Analytical modeling of soft pneumatic actuators constitutes a powerful tool for the systematic design and characterization of these key components of soft robotics. Here, we maximize the quasi-static bending angle of a soft pneumatic actuator by optimizing its cross-section for a fixed positive pressure inside it. We begin by formulating a general theoretical framework for the analytical calculation of the bending angle of pneumatic actuators with arbitrary cross-sections, which is then applied to an actuator made of a circular polymer tube and an asymmetric patch in the shape of a hollow-cylinder sector on its outer surface. It is shown that the maximal bending angle of this actuator can be achieved using a wide range of patches with different optimal dimensions and approximately the same cross-sectional area, which decreases with pressure. We also calculate the optimal dimensions of thin and small patches in thin pneumatic actuators. Our analytical results lead to clear design guidelines, which may prove useful for engineering and optimization of the key components of soft robotics with superior features.
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