
\author[2]{Kai Guo}
\author[2]{Ye Wei}
\author[2]{Jinjiang Cui}
\author[1,*]{Mahmoud Elsamanty}
\affil[1]{Mechanical Department, Faculty of Engineering at Shoubra, Benha University, Cairo 11672, Egypt}
\affil[2]{Suzhou Institute of Biomedical Engineering and Technology, Chinese Academy of Sciences, Suzhou, 215163, China}

\affil[*]{Corresponding authors: mustafa.essam@feng.bu.edu.eg (M.O.); mahmoud.alsamanty@feng.bu.edu.eg (M.E.)}

\begin{abstract}
Soft robotics has emerged as a promising innovation by employing pliable materials such as silicone rubber, enabling safe human–robot interaction and delicate manipulation of fragile objects. Among soft robotic components, soft pneumatic actuators (SPAs) are particularly relevant for applications such as packaging and agricultural harvesting. However, the role of geometric parameters in governing actuator performance remains insufficiently understood. This study introduces a novel geometric parameter for SPAs, focusing on chamber wall thickness and the number of air pillows, to establish predictive relationships between design and performance. A nonlinear finite element analysis model, calibrated with a Yeoh third-order hyperelastic material law obtained from uniaxial tensile tests of silicone rubber, was employed to simulate actuator deformation and stress distribution under pressures from 10 to 90 kPa. The results show that reducing chamber wall thickness increases deformation but reduces structural stability, while increasing the number of pillows enhances bending flexibility but lowers stiffness. To validate the simulations, SPAs were fabricated using silicone casting with 3D-printed molds and tested under controlled laboratory conditions. Experimental measurements of elongation and bending closely match finite element predictions, confirming model accuracy. Furthermore, load-handling experiments demonstrated that the optimized two-finger gripper, equipped with the proposed actuators, could reliably grasp irregularly shaped products without damage. These findings highlight the importance of geometric parameter selection in SPA design and demonstrate the feasibility of deploying such actuators in industrial loading/unloading systems. The integration of experimental validation with simulation provides a robust framework for advancing soft robotic grippers toward practical, scalable applications.
\end{abstract}

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\section*{Introduction}

Soft robotics is a growing field of study which utilizes the adaptability and compliance of soft structures to create exceptionally adaptable robotic systems tailored for soft interactions. An area where soft robotics can have a significant impact is in the advancement and development of soft grippers and manipulators. Significant developments in soft robotics, commonly known as soft pneumatic actuators (SPAs), have contributed to significant progress in this area of research \cite{ref1,ref2}. Soft actuators play an important role in advancing the field of soft robotics and enable a wide range of complex hardware design for soft robots, and their actuation techniques can be divided into three primary categories: variable-length tendon, fluidic actuation, and intelligent material actuation. However, due to the constraints related to the inherent characteristics of soft pneumatic actuator constitutive materials and the limitations of fabrication tools and techniques, they tend to exhibit reduced driving force \cite{ref3}.

Soft robots offer an avenue to achieve previously unattainable levels of societal acceptance, utility in direct interaction with humans and populated environments. Nonetheless, the very flexibility and adaptability that make soft robots appealing also pose significant challenges when it comes to their control and manipulation \cite{ref4}. Soft robots are often regarded to have extensive range of degrees of freedom based on their structural flexibility, which grants them exceptional adaptability to various environments. In comparison to conventional robots, which are typically made of motors, rigid linkages, rotational joints, soft robots are constructed using compliant materials and structures.

One remarkable characteristic of soft robots is their capacity to deform actively or passively, enabling them to conform to a wide range of object shapes that require gripping. Soft actuators can execute complex motions with a high degree of freedom at a lower cost due to their inherent compliance. This unique flexibility makes them a cost-effective choice for achieving intricate tasks and motions \cite{ref5}.

Pneumatic artificial muscles (PAMs) have emerged as a transformative technology in the field of soft robotics, playing a vital role in applications related to muscle assistance and upper limb rehabilitation. PAMs possess distinctive characteristics that facilitate safe and smooth interactions between humans and robots, making them exceptionally well-suited for tasks requiring precision and delicacy. Their versatility extends to various domains, including applications in mobile robots, wearable devices, and exoskeletons, loading/unloading, all of which contribute significantly to the development of assistive and rehabilitative functionalities \cite{ref6,ref7}.

Pneumatic artificial muscles, often referred to as PAMs, represent a type of flexible actuator designed to emulate the movement capabilities of human muscles. Their significance in the fields of robotics and medicine is underscored by continuous research efforts aimed at developing PAMs that are not only compact and lightweight but also boast exceptional power-to-weight ratios. These advancements hold the promise of revolutionizing various industries and applications \cite{ref8}. A unique soft pneumatic gripper with tendon-driven soft origami pump has been developed, in particular, employing the origami pump to provide air to the pneumatic gripper, deviating from the conventional use of air compressors. The incorporation of elastomer-based actuators has additionally advanced the field of soft robotics, demonstrating their capacity for flexible and lifelike motions \cite{ref9}.

The proposal of a segmented soft pneumatic actuator with the ability to achieve substantial bending angles and generate high output forces was driven by the need to tackle various issues, including excessive energy consumption, inadequate energy output per unit volume, and slow response times. The innovative FBA design has indeed greatly improved both the bending angle and the force output of the actuator. However, it is worth noting that there are remaining challenges to address. The actuator's stiffness is still insufficient, and its output force remains constrained. To overcome these limitations, exploring methods such as particle reinforcement or the use of materials with variable stiffness holds promise \cite{ref10,ref11}.

A soft pneumatic actuator (SPA) was predominantly comprised of a continuous rubber tube with an attached strain-limiting layer at its base, typically constructed from materials like paper or plastic. This layer permits bending while preventing elongation. Upon pressurization, the actuator bends in a specific direction. However, these continuous soft actuators have symmetric designs that limit their flexibility and give rise to various disadvantages, including high energy consumption, low energy output density, and sluggish response times. To mitigate these issues, the segmented soft actuator (SSA) was proposed as a solution \cite{ref12}.

