Static Modeling of the Fiber-Reinforced Soft Pneumatic Actuators Including Inner Compression: Bending in Free Space, Block Force, and Deflection upon Block Force

Fiber-reinforced soft pneumatic actuators (FR-SPAs) are among the most successful soft actuators in the soft robotics community considering their structural strength, motion range, and force output. Inspired by the pneumatic artificial muscle, the bending-type tubular SPAs have also been applied with fiber winding for body reinforcement and then utilized in many applications. Due to their superior utility and popularity, FR-SPAs have been extensively modeled using different methods. However, very little attention was given to the compression on the inner wall of the FR-SPAs by the compressed air. Furthermore, there is no unified modeling principle for bending, force output, and deflection of the FR-SPA. In this article, we take into account the inner compression and propose a static modeling approach based on the moment equilibrium for three important and frequently studied cases: free bending, block force, and deflection upon block force of the FR-SPA. Stress analysis of the material inside the fiber wall is conducted, which reveals the influence of radial compression by the input air. Then, the new stress expression is used in the moment equilibrium and results in the SPA models for the three aforementioned cases. The models are experimentally verified using SPAs featuring two profile designs and three different silicone rubbers. The results show that the placement of the fiber wall plays an important role in the SPA behavior. More importantly, the models successfully differentiate the two profiles and produce fairly accurate predictions of the bending angles, block forces, and deflections. The understanding of the compression effect offers a new variable in the FR-SPA design process, which can be used to tune the SPA properties for different applications.