Modeling and experimental evaluation of dynamic behavior of a soft bending actuator with symmetrical fluidic chambers

Shear deformation and nonlinearity are the two main variables that influence the bending behavior of soft actuators with thick cross-sections. However, in most dynamic studies of these actuators, either one such variable is taken into consideration or both are disregarded, resulting in substantial inaccuracies in predicting their dynamic responses. In this work, we present an analytical dynamic model based on Euler-Lagrange dynamics, to predict the bending behavior of a soft pneumatic actuator with symmetrical fluidic chambers, which can capture the shear deformation of the actuator while preserving its nonlinear characteristics. Inspired by the finite element method, we divided the actuator into several regions and calculated the strain potential energy of each region separately. The coupling between different regions was described as geometric constraints based on the constant curvature (CC) model. As the inertia term of the dynamic model, the actuator's kinetic energy was evaluated under an assumption that the actuator's mass distributes along the center line of the neutral layer. These efforts allowed the model to preserve the nonlinearity of the deformation while ensuring its simplicity. By looking for the minimum value of the stress potential energy, the shear deformation of the actuator was assessed. Experiments were carried out to determine the actuator's damping properties, investigate the influence of the gas line on the actuator's dynamic behavior, and validate the model at fluidic pressure with different frequencies. The dynamic model's predictions for transient and steady stages were found to be in good agreement with experimental data. The model's application to other soft actuators with a similar structure was discussed at the end.