Soft pneumatic actuators (SPAs) have been widely explored in diverse domains, ranging from wearable rehabilitation gloves \cite{ref12,ref13,ref14,ref15} to underwater sampling \cite{ref16,ref17} and robotic manipulation \cite{ref18,ref19,ref20}. These studies highlight the versatility of SPAs in adapting to irregular geometries and performing safe, delicate interactions. However, most prior work has focused on medical or laboratory-scale applications. In contrast, the potential of SPAs in agriculture, particularly fruit harvesting and crop handling, remains underexplored. Harvesting tasks impose unique challenges, including variations in fruit size, shape, and fragility. Rigid grippers often cause bruising or damage, while existing soft actuators, though compliant, are susceptible to limited force output and structural failure. To address these limitations, this study investigates the role of geometric parameters (chamber wall thickness and number of air pillows) in governing the deformation, stress response, and grasping efficiency of SPAs specifically designed for agricultural applications.

Soft robotic grippers designed for applications like adaptively grasping delicate marine organisms during deep-sea collection have shown significant promise \cite{ref16,ref17}. Soft pneumatic actuators are a cornerstone of robotic manipulation methods, particularly when it comes to tasks involving grasping. These actuators excel in their ability to adjust their gripping forces, making them adept at handling objects of diverse fragility and hardness without causing any harm to the objects' surfaces. This versatility makes them a valuable asset in the field of robotic manipulation and automation \cite{ref18,ref19,ref20}.

A gripper's design combines elements of both soft and rigid components to enable seamless integration with conventional robotic arm manipulators. The gripper is designed with a two-finger underactuated system, and each finger is constructed using the recommended topology optimization approach. These fingers are then brought to life through 3D printing, utilizing thermoplastic elastomer as the material. This flexible finger design functions as a compliant mechanism, allowing it to operate effectively through elastic deformation \cite{ref21,ref22}. Utilizing the projection micro stereolithography technique, a micro soft pneumatic gripper featuring square air channels measuring 0.4 mm in width and chamber walls with a thickness of 0.2 mm was printed integrally using a DLP printer; this integral printing process was accomplished in under 30 minutes. The resulting gripper displayed excellent surface quality, and its ability to grasp objects was confirmed through experimental testing \cite{ref23}.

A novel bidirectional bending pneumatic soft actuator featuring an integrated curvature sensor in the form of an optical waveguide made from PMMA material has been developed. Through a thorough analysis of the sinusoidal wave chamber's design parameters, specifically pitch and amplitude, using finite element analysis (FEA), their significant impact on the actuator's bending capabilities has been demonstrated. The simulation results highlight that larger amplitudes and smaller pitches enhance the actuator's bending performance. By appropriately selecting these parameters, the soft actuator achieved an impressive bending angle \cite{ref24}. Finite Element Models (FEM) offer the capability to simulate function of the soft actuators and pinpoint specific stress and strain concentrations, particularly in areas where the fibers interacted with the elastomer. Conversely, the simplified analytical method provided a method for predicting the actuator's performance by establishing explicit relationships between input pressure, actuator bending angle, and output force. These modeling findings were further assessed through experimental testing, which provided a better comprehension of the parameters influencing the soft actuators performance \cite{ref11,ref20}.

Three distinct soft silicone rubber types have been investigated, distinguished by their internal channel structures: ribbed, cylindrical, and pleated. Additionally, there are three viable fabrication processes based on casting: lamination-based casting, retractable-pin-based casting, and lost-wax-based casting. Furthermore, two methods for creating a multi-degree-of-freedom (DOF) robot were explored: casting the entire robot as a single unit and casting individual single DOF segments and then connecting them together. Each of these soft actuator and fabrication processes were validated by creating prototypes of soft robots \cite{ref25}.

The edible substance employed in fabrication of the actuator, known as gelatin glycerol material, exhibits mechanical characteristics closely resembling those of silicone elastomers. To gain a deeper understanding of the material's suitability for robotic purposes, it is imperative to evaluate additional attributes, including durability and viscoelastic behavior, under different composition ratios. This assessment will yield valuable insights into the material's potential applicability in the field of robotics \cite{ref26}.

A method for 3D printing silicone elastomers via direct ink writing (DIW) has shown significant promise across various fields, including flexible electronics, medical device manufacturing, and soft robotics. This comprehensive guide outlines the process of printing highly stretchable silicone materials, addressing material selection, equipment considerations, and procedural challenges. Initially, material property evaluations were conducted on Dow Corning silicone. Next, two needles were modeled and simulated frequently to determine the most suitable one. Subsequently, parameter optimization experiments were conducted using the custom DIW printer, focusing on finding the appropriate printing speed and layer height while considering defined air pressure and needle diameter settings \cite{ref27}.

A novel geometric parameter is introduced to enhance our understanding of Soft Pneumatic Actuators (SPAs). This parameter explores how variations in the inclination angle of the air pillow impact the SPA's work envelope and tip reaction force when subjected to a wide range of positive and vacuum pressures applied to the inner surfaces. To delve into this phenomenon, nonlinear static Finite Element Analysis (FEA), grounded in the hyper-elastic material model established through experimentation with a sample of the SPA material, is employed. Furthermore, to validate the findings, three SPAs were fabricated using Fused Deposition Modeling (FDM) with a 3D printer, with a particular focus on evaluating two crucial aspects: the work envelope and the tipping force through experimental testing \cite{ref20,ref28,ref29}.

