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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. A Variable Stiffness Robotic Arm Using Linearly Actuated Compliant Parallel Guided Mechanism

   https://doi.org/https://doi.org/10.1007/978-3-030-00365-4_5  

   Hu, R.; Venkiteswaran, V.; Su, H.-J. (January 2019, IFToMM Symposium on Mechanism Design for Robotics)

   This paper details the mechanical design and control of a human safety robotic arm with variable stiffness, starting from conceptual design to prototype. The mechanism designed is based on parallel guided beam with a roller slider actuated by a power screw and a DC motor with an encoder for position feedback. Unlike conventional robotic systems that control the stiffness in joints, this design introduces compliance to the robotic arm link itself. By controlling the slider position, the effective length of the link can be adjusted to provide the necessary stiffness change. A PID position controller is employed and the position accuracy is experimentally evaluated. The stiffness variation of the prototype is validated by experiments and FEA simulation. The overall stiffness change achieved is 20-fold. 

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4. 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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5. Design and Modeling of a New Variable Stiffness Robotic Finger Based on Reconfigurable Beam Property Change for Flexible Grasping

   https://doi.org/10.1115/DETC2022-89856  

   Xu, Wei; Fu, Jiaming; Gan, Dongming (August 2022, ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   Abstract Flexible grippers can provide fine grasping and manipulation to various objects and environment interactions. However, most current mechanisms can not change the stiffness in a short time, which limits the application scenario of the flexible grippers. This paper presents a novel variable stiffness robotic finger that can adapt to soft and rigid gripping objects by continuously changing its stiffness over a wide range in a short period of time. The principle is to change the second area moment of inertia of the finger by changing the filling ratio of the cavity between two parallel beams. A complete theoretical stiffness model is developed and compared with the finite element analysis (FEA) model. Effects of multiple design parameters on finger stiffness performance are compared and analyzed, and the accuracy of the theoretical model is verified, with a maximum error of less than 6.5%. The performance of the finger is further evaluated through an experimental prototype, which proved that the finger can safely perform a wide range of daily object-grasping tasks with adaptable compliance. The proposed stiffness-varying mechanism can adjust stiffness in a short time with a very large ratio (around 1:37). The design provides a new direction in developing variable-stiffness robotic grippers for flexible grasping. 

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