Variable Stiffness Research Articles

Computational Modeling and Analysis of Fungi‐Inspired Network Systems

Filamentous fungi create complex structures, such as mushrooms, using filaments made of fungal cells, called hyphae. Previous research shows that the presence of distinct types of hyphal filaments can affect the mechanical properties of the mushrooms they form. This study characterizes the structure and mechanical properties of a monomitic white mushroom (one type of hyphal filaments) and a dimitic maitake mushroom (two types of hyphal filaments). This characterization includes properties on the micro‐ and macroscale using imaging, compression testing, and nanoindentation. Using this experimental data and imaging observation, a stochastic cellular structure is proposed and simulated using 3D Voroni structures. Compression test simulations are conducted to investigate the effects of filament orientation on these filamentous network structures. Five main filament orientation angles are used: horizontal (0°), 30°, 60°, and vertical (90°). These orientation angles result in variable stiffness of the structure without the addition of fibers of different mechanical properties, suggesting that the orientation of hyphal filaments can be manipulated to alter the properties of monomitic fungi‐based or fungi‐inspired materials. This study lays a foundation for designing stochastic cellular structures with tunable mechanical properties in different directions.

Synergy-based robotic quadruped leveraging passivity for natural intelligence and behavioural diversity

Abstract Quadrupedal animals show remarkable capabilities in traversing diverse terrains and display a range of behaviours and gait patterns. Achieving similar performance by exploiting the natural dynamics of the system is a key goal for robotics researchers. Here we show a bioinspired approach to the design of quadrupeds that seeks to exploit the body and the passive properties of the robot while maintaining active controllability on the system through minimal actuation. Utilizing an end-to-end computational design pipeline, neuromechanical couplings recorded in biological quadrupeds are translated into motor synergies, allowing minimal actuation to control the full structure via multijoint compliant mechanical couplings. Using this approach, we develop PAWS, a passive automata with synergies. By leveraging the principles of motor synergies, the design incorporates variable stiffness, anatomical insights and self-organization to simplify control while maximizing its capabilities. The resulting synergy-based quadruped requires only four actuators and exhibits emergent, animal-like dynamical responses, including passive robustness to environmental perturbations and a wide range of actuated behaviours. The finding contributes to the development of machine physical intelligence and provides robots with more efficient and natural-looking robotic locomotion by combining synergistic actuation, compliant body properties and embodied compensatory strategies.

Optimising the design of auxetic core airfoil for wing morphing applications

Bird wings demonstrate phenomenal adaptation and aerodynamic performance across varied flight conditions. In contrast, conventional aircraft wings are designed for specific scenarios, limiting their adaptability. Therefore, the integration of smart cellular structures into morphing airfoils is crucial for furthering aircraft development. This entails integrating actuators, sensors, and innovative control systems to modernize aircraft engineering. One intriguing approach is adopting a re-entrant arrangement which exhibits a negative Poisson’s ratio, popularly known as auxetic behaviour. This particular trait can bring substantial advantages to the morphing process. Morphing airfoils containing an auxetic core offer various benefits, including greater deformability, ease of control, variable stiffness, and improved stress tolerance. This research provides a novel approach by discovering the optimal re-entrant unit cell and extending its key advantage within the aerospace sector, focusing on achieving maximal wing trailing edge deflection. The paper explores the in-plane characteristics of a 2D re-entrant auxetic structure and evaluates the consequences of parameter changes on the structure’s negative Poisson ratio. Through multi-objective optimisation employing a genetic algorithm, the study achieves a remarkable 99.53 % enhancement in Poisson’s ratio and a substantial 158.70 % rise in the relative elastic modulus, as evaluated analytically. Further, Finite element analysis (FEA) of the Eppler 420 airfoil reveals that integrating the improved re-entrant core within the airfoil leads to a significant augmentation of 63.56 % in trailing edge deflection compared to past research. This research emphasizes the potential of adopting optimised re-entrant structures to boost the performance and adaptability of aircraft wings.

Robust control of a compliant manipulator with reduced dynamics and sliding perturbation observer