Automating the packaging of lunch boxes poses a formidable challenge because of the substantial deformability and significant variations in the shape and physical properties of food items. Soft robotic grippers have displayed promise in handling such tasks. Soft actuators, constructed from various materials and fabricated using different methods, were employed, and their capabilities were assessed through a comprehensive series of tests \cite{ref30}. Soft robotic grippers, serving as a pivotal element in agricultural robotics, find extensive application in the harvesting of fruits and vegetables, involving tasks such as plucking and picking. Achieving a firm grip poses a significant challenge in agricultural contexts due to the diverse shapes and hardness levels of crops as they mature, along with the wide range and fragility of produce. A fruit recognition technique that employs an adaptive gripper featuring tactile sensing and machine learning algorithms has been described. A specialized robotic gripper has been created and produced to execute adaptive grasping tasks \cite{ref31,ref32}.

A field that holds considerable appeal for its practical application is the automation of the selective harvesting of high-value crops. Within the realm of agricultural tasks, the harvesting of fruits and vegetables remains a persistently time-consuming and labor-intensive endeavor, ultimately leading to reduced operational efficiency and a constrained competitive edge \cite{ref33,ref34}. In the field of agriculture, robots play a significant role in applications such as seeding, monitoring, and harvesting. It is crucial to be careful when using robots for harvesting fruits and vegetables, as excessive force can result in crop damage. In the domain of smart farming, the integration of both artificial intelligence and robotic systems is applied to enhance operational efficiency further. An innovative three-fingered soft robotic gripper has been introduced, designed and assessed using finite element analysis. Each finger of the gripper is created from silicone rubber and is specifically shaped to adeptly manipulate spherical objects like tomatoes or oranges \cite{ref35}.

Focusing on the limitations inherent in rigid robotic systems and the distinct advantages that soft robots offer in tasks involving loading, unloading, or harvesting, it becomes evident that even with the integration of sensor systems, rigid grippers still carry safety concerns due to their inherent hardness, high density, and their inability to adapt to external forces. In contrast, soft robots, with their inherent flexibility and adaptability, have carved out specific niches in grasping applications. However, the current soft actuators, notably those employing pneumatic artificial muscles, are susceptible to damage and exhibit limitations in their performance. Consequently, there is a pressing need for the development of advanced soft actuators that can effectively address these issues, thereby further enhancing the capabilities of soft robotic systems.

The primary objective of this paper is to advance the development of grasp-and-loading and unloading systems for fruits and vegetables. Specifically, we introduce a soft robotic gripper equipped with soft pneumatic actuators (SPAs) designed to minimize the forces applied to harvested items, thereby reducing bruising and surface damage. Unlike rigid grippers, which often fail to adapt to natural variability in crop geometry, the proposed gripper leverages the compliance and adaptability of SPAs to conform to irregular fruit shapes and sizes while maintaining stable and gentle grasping.

A central contribution of this study lies in the systematic exploration of geometrical parameters, particularly chamber wall thickness and the number of air pillows, which directly influence actuator deformation, bending angle, and stress distribution. By tuning these parameters, the gripper can generate sufficient force to lift loads with different geometry while retaining the flexibility necessary to grasp delicate produce without causing structural damage. This balance between load capacity and delicacy makes the design highly suitable for agricultural loading and unloading applications, where crops vary not only in geometry but also in ripeness and fragility.
Through finite element simulations validated by experimental tests, the work demonstrates how optimized actuator geometry enables a high range of motion, controlled force distribution, and robust grasping of irregular agricultural products such as tomatoes and oranges. This investigation provides design guidelines for soft grippers that can both withstand different loads and preserve crop quality, offering practical solutions for automating loading and unloading of fruit and vegetables without structural damage and minimal losses.
\section*{Design and Material Characterization}
\subsection*{Design and Molding}
Soft pneumatic actuators are considered attractive for use in soft robotics applications because of their pliable and expandable characteristics, which enable a wide range of motions and the generation of various levels of grasping force. The design of the soft gripper should be as innovative and unique as the nature of incorporating soft robotics into industrial applications. In order to create a soft gripper suitable for loading and unloading tasks or harvesting as shown in Figure \ref{fig:four_finger}, it is essential to adopt a specific strategy that guarantees the gripper's effective functionality.

Initially, the actuator's cross-section is selected, marking the beginning of the actuator design phase, which is based on the parameters established during cross-section design. The effectiveness of the soft pneumatic actuator relies on key design parameters, primarily encompassing the actuator's cross-sectional, wall thickness, chamber number, and the gap between chambers. Based on this premise, several tests were carried out on multiple actuator designs within this study to identify the most optimal and efficient one suited for the intended application. In this study, a new soft pneumatic actuator design is proposed to grasp complex and irregular shapes. As illustrated in Figure \ref{fig:3d_model}, the soft actuator design incorporates various geometrical parameters, such as the air pillows thickness and the distance between the air pillows.

The soft artificial pneumatic actuator (SPA) model is composed of a single chamber made from a flexible elastomeric material, specifically silicone rubber, and relies on chamber air pillows in lieu of a reinforcing layer. The chamber is pressurized with air or a liquid to deliberately cause controlled inflation of the actuator and prevent unintended enlargement. The relevant actuator parameters as illustrated in Figure \ref{fig:actuator_parameters}, including the chamber length ($L$), chamber width ($W_2$), the chamber height ($H$), pitch ($P$), base thickness ($T_2$), side wall thickness ($T_3$), and chamber thickness ($T_1$), with a variable number of air pillows ($N$), are presented in Table \ref{tab:geometrical_params}. The chamber's bottom layer thickness measures 7 mm and is constructed from a flexible silicone rubber material that can expand, bend, and contract when subjected to pressure fluctuations. Applying pressure to the actuator results in its extension. The inlet port enables fluid connection, allowing the actuator to either inflate or deflate. When designing a soft pneumatic actuator, it is essential to consider factors like the desired range of motion, durability, and force output. These considerations influence the selection of materials, dimensions, geometry, as well as the suitable air pressure and flow rate for inflating the actuator. The typical range for applied pressures in the SPA usually ranges from 10 to 90 kPa.

