Variable Stiffness Research Articles

A novel approach to enhancing smart stiffness of soft robotic gripper fingers for wider grasping capability

AbstractThis paper presents a proposed design of soft gripper fingers with adjustable stiffness that could be employed in the applications requiring adaptable and stable grasping. The main idea is to combine the under-actuated cable driven mechanism of a soft gripper finger with particle and layer jamming mechanisms to create a new grasping function with variable stiffness for different manipulation requirements. The movement of the soft gripper finger is produced by a cable-driven mechanism. However, particle and layer jamming chambers were embodied as a variable stiffness mechanism for the variable stiffness function. A single soft gripper finger module was developed and tested with particle and layer jamming chamber attached to it. The stiffness and response time of the soft gripper finger were measured in three distinct configurations: single finger module, particle jamming chamber attached to the finger, and layer jamming chamber attached to the finger. The comparison reveals that combining a soft finger with particle jamming increased performance by 20% compared to using the soft finger alone, while combining it with layer jamming led to an 80% increase. Additionally, layer jamming combined with a soft finger showed a 28% increase compared to particle jamming combined with a soft finger. Furthermore, simulation of the soft finger was conducted to estimate the deflection of the soft gripper finger under various applied forces. Moreover, proposed closed loop smart stiffness mechanism for the soft gripper was modeled and simulated by evaluating both soft and hard objects and simulation results were obtained for different cases. The findings indicated that the stiffness of the soft gripper finger can be adjusted for different grasping requirements.

Multi‐Material Gradient Printing Using Meniscus‐enabled Projection Stereolithography (MAPS)

AbstractLight‐based additive manufacturing methods are widely used to print high‐resolution 3D structures for applications in tissue engineering, soft robotics, photonics, and microfluidics, among others. Despite this progress, multi‐material printing with these methods remains challenging due to constraints associated with hardware modifications, control systems, cross‐contamination, waste, and resin properties. Here, a new printing platform coined Meniscus‐enabled Projection Stereolithography (MAPS) is reported, a vat‐free method that relies on generating and maintaining a resin meniscus between a crosslinked structure and bottom window to print lateral, vertical, discrete, or gradient multi‐material 3D structures with no waste and user‐defined mixing between layers. MAPS is compatible with a wide range of resins shown and can print complex multi‐material 3D structures without requiring specialized hardware, software, or complex washing protocols. MAPS's ability to print structures with microscale variations in mechanical stiffness, opacity, surface energy, cell densities, and magnetic properties provides a generic method to make advanced materials for a broad range of applications.

A Comparative Analysis and Scoping Review of Soft–Rigid and Industrial Parallel Rigid Grippers

In this research, it is aimed to present a comparative analysis of soft–rigid industrial parallel rigid grippers to compare their technical capabilities and assess the potential for soft–rigid grippers to address the challenge of grasping fragile objects with various shapes and sizes. In this research, 24 soft–rigid grippers are first identified through a scoping review using the Web of Science database, capturing their technical features and performance. Providing a variable stiffness grasp (n = 9, 37.5%) and a limited grasp capability (n = 8, 33.3%) is the most common advantage and challenge, respectively, of soft–rigid grippers. Pneumatic actuators (n = 12, 50.0%), followed by tendon‐driven electric rotary actuators (n = 9, 37.5%), are the predominant actuators used for soft–rigid grippers. Soft–rigid grippers are found to have a lower output force‐to‐weight ratio (n = 9, median , standard deviation (σ) = 15.17) in comparison to industrial parallel rigid grippers (n = 63, , ), but can provide a larger range of motion (n = 20, , ). This is the first quantitative comparative analysis between industrial parallel rigid and soft–rigid grippers, enhancing the understanding of their status and prospects in industrial applications. Herein, a common approach is proposed to standardize reporting to facilitate benchmarking between research‐based and industrial grippers and highlight controlling soft–rigid grippers is an underexplored area that can enhance the technology's performance.

