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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 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 Collaborative robots, or cobots, have been developed as a solution to the growing need for robots that can work alongside humans safely and effectively. One emerging technology in robotics is the use of Discrete Variable Stiffness Actuators (DVSAs), which enable robots to adjust their stiffness in a fast-discrete manner. This enables cobots to work in both low and high stiffness modes, allowing for safe collaboration with human workers or operation behind safety barriers. However, achieving good performance with different stiffness modes of DVSAs is a challenging problem. This paper proposes a method to provide force control of a DVSA by exploiting the dynamic model and the discrete stiffness levels. The two-mass dynamic model, a widely accepted model of flexible systems, is used to model and analyze the DVSA. The proposed method involves using Gain-scheduling and Deterministic Robust Control (DRC) controllers as modelbased control algorithms for the DVSA to achieve high-precision force control. We also conducted a comparison with the commonly used proportional integral derivative (PID) control algorithms. The paper presents a detailed analysis of the dynamic behavior of the DVSA and demonstrates the effectiveness of the proposed control algorithms through simulation with different scenario comparisons, even in the presence of external disturbances. 

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. 

Abstract This paper presents the development of a novel Actuation-Coordinated Mobile Parallel Robot (ACMPR), with a focus on studying the kinematics of the mobile parallel robot with three limbs (3-mPRS) comprising mobile prismatic joint-revolute joint-spherical joint. The objective of this research is to explore the feasibility and potential of utilizing omnidirectional mobile robots to construct a parallel mechanism with a mobile platform. To this end, a prototype of the 3-mPRS is built, and several experiments are conducted to identify the proposed kinematic parameters. The system identification of the 3-mPRS mobile parallel mechanism is conducted by analyzing the actuation inputs from the three mobile base robots. To track the motion of the robot, external devices such as the Vicon Camera are employed, and the data is fed through ROS. The collected data is processed based on the geometric properties, CAD design, and established kinematic equations in MATLAB, and the results are analyzed to evaluate the accuracy and effectiveness of the proposed calibration methods. The experiment results fall within the error range of the proposed calibration methods, indicating the successful identification of the system parameters. The differences between the measured values and the calculated values are further utilized to calibrate the 3-mPRS to better suit the experiment environment. 

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. 

Abstract Variable stiffness manipulators balance the trade-off between manipulation performance needing high stiffness and safe human-robot interaction desiring low stiffness. Variable stiffness compliant links provide a solution to enable this flexible manipulation function in human-robot co-working scenarios. 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 (named Tri-DSU) consists of three tandem DSUs to achieve eight stiffness modes and a maximum stiffness change 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 theoretical model compared with finite element analysis (FEA). The analytical stiffness model is derived using the approach of serially connected beams and superposition combinations. It works not only for thin-walled flexure beams but also for general thick beam models. 3-D printed prototypes were built to verify the feature and performance of the Tri-DSU in comparison with the FEA and analytical model results. It’s demonstrated that our analytical model can accurately predict the stiffnesses of the DSU and Tri-DSU within a certain range of parameters. The developed variable stiffness link method and analytical model are extendable to multiple DSUs with different sizes and parameter configurations to achieve modularization and customization. The advantages of the stiffness change mechanism are rapid actuation, simple structure, and compact layout. These methods and results provide a new conceptual and theoretical basis for the development of new reconfigurable cobot manipulators, variable stiffness structures, and compliant mechanisms.