\begin{table}[H]
\centering
\caption{\label{tab:geometrical_params}Geometrical Parameters of Soft Pneumatic Actuators (SPAs)}
\begin{tabular}{|l|l|}
\hline
\textbf{Parameter} & \textbf{Value} \\
\hline
Chamber Length ($L$) & 160 mm \\
\hline
Chamber Angle ($\gamma$) & 0 \\
\hline
Finger Width ($W_1$) & 30 mm \\
\hline
Pitch ($P$) & 20 mm \\
\hline
Number of Air Pillows ($N$) & 5 to 8 \\
\hline
Chamber Width ($W_2$) & 14 mm \\
\hline
Height ($H$) & 30 mm \\
\hline
Wall Thickness ($T_1$) & 3 to 6 mm \\
\hline
Base Thickness ($T_2$) & 7 mm \\
\hline
Side Wall Thickness ($T_3$) & 4 mm \\
\hline
\end{tabular}
\end{table}

\begin{figure}[H]
\centering
\includegraphics[width=0.5\linewidth]{Figures/four_finger_gripper}
\caption{Installation of the four-finger gripper model.}
\label{fig:four_finger}
\end{figure}

\begin{figure}[H]
\centering
\includegraphics[width=0.6\linewidth]{Figures/3d_model_spa}
\caption{3D model and a soft pneumatic actuator parameter.}
\label{fig:3d_model}
\end{figure}

\begin{figure}[H]
\centering
\includegraphics[width=0.7\linewidth]{Figures/actuator_parameters}
\caption{Visual depiction of the soft pneumatic actuator, illustrating its design and highlighting key parameters.}
\label{fig:actuator_parameters}
\end{figure}
\subsection*{Material Characterization}
Soft robotics incorporates a wide range of materials utilized during the fabrication process, which play a pivotal role in bestowing these robots with remarkable characteristics such as controllability, flexibility, and safety for human interaction. Recent progress in the field of soft robotics has focused on a range of aspects, encompassing the selection of materials, design geometries and manufacturing processes \cite{ref30,ref31}.

These materials possess distinct properties that set them apart from conventional materials employed in additive manufacturing. Typically, such traditional materials encompass thermoplastic polymers such as PLA and ABS, or thermoset polymers like TBU \cite{ref19,ref30}. Recognizing the constraints of the additive manufacturing process in fabricating intricate structures, there has been a growing preference for molding fabrication techniques due to their cost-efficiency and capacity to create complex shapes \cite{ref34}. In this approach, silicone-based elastomers are commonly used.

For the proposed soft pneumatic actuator, silicone rubber was selected as the primary material for the fabrication. The selection of this material that is suitable for the soft actuator should be stiff enough to be reasonable enough to provide a more suitable bending angle and force to perform grasping tasks for applications of soft robotics. Silicone rubber is inexpensive and has a high strain rate. This material can be molded into a lot of geometries with low stress and small actuation pressure and is suitable for the properties that are desirable for the actuator. Dumbbell-shaped specimens were made, and the uniaxial test was conducted in accordance with ASTM No. D412 specifications, as illustrated in Figure \ref{fig:material_char}a. The mold for producing these specimens was made with PLA material using a 3D printer, ensuring accurate and uniform specimen geometries. A silicon rubber specimen has been assessed and tested through a uniaxial test, as depicted in Figure \ref{fig:material_char}b, and subsequently utilized the results obtained from this experimental uniaxial test.

A set of mechanical tests was carried out for silicone rubber material, which encompassed a uniaxial test conducted under controlled and stable conditions, in order to thoroughly characterize the mechanical properties of the silicone rubber material for the fabrication of the soft actuator. The uniaxial test conducted in this study followed the specifications of the ASTM No. D412, utilizing specimens shaped like dumbbells, as illustrated in Figure \ref{fig:material_char}a. PLA material via a 3D printer was used in the creation of mold for the fabricating of these specimens, ensuring accurate and uniform specimen geometries. Following that, the silicon rubber specimens were subjected and underwent the uniaxial test, with the results depicted in Figure \ref{fig:material_char}d. Upon completing and concluding the experimental phase, the most appropriate hyperelastic model was identified through a process of curve-fitting analysis. Finally, the best fit for the silicon rubber material was selected as the Yeoh 3rd-order model. This model can be represented by the following equation:

\begin{equation}
\psi = C_{10} (\lambda_1^2 + \lambda_2^2 + \lambda_3^2 - 3) + C_{20} (\lambda_1^4 + \lambda_2^4 + \lambda_3^4 - 3) + C_{30} (\lambda_1^6 + \lambda_2^6 + \lambda_3^6 - 3)
\label{eq:yeoh}
\end{equation}

\noindent where $\psi$ is the strain energy density function; $C_{10}$, $C_{20}$, and $C_{30}$ are the material constants; and $\lambda_1$, $\lambda_2$, and $\lambda_3$ are the principal stretches. Subsequently, we integrated the parameters of the material obtained from the curve-fitting procedure into the Finite Element Analysis software (ANSYS) to conduct the analysis. Table \ref{tab:yeoh_params} presents the specific parameters of the material related to the hyperelastic model (i.e., $C_{10}$, $C_{20}$, and $C_{30}$) for reference and further analysis.

\section*{Geometrical Parameter Study and Simulation}

This rigorous simulation study was designed to characterize systematically the response of the soft pneumatic actuators for harvesting applications under different loading conditions. The primary aim of this comprehensive analysis was to evaluate the maximum deformation along the $x$ and $y$ axes and quantitatively evaluate the stress and strain distribution within the soft actuator structure. In order to achieve this objective, the actuator was subjected to a meticulous examination with a diverse range of pressure levels applied, ranging from 10 to 90 kPa incrementing in steps of 10 kPa. The application of pressure was implemented with careful consideration, specifically directed towards the inner surfaces of the actuator, while simultaneously maintaining the outer surfaces at a consistent atmospheric pressure.