Variable stiffness composite patch for single-sided bonded repair of composite structures

Variable stiffness composite patch for single-sided bonded repair of composite structures

Significant Within-Individual Variability in VCTE Liver Stiffness Measurements at Two Intercostal Spaces in Subjects with MASLD: Implications for Evaluating Improvement in Liver Fibrosis After Weight-Loss or Liver-Directed Therapy

Introduction: Studies have compared the group-averages of liver stiffness measures (LSMs) from multiple rib spaces by vibration-controlled transient elastography (VCTE) to stage liver fibrosis. No previous study has assessed within-individual liver stiffness variation from two rib spaces in individuals with metabolic-dysfunction associated steatotic liver disease (MASLD). Methods: We evaluated within-individual LSM variation according to body weight classification and its clinical implication. From October 2019 to March 2024, VCTE was performed on MASLD patients or those at high risk, in accordance with FibroScan guidelines. The LSMs were categorized into stages: <5 kPa (stage 0), 5–7.99 kPa (stage 1), 8–9.99 kPa (stage 2), 10–13.99 kPa (stage 3), and 14+ kPa (stage 4). Measurements with 10 values and IQR/median ≤ 0.30 were included, using SPSS V25.0 for analysis. Results: Among 1107 subjects (age 54.4 ± 13.9 years, 56.9% female), 7.7% were normal weight, 20.7% overweight, 28.9% class 1 obesity, 21.3% class 2 obesity, and 21.2% class 3 obesity. Significant within-individual variation was noted: 67% (0–2 kPa) variation, 23.4% (2.1–6 kPa), and 10% (≥6.1 kPa). Class 3 obese individuals had the maximum variation. Comparing the group-average of LSM at each ICS site showed that 95% of individuals were within one fibrosis stage. Conclusions: While LSM group-averages at different rib sites provides reliable fibrosis staging, significant within-individual variability exists especially in class 3 obesity. This should be considered when serial LSM assessments are used to assess medical therapeutic efficacy.

Center of mass kinematic reconstruction during steady-state walking using optimized template models.

Template models, such as the Bipedal Spring-Loaded Inverted Pendulum and the Virtual Pivot Point, have been widely used as low-dimensional representations of the complex dynamics in legged locomotion. Despite their ability to qualitatively match human walking characteristics like M-shaped ground reaction force (GRF) profiles, they often exhibit discrepancies when compared to experimental data, notably in overestimating vertical center of mass (CoM) displacement and underestimating gait event timings (touchdown/ liftoff). This paper hypothesizes that the constant leg stiffness of these models explains the majority of these discrepancies. The study systematically investigates the impact of stiffness variations on the fidelity of model fittings to human data, where an optimization framework is employed to identify optimal leg stiffness trajectories. The study also quantifies the effects of stiffness variations on salient characteristics of human walking (GRF profiles and gait event timing). The optimization framework was applied to 24 subjects walking at 40% to 145% preferred walking speed (PWS). The findings reveal that despite only modifying ground forces in one direction, variable leg stiffness models exhibited a >80% reduction in CoM error across both the B-SLIP and VPP models, while also improving prediction of human GRF profiles. However, the accuracy of gait event timing did not consistently show improvement across all conditions. The resulting stiffness profiles mimic walking characteristics of ankle push-off during double support and reduced CoM vaulting during single support.

Stress level dependent behavior of sand-rubber mixtures

This study investigates the mechanical behavior of sand-rubber mixtures, focusing on the influence of stress levels. Quantitative analysis reveals significant effects of stress levels on void ratio and coordination number, which become more pronounced with increasing rubber content. Small-strain stiffness could be affected by stress level by demonstrating unified relationships between small-strain stiffness and conventional state variables, with the coefficients of determination for fitted relationships increasing from 0.66 to 0.95 as rubber content increases from 0% to 80%. This is attributed to the impact of stress levels on conventional state variables. Alternative state variables that exclude rubber materials more effectively describe the small-strain characteristics of sand-rubber mixtures, suggesting that rubber materials should be excluded when considering these characteristics in practical engineering for conservation purposes. The stress level effect is also evident in the variation of stress ratios with axial strain, particularly when rubber content exceeds 25%, showing that higher stress levels restrict the mobilization of stress ratios for rubber materials. This study highlights the importance of considering stress level effects in the mechanical analysis of sand-rubber mixtures, which exhibit unique characteristics compared to natural sands in both compression and shearing behavior.