Compliant manipulators equipped with Variable Stiffness Actuation (VSA) possess the ability to safely interact with their environment and adapt to complex tasks. However, the tracking performance of such manipulators is significantly influenced by their intrinsic compliance and varying stiffness. This paper presents a robust control strategy for compliant manipulators equipped with Discrete Variable Stiffness Actuation (DVSA), aimed at enhancing tracking performance under both fixed and varying stiffness conditions. By compensating for nonlinear dynamics, joint coupling, frictions, stiffness variability and uncertainties through a Sliding Perturbation Observer (SPO), the proposed approach ensures robust and consistent performance, significantly outperforming traditional controllers. In fixed stiffness scenarios, the proposed controller achieves a reduction in energy consumption of up to 68.1% at the lowest stiffness and 75.5% at the highest stiffness, demonstrating superior efficiency. For abrupt stiffness transitions (lowest–highest–lowest), the proposed controller reduces energy consumption by up to 70.9% compared to traditional controllers. Additionally, it maintains smooth control input and precise tracking, avoiding the chattering and inefficiencies that traditional controllers typically exhibit. The SPO effectively estimates all system states and perturbation, compensating for nonlinearities, disturbances due to variable stiffness, and friction, enabling consistent trajectory tracking with minimal control effort. The proposed controller’s ability to adapt to varying stiffness levels without explicit parameter tuning highlights its robustness and practical viability. Simulation and experimental results validate its superior performance in reducing tracking error and energy consumption, particularly in scenarios where traditional controllers struggle to manage varying stiffness effectively.

Rings in Taylor Spatial Frame: Mechanical testing and finite element analysis.

Taylor Spatial Frame (TSF) is a type of hexapod external ring fixation system. TSF rings are supplied as half rings, whole full rings and two third rings in different sizes. In this work, these components as well as bolted full rings made of two half rings were tested in compression in two or three directions. Tests were simulated by Finite Element (FE) method using 3D solid elements, which were validated against the experimental results. Load-deflection curves and values for stiffness and ultimate loads are presented for each case from both tests and FE analyses. Load-stiffness curves are also presented for each test. The followings were demonstrated by the results: (1) a significant difference between bolted and whole full rings in their respective stiffness behaviour, the clear advantage being with the whole full rings, (2) a variation in stiffness of bolted rings when loaded across their different diameters, (3) a potential problem in the TSF rings: having the same cross section and thickness, smaller rings are stronger than larger ones, whereas in fact the larger ones ought to be stronger due to patient's weight and that (4) the lowest stiffness was exhibited when a 2/3 ring was loaded parallel to the line joining its open ends.

Analysis and modeling of nonlinear saturated behavior of layer jamming soft pneumatic bending actuator

Abstract Soft actuators have become remarkably popular among numerous applications in rehabilitation and manipulation. Despite their numerous advantages, these actuators exhibit a significant limitation in grasping applications. Their inherently low stiffness, a characteristic of soft actuators, leads to considerable deformation when interacting with opposing forces. In this study, a jamming actuator has been integrated into the soft actuator to enable variable stiffness. The system’s behavior has been modeled in both linear and nonlinear states, utilizing both the strain energy theory of hyperelastic materials and a novel hysteresis identification technique based on the Prandtl-Ishlinskii method. Moreover, the results have been validated with experiments. By adding a layer jamming actuator to the soft actuator, the newly structured robot can increase its stiffness up to nine times when the layer jamming is activated. If the layer jamming is deactivated, the robot behaves like a typical soft actuator. Moreover, as the test results indicate, the strain energy-based method shows a 6.3% deviation from the actual behavior in the linear range, while it was unable to accurately characterize the actuator’s behavior in nonlinear states. In contrast, hysteresis modeling displays an 8.5% deviation from experimental data in both linear and nonlinear states. Overall, the combination of the layer jamming and soft bending actuator has resulted in a more versatile manipulator whose behavior could be modeled and anticipated with adequate accuracy considering both modeling techniques.

Study on the Time-Varying Stiffness Characteristics of Four-Point Contact Ball Bearings

This paper takes a four-point contact ball bearing of a wind turbine as the research object, analyzes the force and deformation relationship under the combined action of axial load and radial load, obtains the load distribution of rolling elements, and establishes a time-varying stiffness model of four-point contact ball bearings without clearance. The stiffness variation law of the case bearing in one rolling period is analyzed, and the time-varying characteristics of stiffness are characterized by the average stiffness and stiffness amplitude variation rate. The influence laws of the number of rolling elements, initial contact angle, axial load, and radial load on the time-varying characteristics of bearing stiffness are analyzed. The results show that within one rolling period, the average value of axial stiffness is about 2.21 times that of radial stiffness, and the amplitude variation rates of radial stiffness and axial stiffness are 0.0047% and 0.002%, respectively. The time-varying characteristics of both are not obvious. The influence of the number of rolling elements on the two stiffnesses is almost linear, while the influence of axial load on stiffness is small; the initial contact angle is positively correlated with axial stiffness and negatively correlated with radial stiffness. With the increase in radial load, the two stiffnesses also increase. Finally, the stiffness test of four-point contact ball bearings was carried out, and the error between the test value and the theoretical value was less than 15%, which preliminarily verified the correctness of the stiffness model.