The results obtained from this comprehensive simulation analysis, as visually depicted in Figure \ref{fig:fea_deformation_thickness} and Figure \ref{fig:fea_deformation_number}, have significantly enhanced our comprehension of the soft pneumatic actuator's intricate mechanical characteristics. These findings are of paramount significance as they establish the foundation for the subsequent advancement and refinement of soft robotics customized specifically for harvesting and gripping tasks. This research aimed to acquire a comprehensive understanding of both the characteristics of soft pneumatic actuator deformation and the stress response, through a methodical exploration of the influence of varying input pressures.

From this meticulous analysis using finite element software, several noteworthy results have emerged, providing valuable understanding regarding the performance of the soft actuator concerning deformation and stress. Remarkably, under 90 kPa pressure, the deformation in the length of the $x$ direction ($X$-def) exhibited a considerable measurement, clearly indicating a significant extension predominantly in the $X$-direction.

\begin{table}[htbp]
\centering
\caption{\label{tab:yeoh_params}The parameters of Yeoh 3rd order model of Silicon rubber material}
\begin{tabular}{|l|l|}
\hline
\textbf{Description} & \textbf{Value} \\
\hline
Silicon Rubber Density & 1080 kg/m$^3$ \\
\hline
$C_{10}$ & 0.196259775 MPa \\
\hline
$C_{20}$ & 0.009010431 MPa \\
\hline
$C_{30}$ & -0.000105654 MPa \\
\hline
\end{tabular}
\end{table}


\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{Figures/material_characterization}
\caption{(a) Geometrical dimensions and manufacturing of ASTM D412 specimens of Silicone rubber material. (b) Fabricated ASTM D412 specimen of Silicone rubber after curing. (c) 50 KN tensile testing machine at Cairo University, Egypt. (d) Experimental results: Stress-strain curve for the tested Silicone rubber material.}
\label{fig:material_char}
\end{figure}





\subsection*{Change in Chamber Wall Thickness}

By performing simulations on four distinct models, each featuring different wall thickness values (3 mm, 4 mm, 5 mm, and 6 mm), we acquired valuable insights into how the SPA performs and behaves under different pressure conditions. The outcomes of this comprehensive analysis, as illustrated in Figure \ref{fig:deformation_thickness}, significantly enhance our comprehension of the mechanical characteristics of SPAs, facilitating opportunities for additional innovations and enhancements in the field of soft robotics.

This comparative study is investigated to analyze how variation in chamber wall thickness affects the deformation and stress behavior of the soft pneumatic actuator (SPA) when applying pressure. Specifically, the study is primarily concerned with the variation of the pressure at the inner surface of the chamber while preserving a constant length of the chamber. Throughout this comparative study, the width ($W = 30$ mm), height ($H = 30$ mm), and base thickness ($T_2 = 7$ mm) of the SPA are kept consistent. The analysis unveils significant findings in relation to deformation and stress. At a wall thickness value of $T_1 = 3$ mm, the $x$-axis deformation ($x$-def) is measured to be 198 mm. When the wall thickness value is increased to $T_1 = 4$ mm, the $x$-def decreases to 168 mm. Also, when the wall thickness value is increased to $T_1 = 5$ mm, the $x$-def decreases to 98 mm. Further raising the wall thickness value to $T_1 = 6$ mm results in a lower $x$-def of 42 mm. Consequently, deformation significantly increases from 42 mm to 198 mm as the chamber wall thickness decreases as shown in Figure \ref{fig:deformation_thickness}a,b.

\begin{figure}[H]
\centering
\includegraphics[width=0.8\linewidth]{Figures/fea_deformation_thickness}
\caption{Demonstrate FEA results of accumulated deformation images at different chamber wall thickness at maximum pressure.}
\label{fig:fea_deformation_thickness}
\end{figure}

\begin{figure}[H]
\centering
\includegraphics[width=0.5\linewidth]{Figures/fea_deformation_number}
\caption{Demonstrate FEA results of accumulated deformation images at different chamber numbers at maximum pressure.}
\label{fig:fea_deformation_number}
\end{figure}

\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{Figures/deformation_thickness}
\caption{Demonstrate FEA results of accumulated deformation images at different chamber wall thickness at maximum pressure: (a) demonstrate deformation for $T_1 = 3$, (b) demonstrate deformation for $T_1 = 4$, (c) demonstrate deformation for $T_1 = 5$, (d) demonstrate deformation for $T_1 = 6$.}
\label{fig:deformation_thickness}
\end{figure}

Similarly, the stress undergone by the SPA shows a correlated fluctuation. At a wall thickness value of $T_1 = 3$ mm, the stress is measured to be 3.5 MPa, whereas when the wall thickness value is increased to $T_1 = 4$ mm, the stress decreases to 1.4 MPa. Also, when the wall thickness value is increased to $T_1 = 5$ mm, the stress decreases to 1.2 MPa. Further raising the wall thickness value to $T_1 = 6$ mm results in a lower stress of 1 MPa as shown in Figure \ref{fig:thickness_graphs}c. The increase in wall thickness leads to decreased stress undergone by the SPA. It is important to highlight that in this comparison, the deformation impact along the $x$ and $y$ axes is not negligible and, as a result, makes a substantial contribution to the overall analysis.

\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{Figures/thickness_graphs}
\caption{Demonstration of the Finite Element Analysis results of accumulated deformation at different chamber wall thickness at various applied pressure: (a) demonstration of $x$-axis deformation vs.\ applied pressure, (b) demonstration of $y$-axis deformation vs.\ applied pressure, (c) demonstration of stress vs.\ applied pressure.}
\label{fig:thickness_graphs}
\end{figure}

\subsection*{Number of Air Pillows ($N$)}

By performing simulations on four distinct models, each featuring different chamber number values ($N = 5$, $N = 6$, $N = 7$, and $N = 8$), we acquired valuable insights into how the SPA performs and behaves under different pressure conditions. The results of this comprehensive analysis, as shown in Figure \ref{fig:deformation_number}, significantly enhance our comprehension of the mechanical characteristics of the SPAs, facilitating opportunities for additional innovations and enhancements in the field of soft robotics.

