Printing bending pneumatic artificial muscles with variable stiffness and curvature: Theoretical, simulation and experimental results

Soft actuators, capable of mimicking the motion of biological organisms, enable precise and gentle operations in complex environments. While conventional pneumatic artificial muscles (PAMs) are typically fabricated from materials with fixed stiffness, this study introduces shape-memory polymers (SMPs) to achieve tunable stiffness, thereby enhancing both deformability and load-bearing capacity. By replacing traditional bladders and constraint frameworks with 3D-printed SMP structures, we have developed SMP-PAMs that exhibit temperature-controlled bending and elongation. We analyze the kinematics of the printed PAM, evaluate its output force and bending moment at varying temperatures. A nonlinear quasi-static model, based on the virtual work principle, is developed to capture the interaction between pneumatic input and structural mechanics and its effect on actuation performance. Finite element analysis (FEA) is employed to simulate the PAM's motion, where a full-scale braided tube is first modeled, followed by a simplified equivalent cross-section model for coupled simulation with the internal elastomer. Experimental validation confirms the SMP-PAM's shape recovery rate, temperature response, kinematic deformation, and bending stiffness. Through a combination of theoretical modeling, simulation, and experiments, this study provides a comprehensive performance evaluation of the novel PAM, offering key insights for future research and innovative design approaches.