Soft fingers with variable stiffness for space gripping tasks: An assessment

The miniaturization of satellites and the problem of uncontrolled space debris demand highly flexible methods for space grippers. Soft grippers have surged as viable alternatives to overcome the limitations of traditional rigid grippers, such as lack of adaptability and dexterity. Although existent models have shown promising features, most have a high part count or make use of actuation systems that are inadequate for space, like pneumatic pumps or temperature-dependent materials. This work introduces novel designs of soft fingers that address the inherent challenges of grasping objects in space while overcoming these limitations. The proposed fingers use compliant structures based on several geometries of metamaterials. A detailed compliance and compressibility analysis is conducted using finite element methods to highlight the performance and behavior of each proposed design. Prototypes were fabricated, and their ability to exhibit different modes of actuation (variability in stiffness) by tendon compression was confirmed. The most apt design was selected and showcased in a three-fingered gripper to demonstrate the ability to grasp a given set of geometries with different sizes.

Dynamic of composite nanobeams resting on an elastic substrate with variable stiffness

This study introduces a novel approach by combining finite simulation and an enhanced shear deformation theory to analyze the dynamic behavior of multi-layer composite nanobeams supported by an elastic foundation. The calculation formulae are derived from nonlocal theory in order to account for the impact of size effect. An intriguing aspect of this research is the presence of intricate curved profiles in the two material layers of the beam. The elastic foundation exhibits varying stiffness throughout the beam's length, accounting for many imperfections in the beam and including the drag parameter of the material. These elements contribute to the steady evolution of the issue model towards more realistic structures. Nevertheless, the computation gets intricate and impedes the precise approach. However, our work has successfully resolved this difficult and significant difficulty using the two-node element. This research demonstrates the temporal evolution of the dynamic reactions of the point with the greatest displacement and velocity, as dictated by the law of change. Simultaneously, it also presents visual representations of every point on the beam as it undergoes temporal variations. These conclusions possess both scientific and practical value, establishing a foundation for real-world implementations.

Impact of Porosity and Stiffness of 3D Printed Polycaprolactone Scaffolds on Osteogenic Differentiation of Human Mesenchymal Stromal Cells and Activation of Dendritic Cells.

Despite the potential of extrusion-based printing of thermoplastic polymers in bone tissue engineering, the inherent nonporous stiff nature of the printed filaments may elicit immune responses that influence bone regeneration. In this study, bone scaffolds made of polycaprolactone (PCL) filaments with different internal microporosity and stiffness was 3D-printed. It was achieved by combining three fabrication techniques, salt leaching and 3D printing at either low or high temperatures (LT/HT) with or without nonsolvent induced phase separation (NIPS). Printing PCL at HT resulted in stiff scaffolds (modulus of elasticity (E): 403 ± 19 MPa and strain: 6.6 ± 0.1%), while NIPS-based printing at LT produced less stiff and highly flexible scaffolds (E: 53 ± 10 MPa and strain: 435 ± 105%). Moreover, the introduction of porosity by salt leaching in the printed filaments significantly changed the mechanical properties and degradation rate of the scaffolds. Furthermore, this study aimed to show how these variations influence proliferation and osteogenic differentiation of human bone marrow-derived mesenchymal stromal cells (hBMSC) and the maturation and activation of human monocyte-derived dendritic cells (Mo-DC). The cytocompatibility of the printed scaffolds was confirmed by live-dead imaging, metabolic activity measurement, and the continuous proliferation of hBMSC over 14 days. While all scaffolds facilitated the expression of osteogenic markers (RUNX2 and Collagen I) from hBMSC as detected through immunofluorescence staining, the variation in porosity and stiffness notably influenced the early and late mineralization. Furthermore, the flexible LT scaffolds, with porosity induced by NIPS and salt leaching, stimulated Mo-DC to adopt a pro-inflammatory phenotype marked by a significant increase in the expression of IL1B and TNF genes, alongside decreased expression of anti-inflammatory markers, IL10 and TGF1B. Altogether, the results of the current study demonstrate the importance of tailoring porosity and stiffness of PCL scaffolds to direct their biological performance toward a more immune-mediated bone healing process.