The number of chamber units $N$ is considered as a secondary influence parameter. The FEM analysis demonstrated that there was an influence of the change in the number of chamber units on the deformation of the soft actuator and the bending angle. As illustrated in Figure \ref{fig:number_graphs}, there is an increase in the deformation along the $x$-axis of the actuator as the number of chamber units increases. From this meticulous analysis using finite element software, as the bending of the entire actuator depends on the deviation of each chamber unit when the actuator length is still constant, the equal bending length of all actuators with variable chamber unit remains unchanged. Furthermore, any excess in chamber units may make the actuator design very difficult and increase the manufacturing failure rate and also lead to a decrease in stiffness and this causes a slight growth in the bending angle.

This comparison is conducted to analyze the influence of the chamber number variation on the deformation of the soft actuator and the stress behavior of the SPA when the inner surface of the soft actuator is subjected to pressure. This research focuses on altering the pressure applied to the inner surface of the chamber while keeping the length of the actuator chamber constant. Throughout this comparative study, the actuator length ($L = 160$ mm) of the SPA was kept consistent with the chamber number ranging from 5 to 8 with step 1. The analysis unveils significant findings in relation to deformation and stress. At a chamber number value of $N = 5$, the $y$-axis deformation ($y$-def) is measured. When the chamber number value is increased to $N = 6$, the $y$-def increases. Further raising the chamber number value to $N = 8$ results in a larger increase in $y$-def as shown in Figure \ref{fig:number_graphs}. Consequently, deformation significantly increases as the chamber number increases, and a large bending angle is made by the actuator. Similarly, the stress undergone by the SPA shows a correlated fluctuation. The increase in chamber number leads to decreased stress undergone by the SPA. It is important to highlight that in this comparison, the deformation impact along the $x$ and $y$ axes is not negligible and, as a result, makes a substantial contribution to the overall analysis.

\begin{figure}[H]
\centering
\includegraphics[width=0.8\linewidth]{Figures/deformation_number}
\caption{Demonstrate FEA results of accumulated deformation images at different chamber numbers at maximum pressure: (a) demonstrate deformation for $N=5$, (b) demonstrate deformation for $N=6$, (c) demonstrate deformation for $N=7$, (d) demonstrate deformation for $N=8$.}
\label{fig:deformation_number}
\end{figure}

\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{Figures/number_graphs}
\caption{Demonstration of the Finite Element Analysis results of accumulated deformation at different chamber numbers at various applied pressure: (a) demonstration of $x$-axis deformation vs.\ applied pressure, (b) demonstration of $y$-axis deformation vs.\ applied pressure, (c) demonstration of stress vs.\ applied pressure.}
\label{fig:number_graphs}
\end{figure}

In conclusion, the comprehensive finite element analysis has provided a clear understanding of the influence of key geometrical parameters on the performance of the soft pneumatic actuator. The results demonstrate that decreasing the chamber wall thickness significantly enhances actuator deformation, with the maximum deformation achieved at a wall thickness of $T_1 = 3$ mm, albeit with a corresponding increase in stress. Additionally, increasing the number of air pillows (chambers) improves the bending behavior and overall deformation, with the configuration $N=8$ yielding the most favorable performance in terms of deformation and reduced stress. Based on this systematic investigation, the optimal geometrical parameters are identified as $T_1 = 3$ mm and $N = 8$. These parameters will be adopted for the fabrication of the soft actuator prototype, which will be experimentally tested to validate the simulation results.

\section*{Materials and Fabrication}

The fabrication process of the soft actuator for robotic loading and unloading systems for delicate fruits, vegetables, and berries hinges on the developments achieved in soft robotics technology and the refinements in molding techniques. These techniques have garnered substantial interest and acclaim in diverse fields, encompassing medical devices, harvesting, and packaging, among others, with each of these domains embracing this approach. Soft actuators possess inherent attributes of pliability and versatility, rendering them highly favorable for harvesting tasks in which they can delicately gather mature crops without inducing harm, thus diminishing the reliance on manual labor. The primary objective in developing soft actuators for harvesting systems is to construct devices that accurately mimic the functionalities of natural hands and tendons. These devices are intended to deliver the necessary power and range of motion to facilitate the harvesting process.

In order to accomplish this aim, it is imperative to carefully select and optimize both the mold's shape and the material properties of the silicone. Silicone material is an ideal material for use in harvesting and crop inspection due to its elasticity, durability, and biocompatible characteristics. Moreover, the distinctive properties of silicone rubber facilitate the shaping of silicone into customized forms, enabling the design of soft actuators to align with the specific requirements and physical attributes of fruits and vegetables during harvesting. This characteristic also lends itself to the ability to tailor these soft actuators according to individual preferences. Integrating air pillows into the design of soft actuators allows for precise regulation of their expansion and contraction. By adjusting the air pressure within the soft actuator, it becomes possible to provide the necessary degree of support or grasping force during the harvesting process, thereby facilitating the protocols specific to harvesting operations. Furthermore, the inclusion of air pillows enhances the comfort level of soft actuators, enabling them to precisely conform to the object's shape. Additionally, these air pillows augment their overall flexibility, enabling them to easily adapt to the product's form, thus reducing the risk of product damage during the harvesting process.

The fabricating process involves employing silicone-based materials and the creation of a hollow soft actuator model through the use of three distinct 3D-printed molds, as illustrated in Figure \ref{fig:mold_components}.

