Design and Analysis of a Load-Dependent Contact-Aided Compliant Joint

Abstract

Passive stiffness modulation is essential for compliant robotic systems in dynamic and uncertain environments, where rigid actuators or constant stiffness designs are often insufficient to ensure safety and adaptability. This paper presents the design, modeling, optimization, and experimental validation of a Load-Dependent Contact-Aided Compliant Joint (LCCJ) that passively modulates stiffness in response to external torque. An integrated design pipeline is established, which bridges a high-fidelity analytical framework with a physically-motivated optimization strategy. The framework combines a chained pseudo-rigid-body model (CPRBM) with Karush-Kuhn-Tucker (KKT) conditions to describe the complex beam-boundary interactions. Using the distinct deformation regimes of the mechanism, the pipeline employs a two-stage optimization strategy to precisely map the desired stiffness modulation back to the physical geometric parameters. Simulation results demonstrate that, across the benchmark and optimized-design validation cases, the model predictions agree closely with finite element analysis (FEA), with maximum relative errors in the torque–deformation response of 4.02% and 3.18% in the pre- and post-contact regions, respectively. Experimental validation confirms the effectiveness of the proposed design; compared to the FEA predictions, the experimental results exhibit relative errors below 2.6% in the pre-contact region and 5.22%–6.21% in the post-contact region. The LCCJ offers a compact and monolithic solution for passive stiffness modulation in compliant joint applications.