Soft robotics, a recent advancement in robotics systems, distinguishes itself by utilizing soft and flexible materials like silicon rubber, prioritizing safety during human interaction, and excelling in handling complex or delicate objects. Soft pneumatic actuators, a prevalent type of soft robot, are the focus of this paper. A new geometrical parameter for soft artificial pneumatic muscles is introduced, enabling the prediction of actuation behavior using analytical models based on specific design parameters. The study investigated the impact of the chamber pitch parameter and actuation conditions on the deformation direction and internal stress of three tested soft pneumatic muscle (SPM) models. Simulation involved the modeling of hyperelastic materials using finite element analysis. Additionally, an artificial neural network (ANN) was employed to predict pressure values in three chambers at desired Cartesian positions. The trained ANN model demonstrated exceptional performance. It achieved high accuracy with training, validation, and testing residuals of 99.58%, 99.89%, and 99.79%, respectively. During the validation simulations and neural network results, the maximum errors in the x, y, and z coordinates were found to be 9.3%, 7.83%, and 8.8%, respectively. These results highlight the successful performance and efficacy of the trained ANN model in accurately predicting pressure values for the desired positions in the soft pneumatic muscles. Significant advancements in soft pneumatic actuators, commonly known as pneumatic artificial muscles (PAMs), have led to notable progress in soft robotics. The origins of soft robotic muscles can be traced back to the 1950s when McKibben actuators were introduced as linear actuators, laying the foundation for the subsequent development of pneumatic muscles . The intPneumatic artificial muscles (PAMs) have emerged as a powerful technology in soft robotics, playing a crucial role in assistive muscle and upper limb rehabilitation applications. PAMs possess unique properties that enable safe and seamless interactions between humans and robots, making them highly suitable for performing intricate or delicate tasks. These versatile actuators find applications in diverse domains, including mobile robots, wearable devices, and exoskeletons, contributing to realizing assistive and rehabilitative functionalities ,4. LeverA seminal study ,8 presenIn contrast to the extensive field of conventional robotics, soft robotics has emerged as a distinct and promising research domain, reshaping the landscape of robot design and motion. Soft robotics represents a paradigm shift from traditional approaches, as it leverages the inherent properties of its actuators to achieve motion without relying on external torque or conventional motors ,12,13,14The deformation behavior of soft robots is influenced by various factors, including the selection of materials ,23,24, fSoft pneumatic muscles, also known as flexible artificial pneumatic actuators, are designed to mimic the actuation properties of human muscles ,32. ThesSignificant advancements have been made in the field of fluidic actuators, contributing to the development of innovative solutions for various applications in robotics and automation. One noteworthy example is the bidirectional electrohydrodynamic pump (BEDP), which has gained attention due to its high symmetrical performance and its potential application in tube actuators. The BEDP utilizes the principles of electrohydrodynamics, employing an electric field to induce fluid flow in a conductive medium. This technology enables precise control and efficient actuation, making it a promising candidate for integration into artificial pneumatic muscle systems for human assistive devices . AnotherA proposed strategy, referred to as echo-state Gaussian process-based nonlinear model predictive control (ESGP-NMPC), addresses challenges related to trajectory tracking using pneumatic muscle actuators (PMAs) in rehabilitation robots ,43,44. TThis study aims to design and determine the geometrical parameters for the SPM and soft parallel muscle, model the soft actuators using finite element analysis (FEA), and investigate the influence of varying the parameter P with sequential values of pressures. Additionally, the study focuses on applying these soft muscles for rehabilitation purposes. Furthermore, an (ANN) is employed to establish both forward and inverse kinematics for the SPM and soft parallel muscle models, enabling the estimation of pressure values given the endpoint Cartesian coordinates . The manuscript’s structure is organized as follows: Human assistive devices play a vital role in enhancing the quality of life for individuals with physical disabilities or impairments. These devices encompass a broad range of technologies designed to aid individuals in overcoming mobility challenges, improving functional capabilities, and promoting independence. Soft pneumatic muscles, as described in our study, have promising applications in the field of human assistive devices for upper limb support due to their inherent flexibility, adaptability, and safety characteristics.One prominent application of soft pneumatic muscles is in the development of wearable exoskeletons for upper limb assistance. These devices provide external support and assistance to the wearer’s arms and hands, helping them perform daily tasks that may have been difficult or impossible due to physical limitations. Soft pneumatic muscles can be integrated into upper limb exoskeletons in order to provide a more natural and compliant interaction between the device and the human body, reducing the risk of injury and discomfort while improving overall functionality.The proposed soft