Decoupled robust backstepping tracking control for variable stiffness actuated robot with input saturation

Due to the energy storage and release capability introduced by stiffness adjustment, a variable stiffness actuator is essential to achieve human-like energy efficiency for robots. However, it is not trivial to control the strongly coupled and nonlinear system, especially with highly dynamic stiffness variation. In this work, decoupled and robust command filtered backstepping tracking controllers for position and stiffness are proposed. Furthermore, a disturbance observer is introduced to estimate the lumped disturbances caused by directly decoupled dynamics and unmodeling errors. Since the input control torques can be easily saturated due to limited deformation of elastic elements, anti-windup compensation is introduced into the tracking control laws to reduce its negative influence. Thus, by combining the command filtered backstepping controller, disturbance observers, and anti-windup compensation, the stability proof of the proposed composite controller is provided. The tracking control performance is validated through simulations of multi-DoF variable stiffness actuated robots.

Extracting fiber paths from the optimized lamination parameters of variable-stiffness laminated shells based on physic-informed neural network

This paper presents a novel approach for extracting fiber paths from the optimized lamination parameters (LPs) of variable stiffness laminated shells, utilizing the framework of physics-informed neural network (PINN). In this methodology, each fiber layer is associated with a specific stream function, which is approximated by an independent neural network. The stream function is governed by a partial differential equation (PDE) derived from the fiber orientation field in the parameter space. Moreover, the isocontours of the stream function are transformed into the actual fiber paths in the physical space. To account for manufacturing constraints, Riemannian geometry serves as a computational tool to determine the intrinsic distance between adjacent fiber paths and the geodesic curvature of the isocontours. By incorporating regularization terms into the loss function based on the physical relationships, the constrained optimization problem is converted into an unconstrained one, making it more suitable for neural network training. Meanwhile, a fiber path extraction (FPE) algorithm is used to minimize the loss function at randomly sampled points through gradient descent. The numerical results suggest that the extraction of fiber paths using PINN can achieve satisfactory levels of accuracy while effectively satisfying the imposed constraints.

Nonlinear Dynamics and Motion Bifurcations of 12-Pole Variable Stiffness Rotor Active Magnetic Bearings System under Complex Resonance

Nonlinear Dynamics and Motion Bifurcations of 12-Pole Variable Stiffness Rotor Active Magnetic Bearings System under Complex Resonance

Tendon‐Driven Stiffness‐Tunable Soft Actuator via Thermoelectric‐based Bidirectional Temperature Control

AbstractSoft robots have excellent spatial adaptability and high flexibility, but they are limited by the low stiffness of their constituent materials when faced with high‐load tasks. In recent years, there have been many works on the development of stiffness‐tunable soft actuators by introducing variable stiffness materials into soft actuators, but the existing solutions usually suffer from the problems of slow response, complex structure, and the need of many auxiliary devices to support the completion of the stiffness tuning cycle. This paper proposes a tendon‐driven stiffness‐tunable soft actuator that addresses these issues. Benefiting from the bidirectional temperature control of thermoelectric modules and the excellent in‐plane thermal conductivity of graphene, the actuator is capable of achieving the heating and cooling process by transferring the heat flow through the graphene structure into and out of the shape‐memory polymer (SMP) layer of the tendon‐driven actuator. This enables stiffness tuning via a single device, reducing the dependence on complex external cooling systems. The use of tendon‐driven actuators further eliminates the complex bellow structure of conventional pneumatic actuators and dramatically reduces the size and manufacturing difficulty of individual actuators. Finally, the high load capacity and shape adaptability of the actuator are demonstrated by a gripper equipped with three actuators, which successfully grips objects of various shapes and weights, ranging from less than 10 g to up to 1.6 kg.

