Design, Modeling and Performance Analysis of an Actively Variable Stiffness Pneumatic Flexible Bending Joint

The contradiction between high compliance and low load-bearing capacity of flexible manipulators limits their engineering applications. Meanwhile, the theoretical modeling of the deformation and variable stiffness characteristics of flexible joints still faces considerable challenges. This paper proposes a positive-pressure double-airbag gap-constrained particle-jamming variable stiffness method and develops a novel actively variable stiffness pneumatic flexible bending joint with an integrated configuration of actuator, variable stiffness device (VSD), and primary structure. Based on classical elasticity theory and Coulomb–Amontons’ law of friction, theoretical models for the bending angle and tangential stiffness are established and verified through prototype experiments. With VSD activation, the joint reaches a bending angle of 56.35° at 0.4 MPa. At 40° forward bending, VSD activation increases the tangential stiffness from 0.167 N/mm to 0.832 N/mm, with the stiffness ratio between 40° and 0° increasing from 1.56 without VSD to 4.80 with VSD activation. Model predictions agree well with experimental data, yielding mean relative errors of 6.77% for the bending-angle model with VSD and 6.76% for the forward tangential-stiffness model with VSD activation. A coupling effect between bending deformation and stiffness is observed. The results demonstrate that the proposed joint achieves substantial stiffness regulation, providing a basis for its application in flexible robotic systems.