The mold comprises an upper section made of silicone rubber material and a lower section designed to form the air pillows that create the cavity. It is composed of an upper part for pouring the silicone material and a lower part serving as the designated cavity for the air pillows. Both the upper and lower molds feature four guide holes, guaranteeing ideal symmetry in the finished product. Both the upper and lower molds are equipped with four holes. A release agent is thoughtfully applied to both molds at the outset of the process, making it easier to extract the shaped soft actuator without any difficulties. The silicon material and silicone curing agent are blended with great precision, maintaining a ratio of 100 grams to 2 grams to ensure a consistent mixture. This well-homogenized composition is then poured carefully into the upper mold, and subsequently, the upper and lower molds are tightly sealed and secured. The curing procedure includes subjecting the mold to vacuum pressure within a vacuum oven at a consistent temperature of 40 degrees Celsius. It also incorporates applying pressure. Subsequently, the next phase entails unsealing both the upper and lower molds, unveiling the half-actuator, which can then be readily connected to its corresponding counterpart, as illustrated in Figure \ref{fig:fabrication_process}, and clearly visualizing the mold design components and assembly for creating the final soft gripping product.

The operation of casting a soft pneumatic actuator is a time-consuming process. First, a syringe was used to ensure that the proportions of each part of the mixture were accurate as shown in Figure \ref{fig:casting_operation}. The silicone rubber was mixed well with the mixer and poured into the upper body mold and the lower body mold until the molds were filled.

The silicone rubber was mixed well with the mixer and poured into the upper body mold and the lower body mold until the molds were completely filled. In Step 2, the upper and lower molds after pouring silicone were exposed to 50\,$^{\circ}$C for 35 minutes.

Drawing from prior experiments and empirical findings, it was determined that the most efficient adhesive for joining two silicone components is the silicone material itself, as depicted in Figure \ref{fig:assembly}. This confirms that the silicone material itself serves as the optimal bonding agent. Following the successful assembly of the two parts of the soft actuator, a thorough examination is conducted to ensure there are no air leaks. This evaluation involves immersing the assembled halves in a container of water while subjecting them to varying levels of air pressure. This review verifies the robustness and dependability of the ultimate soft actuator, affirming its appropriateness and efficiency for harvesting tasks while ensuring its integrity and reliability.


\begin{figure}[H]
\centering
\includegraphics[width=0.6\linewidth]{Figures/mold_components}
\caption{Depicts the two 3D-printed mold components used in the soft finger fabrication process for the gripping device. The lower mold serves as the base for pouring the silicone material, while the upper mold creates the cavity space necessary for forming the air pillows.}
\label{fig:mold_components}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width=0.8\linewidth]{Figures/fabrication_process}
\caption{Illustrate the detailed fabrication process of the soft finger for gripping device, highlighting the steps involved in mixing and pouring the silicone material.}
\label{fig:fabrication_process}
\end{figure}



\begin{figure}[H]
\centering
\includegraphics[width=0.7\linewidth]{Figures/casting_operation}
\caption{Operation of casting a soft pneumatic actuator.}
\label{fig:casting_operation}
\end{figure}


\begin{figure}[H]
\centering
\includegraphics[width=0.7\linewidth]{Figures/assembly}
\caption{Depicts the mold components and the resulting soft muscles after extraction from the molds, as well as the process of adhering the two muscle halves together to form the complete soft finger for grasping applications.}
\label{fig:assembly}
\end{figure}

\section*{Experiment Test Rig and Results}

A meticulous experimental platform was developed and implemented in detail to investigate the deformation of the soft actuator while it undergoes actuation with various pressures ranging from 10 to 60 kPa, as part of the harvesting process. The experimental setup consisted of several critical components, each serving a specific purpose to ensure accurate and reliable results. Upon the implementation of each component of the system, it is essential to combine these various parts to construct a comprehensive experimental setup, as depicted in Figure \ref{fig:experimental_platform}. The current configuration comprises an image recognition module utilizing a camera, a pneumatic and signal transmission component, and a soft finger module. These three constituent parts are harmoniously merged to establish a fully functional experimental platform, facilitating further research and experiments. The entire system is operated using compressed air sourced from the compressor, with the air supply linked to the proportional valve. The proportional valve regulates the air pressure based on an electrical signal from the controller, after which the adjusted air pressure is channeled to the soft finger.

\begin{figure}[H]
\centering
\includegraphics[width=0.8\linewidth]{Figures/experimental_platform}
\caption{Experimental Platform Setup with the wiring and the system flowchart.}
\label{fig:experimental_platform}
\end{figure}

A control unit is employed for the rapid assessment of the soft pneumatic actuator (SPA). Its primary function is to manage and oversee the operation of the SPA. This control unit comprises several components, including an air compressor for supplying pressurized air to the system, a set of solenoid valves responsible for directing the airflow, a microcontroller that governs system operations, an electro-pneumatic regulator for adjusting air pressure, a mechanical regulator, and a group of pressure sensors. These pressure sensors measure internal system pressure, providing valuable feedback. This entire setup is illustrated in Figure \ref{fig:experimental_platform}. The microcontroller allows users to interact with the hardware via a serial port connection, granting control and operation capabilities to the control unit.

\subsection*{Deformation Experiment}

Initially, the soft actuator was securely fixed at one end within a three-dimensional environment to enable unhindered movement and deformation. This unrestrained motion was crucial for observing the actuator's response under varying pressure conditions. To facilitate precise measurements of the actuator's displacement, a 40 cm $\times$ 40 cm cubic workspace was employed, and a grid sheet was positioned behind the actuator as a point of reference to ensure accurate displacement measurements throughout the experiment, as depicted in Figure \ref{fig:actuator_length}. The grid sheet was positioned at a fixed distance behind the actuator, and its lines were of a contrasting color to the actuator to facilitate easy tracking of the actuator's displacement.

