The combination of flexible structures, external forces, and various soft material blends commonly causes complex deformations in continuum robots, making their modeling challenging. In this paper, we propose a bending model for pneumatic soft actuators. The chamber layer is being modeled as two states: (1) Free space expansion: using a modified virtual work principle, that is, algebraic calculation of the deformed volume of the chamber; (2) Contact expansion: Finite-strain membrane theory for modeling chamber layers. Modeling of constrained layers using Euler-Bernoulli finite-strain hyperelastic beam theory. Influence of gravity and axial tension is taken into account in the model; the model only requires input material parameters, structural parameters, and pressure for both the constraint and chamber layers. The data are then used to predict the bending behavior of soft actuators in free space. Soft actuators with different combinations of constraint and chamber layers were produced to carry out the experiment, enabling the validation of theoretical predictions. Additionally, the results were compared with those obtained via finite element analysis models. The proposed approach applies to Soft PneuNet Actuators (SPNA) with similar structures.
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