Design and Analysis of a Cable-Driven Lower Limb Rehabilitation Robot with Variable Stiffness Joints

Abstract The cable driven mechanism combines the advantages of rigid linkage mechanisms and flexible cable systems, featuring a compact structure, large workspace, low mass and inertia, and flexible motion capabilities. These characteristics hold significant theoretical and practical value in the field of lower limb rehabilitation robots. This paper proposes a cable driven lower limb rehabilitation robot with variable stiffness properties, consisting of a seat mechanism and a rehabilitation mechanism. Additionally, variable stiffness joints are introduced, enabling both active and passive stiffness adjustment. First, based on Lie group theory, the dynamic equations of the lower limb rehabilitation mechanism were derived, providing an efficient modeling method for multi-body systems with flexible joints. Second, this model was used to calculate the stiffness of the robot's joints, which was then set as a constraint to construct a quadratic optimization function for the cable tension. This function is used to evaluate the changes in the robot's joint stiffness and cable tension during rehabilitation training. Finally, simulation examples and experimental tests were conducted to verify the accuracy of the model and the feasibility of the rehabilitation training program.

A Multi-Objective Sensor Placement Method Considering Modal Identification Uncertainty and Damage Detection Sensitivity

Structural Health Monitoring relies on accurate modal identification and effective damage detection to assess structural performance and safety. However, traditional sensor placement methods struggle to balance modal identification uncertainty, which arises from limited sensor coverage and measurement noise and damage detection sensitivity, which requires sensors to be optimally positioned to capture structural stiffness variations. To address this challenge, this study proposes a multi-objective sensor placement optimization method based on the Non-Dominated Sorting Genetic Algorithm. The method introduces two key objective functions: minimizing modal identification uncertainty by leveraging Bayesian modal identification theory and information entropy and maximizing damage detection sensitivity by incorporating an entropy-based measure to quantify the uncertainty in stiffness variation estimation. By formulating the problem as Pareto-based multi-objective optimization, the method efficiently explores a trade-off between the two competing objectives and provides a diverse set of optimal sensor placement solutions. The proposed approach is validated through numerical experiments on a simply supported beam and a benchmark bridge structure, demonstrating that different optimization objectives lead to distinct sensor placement patterns. The results show that solutions prioritizing modal identification distribute sensors across the structure to improve global response estimation, while solutions favoring damage detection concentrate sensors in critical areas to enhance sensitivity. The proposed method significantly improves sensor placement strategies by offering a systematic and flexible framework for SHM applications, enabling engineers to tailor monitoring strategies based on specific structural assessment needs.

Dynamic analysis of cross brace anti-warp stiffness performance for heavy haul freight wagon

A dynamic model was developed to assess the impact of cross braces on the lateral stability and curve navigability of heavy haul freight wagons. Simulations evaluated the dynamic performance of empty and loaded wagons under varying cross-brace anti-warp stiffness. The study focused on stability, ride quality during straight-line travel and safety indices across different curve radii. The results show that cross braces significantly enhance vehicle nonlinear critical speed. In straight-line sections, variations in anti-warp stiffness have a minimal impact on vertical ride quality but improve lateral ride quality. In curved sections, stiffness changes have little impact on derailment coefficient, wheel load reduction rate and attack angle but notably affect wheelset lateral force and wear index. Safety and ride quality indices decrease with increasing vehicle speed, while the impact on vertical indices remains minimal. As the curve radius increases, safety indices decrease. Significant changes in attack angle and derailment coefficient are observed when the curve radius shifts from R400 to R600. The study confirms that larger bolt preloads increase anti-warp stiffness while larger mounting angles decrease it. Selecting the appropriate bolt preload and cross-brace angle is crucial for optimising performance and safety in vehicle engineering applications.

Improved Boussinesq-type equations for flexural-gravity waves

Improved Boussinesq-type equations for flexural-gravity waves

The mechanisms of frequency tuning in gecko auditory hair cells.

The mechanisms of frequency tuning in gecko auditory hair cells.

Treating Facial Scars using Polydioxanone Threads.

Traditional scar treatments, such as laser therapy, chemical peels, and surgery, are expensive and require long recovery times. Polydioxanone (PDO) threads offer a minimally invasive and cost-effective solution that enhances collagen production and skin texture. This study aimed to evaluate the effectiveness of PDO threads in the management of atrophic facial scars due to the lack of clinical research on this topic. A prospective clinical study was conducted on 20 patients with facial atrophic scars caused by accidents or previous surgical procedures. The patient and observer scar assessment scale was used to evaluate the scars from the observer's and patient's perspectives at three-time points for each patient. The observer assessment included the following variables: vascularity, pigmentation, thickness, pliability, surface area, and homogeneity. The patient assessment included the following variables: pain, color, stiffness, thickness, appearance, and itching. Statistically significant improvement was observed in atrophic facial scars treated using PDO threads in all observer variables (p<0.001). Significant improvement was recorded in the patient's color, stiffness, thickness, and appearance variables; however, itching sensation increased between T0 and T1 with no statistically significant differences in the pain variable. Within the limits of this study, we conclude that PDO threads are known for ease of use, availability, and biocompatibility. They biodegrade naturally, reducing irritation risk. By stimulating collagen, PDO threads promote natural skin regeneration and thereby improve scars without using foreign materials. The treatment method is safe and minimally invasive, with short recovery times. Clinical studies showed significant improvements in atrophic facial scars with high patient satisfaction.

