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Abstract The growing demand for flexible robotic grasping in industry calls for adaptable solutions capable of handling diverse objects across stiffness regimes. We present a novel variable-stiffness gripper with a parallel-guided beam and sliding-block mechanism, enabling continuous stiffness modulation (0.143–2.021 N/mm) without component replacement. However, transmission nonlinearities, friction, stiffness-dependent effects, and, in particular, frequency drift arising from stiffness variations significantly hinder precise force control. To overcome these challenges, we propose a parameter-learning active disturbance rejection control (PL-ADRC) framework, integrating online adaptive parameter identification with a model-based extended state observer for real-time estimation and rejection of disturbances arising from unmodeled dynamics and parametric uncertainties. Experimental results demonstrate the superior performance of PL-ADRC: PL-ADRC reduces the band settling time by 0.13 s compared to model-free active disturbance rejection control (MF-ADRC), limits the steady-state force error to 0.01 N, and exhibits robust adaptability in stiffness modes. It outperforms model-based and model-free methods in fragile-object manipulation (e.g., egg grasping without fracture) and high-noise scenarios, achieving faster stabilization and reduced overshoot. This framework bridges precision and adaptability, advancing safe human–robot collaboration in dynamic industrial tasks. 

Abstract This article introduces a novel compact discrete variable stiffness actuator, distinguished by its design topology enabling compactness and independent stiffness adjustment regardless of position, without relying on complex stiffness tuning mechanisms. The compactness is achieved through a rotary spring module comprising six linear springs. Variation in stiffness is attained by adjusting the number of engaged elastic elements (springs) using linear actuators. The article comprehensively covers the design, modeling, prototyping, and control of the actuator. A mathematical model, encompassing stiffness and dynamic aspects of the system, is developed and analyzed. Robust controllers are devised to ensure stability across different stiffness levels and under varying loads. Simulation and experimental findings provide empirical validation of the effectiveness of this innovative compact actuation system, underscoring its suitability for diverse applications across sectors such as manufacturing, healthcare, and assistive robotics. 

Abstract The demand for flexible grasping of various objects by robotic hands in the industry is rapidly growing. To address this, we propose a novel variable stiffness gripper (VSG). The VSG design is based on a parallel-guided beam structure inserted by a slider from one end, allowing stiffness variation by changing the length of the parallel beams participating in the system. This design enables continuous adjustment between high compliance and high stiffness of the gripper fingers, providing robustness through its mechanical structure. The linear analytical model of the deflection and stiffness of the parallel beam is derived, which is suitable for small and medium deflections. The contribution of each parameter of the parallel beam to the stiffness is analyzed and discussed. Also, a prototype of the VSG is developed, achieving a stiffness ratio of 70.9, which is highly competitive. Moreover, a vision-based force sensing method utilizing ArUco markers is proposed as a replacement for traditional force sensors. By this method, the VSG is capable of closed-loop control during the grasping process, ensuring efficiency and safety under a well-defined grasping strategy framework. Experimental tests are conducted to emphasize the importance and safety of stiffness variation. In addition, it shows the high performance of the VSG in adaptive grasping for asymmetric scenarios and its ability to flexible grasping for objects with various hardness and fragility. These findings provide new insights for future developments in the field of variable stiffness grippers. 

Abstract This research presents a novel design of a four-bar mechanism featuring a variable stiffness link (VSL) as the output component, aimed at enabling diverse end-effector trajectories without modifying the link length or moment input. By employing both single-beam and multi-section beam configurations within a large deflection model, the study investigates the effect of varying link stiffness under constant load and geometric conditions on the mechanism’s trajectory outcomes. The proposed design was validated through both numerical modeling and experimental testing of a built prototype. The findings confirm the prototype’s alignment with theoretical predictions, highlighting the VSL’s key role in significantly enhancing the adaptability and application range of four-bar mechanisms. This advancement circumvents the traditional constraints of fixed-trajectory mechanisms, proposing a versatile, efficient, and cost-effective solution for complex motion applications in compliant mechanism design. 

Abstract Variable stiffness manipulators balance the trade-off between manipulation performance needing high stiffness and safe human–robot interaction desiring low stiffness. Variable stiffness links enable this flexible manipulation function during human–robot interaction. In this paper, we propose a novel variable stiffness link based on discrete variable stiffness units (DSUs). A DSU is a parallel guided beam that can adjust stiffness discretely by changing the cross-sectional area properties of the hollow beam segments. The variable stiffness link (Tri-DSU) consists of three tandem DSUs to achieve eight stiffness modes and a stiffness ratio of 31. To optimize the design, stiffness analysis of the DSU and Tri-DSU under various configurations and forces was performed by a derived linear analytical model which applies to small/intermediate deflections. The model is derived using the approach of serially connected beams and superposition combinations. 3D-Printed prototypes were built to verify the feature and performance of the Tri-DSU in comparison with the finite element analysis and analytical model results. It’s demonstrated that our model can accurately predict the stiffnesses of the DSU and Tri-DSU within a certain range of parameters. Impact tests were also conducted to validate the performance of the Tri-DSU. The developed method and analytical model are extendable to multiple DSUs with parameter configurations to achieve modularization and customization, and also provide a tool for the design of reconfigurable collaborative robot (cobot) manipulators.