Comprehensive Model of Laminar Jamming Variable Stiffness Driven by Electrostatic Adhesion

Variable stiffness mechanisms empower robots to become compliant or rigid on demand for adapting to challenging scenarios, such as gripping irregular fragile objects without damaging them or exploring complicated environments, i.e., natural channels inside human bodies, safely. However, variable stiffness mechanisms are typically constrained by bulky structures, slow actuation, low stiffness variation, and especially the lack of nonlinear behaviors modeling. We aim to build an explicit analytical model to characterize nonlinear behaviors of the laminar jamming variable stiffness mechanism. In this work, we demonstrate a low-cost (<0.08 USD for each layer), lightweight (0.5 g each layer), compact (85
$\,\mu \text{m}$
thick each layer), and scalable (arbitrary dimensions of electrodes) laminar jamming structure based on electrostatic adhesion. The analytical model that explains thorough mechanical behaviors of a two-layer structure, including linear (constant stiffness) and nonlinear (stiffness varies) regimes, is developed, showing high accuracy with experimental results under different driving voltages. Based on the model, the influences of parameters such as material properties, geometry, and voltages on the stiffness performance are analyzed, giving potential improvement directions in materials, design, and actuation. The mechanical behaviors of two-layer and four-layer structures are characterized through three-point bending tests. The performances, including the stiffness variation (4 layers, up to 11 times), responding time (700–800 ms), and power consumption (1 mW), are also evaluated experimentally. We demonstrate the response speed, the impact absorption functionality, and the deflection prediction. The design, fabrication, and modeling herein pave the way for developing multifunctional robots with variable stiffness.