A simple analytical model for static and dynamic analysis of unsymmetrical bi-stable variable stiffness composite laminated plates

A simple analytical model for static and dynamic analysis of unsymmetrical bi-stable variable stiffness composite laminated plates

Aero-thermo-elastic stability analysis of supersonic variable stiffness sandwich panels using refined layerwise models

Aero-thermo-elastic stability analysis of supersonic variable stiffness sandwich panels using refined layerwise models

Modeling, optimization, and control of a variable stiffness pneumatic rotary joint with soft-rigid hybrid twisting modules

Modeling, optimization, and control of a variable stiffness pneumatic rotary joint with soft-rigid hybrid twisting modules

Multistable nonlinear energy sink with variable stiffness of seismic vibration control

Multistable nonlinear energy sink with variable stiffness of seismic vibration control

Numerical and experimental study on adaptive stiffness yaw damper for suppressing abnormal vibration of high-speed trains

The mismatch between the parameters of the yaw damper and the equivalent conicity of wheel rail contact can lead to abnormal vibration of rail vehicles, while the stiffness variation range of traditional yaw dampers is very small, covering a limited range of equivalent conicity of wheel rail contact, resulting in the risk of carbody hunting at low conicity and bogie hunting at high conicity. To overcome the abovementioned shortcomings of traditional yaw dampers and reduce the abnormal vibration of high-speed trains under various operating conditions, this study proposes an adaptive stiffness yaw damper. The effectiveness of this solution was confirmed through roller testing rig and multi-body dynamic simulations. The results show that the device can dynamically adjust the stiffness according to the operating conditions of the vehicle, effectively reducing the carbody and bogie hunting under extreme wheel rail contact conditions, and thereby reducing the abnormal vibration of high-speed trains. At the same time, this device helps reconcile the trade-off between the curve negotiation performance and stability of vehicle, indirectly lessening the requirement for wheel–rail maintenance and reducing operational and maintenance expenses.

Numerical analysis on dynamic response of the variable stiffness composite structures including the damage effect

This work investigates the influence of damage on the modal characteristics of variable stiffness laminated composite structures. The study focuses on four distinct curvilinear fiber paths to evaluate the effects of damage on the laminated composites. The finite element modeling incorporates the first-order shear deformation theory (FSDT) with an enhanced shear correction factor to simulate the damage. The impact of damage on natural frequencies and mode shapes is analyzed for various fiber paths. The numerical investigation is extended for different delamination sizes, positions, boundary conditions, and lamination sequences. The presented results concluded that the influence of damage can be minimized by choosing the best fiber path. Mode shapes can be easily adjusted by varying the stiffness within a plane, thus, the variable stiffness laminates are pretty useful for applications where mode shapes are critical to preventing structural failure. The difference in the mode shape is presented in the contour plot, and these results could be useful in finding the delamination location in composite laminates.

Biofabrication of Tunable 3D Hydrogel for Investigating the Matrix Stiffness Impact on Breast Cancer Chemotherapy Resistance.

Matrix stiffness is a key factor in breast cancer progression, but its impact on cell function and response to treatment is not fully understood. Here, we developed a stiffness-tunable hydrogel-based three-dimensional system that recapitulates the extracellular matrix and physiological properties of human breast cancer in vitro. Adjusting the ratio of GelMA to PEGDA in the hydrogel formulation enabled the fine-tuning of matrix stiffness across a range of 7 to 52 kPa. Utilizing this three-dimensional (3D) hydrogel platform for a breast cancer cell culture has enabled precise functional evaluations. Variations in matrix stiffness resulted in significant changes in the morphology of breast cancer cells after 2 weeks of incubation. The analysis of transcriptomic sequencing revealed that the 3D microenvironment significantly changed the expression of a wide panel of transcriptomic profiles of breast cancer cells in various matrix stiffness. Gene Ontology analysis further suggested that specific biological functions could potentially be linked to the magnitude of the matrix stiffness. According to our findings, extracellular matrix rigidity modulates the sensitivity of breast cancer cells to paclitaxel and adriamycin. Notably, the expression of ABCB1 and YAP1 genes may be upregulated in the 3D culture environment, potentially contributing to the increased drug resistance observed in breast cancer cells. This work aims to establish facile adjustable hydrogels to deepen insights into matrix rigidity effects on breast cancer cells within 3D microenvironments, highlighting the critical role of extracellular matrix stiffness in modulating cell-matrix interactions.