Precise recording of the actuator's motion was crucial for assessing its performance in the experiment. To achieve this, a high-quality camera with a high resolution was used to capture video footage of the actuator's movement in both the $X$ and $Y$ directions. The high resolution of the camera ensured a precise and comprehensive record of the actuator's response during the variation conditions of pressure, which was synchronized with other experimental variables using LabVIEW software. The camera was set at a consistent distance from the actuator. It was positioned perpendicular to the grid sheet to guarantee precise measurement of the actuator's displacement in all three dimensions.

\begin{figure}[H]
\centering
\includegraphics[width=0.8\linewidth]{Figures/actuator_length}
\caption{Illustrates the original length of the actuator and its changes under varying pressure conditions.}
\label{fig:actuator_length}
\end{figure}

Position estimation models based on physical tracking were employed to locate and measure the position ($x$, $y$) of the soft actuator's end tip. This was done to investigate the correlation between variation in pressure and the elongation of the soft actuator for the loading/unloading and harvesting process. The noted changes in position were subsequently graphed in relation to the change of pressure, as shown in Figure \ref{fig:actuator_length}. This figure illustrates the original length of the actuator and its changes under varying pressure conditions, compared to the simulated results. The simulated data closely aligns with the experimental data, demonstrating the precision and dependability of both the experimental setup and the position estimation models. In essence, this experimental study sought to elucidate the intricate connection between alterations in pressure heads and the elongation of soft actuators during the harvesting process. The sophisticated configuration of the experimental setup, coupled with the implementation of LabVIEW for data collection and control, enabled accurate regulation and measurement of the actuator's behavior, establishing it as a valuable instrument for exploring the mechanics of soft actuator systems. The outcomes of this research are anticipated to enhance our comprehension of how soft actuator systems behave when subjected to different pressure conditions. These findings hold promise for potential applications in fields like bioengineering and biomechanics.

\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{Figures/deformation_behavior}
\caption{Illustrates the deformation behavior of the actuator in the $X$-axis, $Y$-axis, and the resulting $X$--$Y$ trajectory under varying pressure conditions, comparing experimental and simulation results.}
\label{fig:deformation_behavior}
\end{figure}

The comparison between the simulation and experimental deformation profiles, as shown in Figure \ref{fig:deformation_behavior} (deformation behavior of the actuator in the $X$-axis, $Y$-axis, and $X$--$Y$ trajectory under varying pressure conditions), reveals a generally consistent bending behavior, with both datasets exhibiting a similar overall curvature trend. However, noticeable deviations are observed, particularly at higher deformation levels. The experimental results show reduced displacement compared to the simulation, indicating a slight underperformance of the fabricated actuator. This discrepancy can be attributed to several practical factors not fully captured in the numerical model, including material nonlinearity, air leakage, and fabrication imperfections. Additionally, the experimental data demonstrate minor irregular fluctuations along the deformation trajectory, which are likely due to measurement noise and pressure instability during testing. It is also evident that the experimental profile reaches its maximum deformation earlier than the simulation, suggesting increased stiffness and energy losses in the real system. Despite these differences, the close agreement in the overall deformation pattern confirms the validity of the simulation model in predicting the actuator's behavior with acceptable accuracy.

\subsection*{Load and Grasping Experiment}

The half-circular actuator emerges as the optimal design for integration into the two-finger gripper because of its ability to operate effectively with low pressure and fast response. Furthermore, practical tests validate the gripper's capability to handle irregular and complex geometry, including delicate and small objects, as depicted in Figure \ref{fig:grasping}. The included control system demonstrated its effectiveness by enabling the gripper to handle various objects independently, without any external intervention from the operator during both loading and unloading operations.

\begin{figure}[H]
\centering
\includegraphics[width=0.9\linewidth]{Figures/grasping.png}
\caption{Grippers carrying different objects with irregular and complex geometry.}
\label{fig:grasping}
\end{figure}

\section*{Conclusion }
This study introduced and analyzed a novel SPA design by systematically investigating the role of chamber wall thickness and number of air pillows on actuation performance. The key outcomes are:
Finite element simulations, validated by experiments, confirmed that reducing wall thickness significantly enhances actuator deformation, while increasing N improves bending flexibility but reduces stiffness. 
Material characterization using the Yeoh 3rd-order hyperelastic model ensured accurate representation of silicone rubber behavior in simulations.
Experimental tests demonstrated successful integration of the actuator into a two-finger gripper capable of handling irregular and complex geometry. Without damage the structure. These findings advance the understanding of SPA design and provide practical guidelines for optimizing soft robotic grippers in industrial and agricultural applications. Future work will focus on integrating embedded sensing, improving durability, and scaling designs for large-scale harvesting operations.
\section*{Declarations}
\subsection*{Author Contributions}
Conceptualization, M.E. and M.O.; methodology, M.E. and M.O.; software, B.A.; validation, B.A and MME.; formal analysis, B.A and M.O.; resources, M.E. and MO.; data curation, B.A, M.M.E and M.O.;  writing original draft preparation, B.A,M.O,M.M.E, M.E., and GK.; writing review and editing, M.E. and M.O.; visualization, M.O.; supervision, M.E. and M.O.; project administration, M.E.,M.O, and K.G; funding acquisition, M.E.,M.O, J.C, Y.W and K.G.
B.A. and M.O. contributed equally to this work as first authors. All authors have read and agreed to the published version of the manuscript.
\subsection*{Funding} 
This research was funded by Natural Science Foundation Project of Chongqing (Grant No. 2024NSCQ-MSX0007), Key Innovation Project of Brain-Computer Interface of SIBET (BCI-2026-003), the Project of the State Administration of Foreign Experts Affairs (Grant No. H20240225), the Chinese Academy of Sciences International Talent Plan (PIFI) Project (Grant No. 2024VBB0010), the pilot projects for fundamental research in Suzhou (Grant No. SSD2023014), the Science and Tech-nology Development Plan Project of Jilin Province (Grant No. 20240305049YY, Grant No. 20260301020YY), and the Natural Science Foundation Project of Shandong Province (Grant No. ZR2022QH214).
\subsection*{Acknowledgements} Not applicable
\subsection*{Ethics approval and consent to participate} Not applicable
\subsection*{Consent for publication} Not applicable
\subsection*{Institutional Review Board Statement} Not applicable.
\subsection*{Data Availability Statement} The data presented in this study are available on request from the corresponding author.
\subsection*{Conflicts of Interest} The authors declare no conflict of interest.

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