muscle will be suitable to fit a wearable exoskeleton design for the shoulder joint and incorporates three parallel soft pneumatic muscles, strategically arranged to enable efficient actuation and a wide range of motion. Each muscle is designed to be identical and consists of three chambers, allowing for tailored pressure application and control in each chamber, as shown in In addition to the shoulder actuation, another SPM is integrated into the design to operate and assist the human forearm and enable elbow joint rotation. This single-chamber muscle, also constructed from flexible elastomeric material, can be pressurized to induce controlled bending and extension of the elbow joint, effectively assisting the user in daily tasks that require forearm movement and manipulation. The muscle’s geometry and pressure control can be optimized to provide the desired range of motion, force output, and responsiveness, considering the user’s specific needs and physical abilities.The combination of the three parallel soft pneumatic muscles for shoulder actuation and the additional muscle for elbow joint rotation presents a comprehensive solution for upper limb assistance. This soft wearable exoskeleton design offers a more natural and intuitive interaction between the device and the human body, closely replicating the complex biomechanics of the upper limb. By incorporating soft pneumatic muscles into the exoskeleton, users can benefit from enhanced mobility, improved force output, and a greater sense of embodiment, ultimately leading to a better user experience and satisfaction with the assistive device.Soft pneumatic muscles are regarded as attractive for soft robotics applications due to their flexible and inflatable nature, enabling a wide range of motions and forces. Typically, a SPMdesign consists of three parallel muscles, thereby facilitating stimulating motion in multiple movement spaces. By incorporating a model with more than one chamber, achieving larger workspace movements for actuated muscles becomes possible. This study devised a three-chamber model, with each chamber designed to be identical. The selection of geometrical parameters was undertaken following a rigorous benchmarking process to ensure the optimal performance of the soft pneumatic muscles. The resulting model exhibits motions with potential applications in post-stroke patient rehabilitation and physical therapy. An in-depth analysis was conducted to examine the motion under different conditions at predetermined air pressure values. The geometrical parameters utilized in the models are visually represented in The soft artificial pneumatic muscle (SPM) model comprises three chambers constructed from a flexible elastomeric material, specifically silicone rubber, and utilizes chamber rings instead of a reinforcement layer. These chambers are pressurized with air or fluid to induce controlled muscle inflation and prevent unintended expansion. The relevant muscle parameters, including the length of the chamber (L), outer diameter (Do), the height of the chamber (H), pitch (P), and chamber thickness (T), with a constant number of rings, are presented in Soft robotics encompasses a wide range of materials employed in the manufacturing process, which contribute to the remarkable characteristics of these robots, including their flexibility, controllability, and human-safe nature. Recent advancements in soft robotics have focused on various aspects, including material selection, construction geometries, control systems, modeling techniques, and production methods . The fieIn order to comprehensively characterize the mechanical behavior of the silicon rubber material, a series of mechanical tests were conducted, including a uniaxial test performed under stable conditions. The test followed the ASTM No. D412 specifications, utilizing dumbbell-shaped specimens, as depicted in Upon completing the experimental phase, the most suitable hyperelastic model was determined through curve fitting analysis. The Yeoh 3rd-order model was identified as the best fit for the silicon rubber material. The Yeoh model can be represented by the following equation:The selection of silicon synthetic rubber as the material for fabricating the soft pneumatic muscle (SPM) was based on its exceptional hyperelastic performance, high-pressure resistance, and desirable mechanical properties, particularly its stress–strain behavior. The Yeoh 3rd-order hyperelastic model was identified as the best fit for the silicon rubber material through a rigorous curve-fitting process. This model was subsequently integrated into the FEA software, ANSYS, to facilitate further analysis. The non-linear finite element analysis was carried out using ANSYS Workbench, primarily investigating various geometric aspects. To initiate the simulations, the CAD models of the soft pneumatic muscles were directly imported into the ANSYS Design Modeler, enabling the subsequent analysis of their behavior.The simulation was designed to characterize the muscle’s response under different conditions comprehensively. This included evaluating the maximum deformation length in the x, y, and z directions and mapping the distribution of stress and strain within the structure. A pressure range from 100 to 160 kPa was applied to capture a wide range of scenarios, incrementing in steps of 10 kPa. Specifically, the pressure was selectively applied to two of the three chambers while the remaining chamber was kept at a constant pressure.By conducting simulations for three distinct models, each featuring different pitch chamber values , valuable insights were gained into the performance and behavior of the SPM under varying pressure conditions. The results obtained from this