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1. A Novel Variable Stiffness Compliant Robotic Link Based on Discrete Variable Stiffness Units for Safe Human–Robot Interaction

   https://doi.org/10.1115/1.4056957  

   Fu, Jiaming; Yu, Ziqing; Lin, Han; Zheng, Lianxi; Gan, Dongming (January 2024, Journal of Mechanisms and Robotics)

   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. 

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2. Machine Learning Based Deflection Prediction and Inverse Design for Discrete Variable Stiffness Units

   https://doi.org/10.1115/DETC2023-117322  

   Fu, Jiaming; Guo, Qianyu; Gan, Dongming (August 2023, American Society of Mechanical Engineers)

   Abstract Large deflection modeling is a crucial field of study in the analysis and design of compliant mechanisms (CM). This paper proposes a machine learning (ML) approach for predicting the deflection of discrete variable stiffness units (DSUs) that cover a range from small to large deflections. The primary structure of a DSU consists of a parallel guide beam with a hollow cavity that can change stiffness discretely by inserting or extracting a solid block. The principle is based on changing the cross-sectional area properties of the hollow section. Prior to model training, a large volume of data was collected using finite element analysis (FEA) under different loads and various dimensional parameters. Additionally, we present three widely used machine learning-based models for predicting beam deflection, taking into account prediction accuracy and speed. Several experiments are conducted to evaluate the performance of the ML models that were compared with the FEA and analytical model results. The optimal ML model, multilayer perceptron (MLP), can achieve a 7.9% maximum error compared to FEA. Furthermore, the model was employed in a practical application for inverse design, with various cases presented depending on the number of solved variables. This method provides a innovative perspective for studying the modeling of compliant mechanisms and may be extended to other mechanical mechanisms. 

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3. Design and Modeling of Compliant Four-Bar Mechanisms With Variable Stiffness Links for Multi-Output Trajectory

   https://doi.org/10.1115/DETC2024-143364  

   Luo, Jiayu; Alvi, Muhammad Hammad; Lin, Han; Huang, Xiaotong; Gan, Dongming (August 2024, American Society of Mechanical Engineers)

   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. 

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4. Design and Modeling of a Continuously Tunable Stiffness Arm for Safe Physical Human–Robot Interaction

   https://doi.org/10.1115/1.4044840  

   She, Yu; Su, Hai-Jun; Meng, Deshan; Lai, Cheng (February 2020, Journal of Mechanisms and Robotics)

   Abstract To reduce injury in physical human–robot interactions (pHRIs), a common practice is to introduce compliance to joints or arm of a robotic manipulator. In this paper, we present a robotic arm made of parallel guided beams whose stiffness can be continuously tuned by morphing the shape of the cross section through two four-bar linkages actuated by servo motors. An analytical lateral stiffness model is derived based on the pseudo-rigid-body model and validated by experiments. A physical prototype of a three-armed manipulator is built. Extensive stiffness and impact tests are conducted, and the results show that the stiffness of the robotic arm can be changed up to 3.6 times at a morphing angle of 37 deg. At an impact velocity of 2.2 m/s, the peak acceleration has a decrease of 19.4% and a 28.57% reduction of head injury criteria (HIC) when the arm is tuned from the high stiffness mode to the low stiffness mode. These preliminary results demonstrate the feasibility to reduce impact injury by introducing compliance into the robotic link and that the compliant link solution could be an alternative approach for addressing safety concerns of physical human–robot interactions. 

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5. A Novel Discrete Variable Stiffness Gripper Based on the Fin Ray Effect

   https://doi.org/10.1007/978-3-031-13835-5_71  

   Fu, J.; Lin, H.; Prathyush, I.V.S.; Huang, X.; Zheng, L.; Gan, D. (August 2022, Intelligent Robotics and Applications)

   Liu, H.; Yin, Z.; Liu, L.; Jiang, L.; Gu, G.; Wu, X.; Ren, W. (Ed.)

   Variable stiffness grippers can adapt to objects with different shapes and gripping forces. This paper presents a novel variable stiffness gripper (VSG) based on the Fin Ray effect that can adjust stiffness discretely. The main structure of the gripper includes the compliant frame, rotatable ribs, and the position limit components attached to the compliant frame. The stiffness of the gripper can be adjusted by rotating the specific ribs in the frame. There are four configurations for the gripper that were developed in this research: a) all ribs OFF (Flex) mode; b) upper ribs ON and lower ribs OFF (Hold) mode; c) upper ribs OFF and lower ribs ON (Pinch) mode; d) all ribs ON (Clamp) mode. Different configurations can provide various stiffness for the gripper’s finger to adapt the objects with different shapes and weights. To optimize the design, the stiffness analysis under various configurations and force conditions was implemented by finite element analysis (FEA). The 3-D printed prototypes were constructed to verify the feature and performance of the design concept of the VSG compared with the FEA results. The design of the VSG provides a novel idea for industrial robots and collaborative robots on adaptive grasping. 

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