Design and Kinematic Modeling of a Pneumatic Soft Bellow-Type Wrist

In this letter, we aim to develop an efficient and accurate kinematic model of a soft wrist that consists of pneumatic bellows configured in parallel, toward dexterous manipulation in confined space. The challenge arises from the distributed nature and deformation-dependency of the generated pneumatic actuation forces along the air chamber, making it difficult to obtain the equivalent generalized forces. To achieve a trade-off between accuracy and computational efficiency, we first establish a simplified geometric model of local deformation of the bellow by using the global state variables, based on simulations and experimental observations of bellow-type actuators. Then we define the deformation gradient of the chamber's wall. Subsequently, we develop forward and inverse kinematics by utilizing the principle of minimum potential energy. The analyses of the wrist's workspace and payload limit are conducted, and trajectory tracking experiments are performed to validate the proposed kinematics. The average error for the circle and tetrahedron trajectories with no load reaches about 2.40% and 5.25% of the characteristic length of the trajectory, respectively, with an average computation time of 0.17 s and 0.16 s per point, and the model maintains a certain level of accuracy under a permissible range of loads. Finally, we mount a suction cup at the end of the soft wrist and successfully perform the pick-and-place task in confined space.