extensive analysis, as visualized in This comparison aims to analyze the influence of pitch variation on the deformation and stress behavior of the soft pneumatic muscle (SPM) when applying pressure. Specifically, the study focuses on altering the pressure in two chambers while maintaining a constant pressure in the third chamber. Throughout this comparison, the height (H = 20 mm) and thickness (T = 7 mm) of the SPM are kept consistent. The analysis reveals noteworthy findings in terms of deformation and stress. At a pitch value of P = 30 mm, the y-axis deformation (y-def) is measured to be 113 mm. When the pitch value is increased to P = 34 mm, the y-def increases to 130 mm. Further raising the pitch to P = 38 mm results in a higher y-def of 163 mm as shown in Similarly, the stress experienced by the SPM exhibits a corresponding variation. At P = 30 mm, the stress is measured to be 0.83 MPa, whereas, at P = 38 mm, the stress escalates to 2.2 MPa. The increase in pitch leads to increased stress experienced by the SPM. It is worth noting that the deformation effect in the x and z axes is minimal in this comparison and hence does not significantly contribute to the overall analysis. The visual representation in  further ANNs have found extensive applications in soft robotics for controlling the behavior of soft robots, making them a powerful tool for modeling complex nonlinear systems ,37. ANNsThe soft pneumatic muscles’ (SPMs) workspace was investigated using forward kinematics, established through FEA software (ANSYS) workbench simulations. This analysis provided a comprehensive understanding of the total workspace position and orientation of the SPMs in Cartesian coordinates. The workspace assessment was crucial in evaluating the range of motion and capabilities of the SPMs across a full 360-degree span. The obtained workspaces demonstrated the SPMs’ ability to perform various motions, including extension, bending, and twisting, within the Cartesian coordinate system. As depicted in The kinematic model of soft pneumatic muscles (SPMs) encompasses both forward and inverse kinematics. Forward kinematics calculates the X, Y, and Z coordinates of the tip center point based on a given pressure value, while inverse kinematics determines the input pressure required to achieve a desired tip position . In thisFor training the ANN, we utilized a dataset consisting of 66 samples, which included finite element analysis (FEA) results for pressures P1, P2, and P3, as well as deformation in the X, Y, and Z axes. To ensure a robust and accurate model, we adopted a Bayesian regularization (BR) approach. This type of ANN is particularly suitable for quantitative studies with smaller datasets as it can handle complex relationships without compromising power or precision. To assess the model’s performance, the dataset was divided into training, validation, and test sets, with a recommended split ratio of 70%, 15%, and 15%, respectively. The optimal ANN structure, comprising one hidden layer with ten neurons, was determined through iterative adjustments during training to minimize the mean squared error (MSE). After 300 iterations, the best-performing ANN achieved a validation MSE of 2.8655, demonstrating its accuracy in predicting pressure values for desired tip positions.The inverse kinematics modeling employed an ANN with three inputs representing Cartesian X, Y, and Z coordinates, and three outputs representing the corresponding pressure values. Using the MATLAB neural network toolbox, the ANN was trained by iteratively adjusting the network output to optimize validation performance, as quantified by the lowest MSE. After 300 iterations, the trained ANN demonstrated an MSE of 2.8655, indicating its accuracy in predicting pressure values for desired tip positions. The training, validation, and testing process of the ANN is depicted in To validate the ANN’s performance, a comparison was made between its results and finite element analysis (FEA) simulations. The observed maximum errors in the X, Y, and Z coordinates were 9.3%, 7.83%, and 8.8%, respectively, demonstrating the network’s capability to accurately predict future values. These results provide validation for the reliability and performance of the trained ANN, underscoring its effectiveness in predicting the required pressure values to achieve desired tip positions in the SPMs. Leveraging the predictive capabilities of the ANN enables the precise control and manipulation of SPMs, contributing to the advancement of soft robotics and its broad range of applications.A comprehensive comparison was conducted between the mean absolute error (MAE) associated with two predictive models: finite element analysis (FEA) and artificial neural network (ANN). The primary objective was to predict the behavior of soft pneumatic muscles by considering key performance parameters such as force output, range of motion, and pressure response. Visual representation in the form of a bar chart was employed to illustrate the disparities in accuracy between the models, ultimately revealing the ANN model’s consistent superiority in prediction accuracy. This observation highlights the enhanced capability of the ANN model in capturing the intricate and nonlinear relationships between design parameters and muscle performance. The MAE values obtained for the ANN model were 0.2251, 0.3739, and 0.3761 for the x, y, and z directions, respectively, as indicated in the corresponding In this study, the development and analysis of three soft pneumatic muscles (SPMs) were conducted in order to explore their potential use in human assistive devices for individuals with disabilities. The SPMs’ geometric characteristics were meticulously designed and presented in