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.