A Crawling Robot with Temperature-Controlled Variable Stiffness Feet: Strong Surface Adaptability

Abstract Existing soft robots have not shown the same level of adaptability on diverse terrains when compared to natural animals that possess variable stiffness characteristics. In this paper, utilizing the mutual transformation between the glassy and molten states of rosin materials, temperature-controlled variable stiffness feet (TVSF) are achieved by filling the rosin into an array of soft cavity villi. A single motor is utilized as the vibration-driven actuator of the robot. It is found that the feet stiffness can be changed ranging from 0.6227 N/mm to 0.9611 N/mm, which has a significant impact on the robot’s velocity and follows a nonlinear relationship. A smooth motion surface requires a high-stiffness foot to provide support and stability for the robot, while a rough motion surface necessitates a low-stiffness foot to reduce friction and resistance allowing for quick movement for the driving voltage of 1.6 V. Furthermore, the TVSF enable stable operation on complex surfaces, including a 30°slope, pipes, and pothole surfaces. This research provides a new technological approach to designing and manufacturing variable stiffness robots with enhanced surface adaptability.

Model-based design of a mechanically intelligent shape-morphing structure

Soft robotics has significant interest within the industrial applications due to its advantages in flexibility and adaptability. Nevertheless, its potential is challenged by low stiffness and limited deformability, particularly in large-scale application scenarios such as underwater and offshore engineering. The integration of smart materials and morphing structures presents a promising avenue for enhancing the capabilities of soft robotic systems, especially in large deformation and variations in stiffness. In this study, we propose a multiple smart materials based mechanically intelligent structure devised through a model-based design framework. Specifically, the intelligent structure incorporates smart hydrogel and shape memory polymer (SMP). Employing the finite element method (FEM), we simulated the complex interactions among smart material to analyze the performance characteristics of the intelligent structure. The results demonstrate that, utilizing smart hydrogel and shape memory polymer (SMP) can effectively attain large deformation and exhibit variable stiffness due to the shape memory effect. Besides, the shape-morphing structures exhibit customized behaviours including bending, curling, and elongation, all while reducing reliance on external power sources. In conclusion, utilizing multiple smart materials within the model-based design framework offers an efficient approach for developing mechanically intelligent structure capable of complex deformations and variable stiffness, thereby providing support for underwater or offshore engineering applications.

Design method for individualised 3D printed lattice shoe midsoles

Additive manufacturing has enabled the production of individualised 3D printed shoe soles with improved properties. A promising approach is to use lattice structures that have high energy absorption properties and low weight. A design method of a cellular shoe midsole with optimised strut diameters of lattice structures is proposed. The shoe sole model is obtained by re-modelling a 3D scan of a foot to ensure a customised fit. The optimisation of strut thicknesses is based on a simplified stress distribution acting on the shoe sole during walking or running, using finite element simulations. Therefore, the optimal strut thickness for each region of the sole can be determined and adjusted. Two types of lattice structures with different topology and thus significant variations in stiffness are chosen, resulting in a wide range of required strut thicknesses. The developed design process allowed for the creation of a 3D printed shoe sole with improved strut thicknesses and a customised fit. The resulting cellular shoe soles are additively manufactured and experimental compressive tests are conducted to investigate the mechanical behaviour and differences between the shoe soles with the corresponding lattice types. The results show that both shoe soles have a similar behaviour under compression. The design tool developed has the potential to improve foot health and comfort, especially for people with foot problems, as all parameters affecting the performance of a shoe sole can be adjusted. However, more research is needed to fully understand the durability and performance of these shoe soles in real-world conditions.

Flexible Continuum Robot with Variable Stiffness, Shape‐Aware, and Self‐Heating Capabilities

Conventional continuum robots have outstanding flexibility and dexterity. However, when the robot needs to interact with the environment, the softness may affect the performance of the robot. Especially in transport tasks, the softness of continuum robots can lead to handling failures and drastic drops in precision. The variable stiffness continuum robot combines the advantages of flexibility and rigidity, which is conducive to expanding the application scenarios of flexible continuum robots. This article proposes a flexible continuum robot that simultaneously realizes variable stiffness, shape‐aware, and self‐heating functions using liquid metal. The low‐temperature phase transition property of liquid metal is utilized to realize the variable stiffness function; the overall stiffness of the robot can reach the range of 18.5–183 N m−1, which can realize a tenfold stiffness gain. The conductivity of liquid metal is utilized to develop the shape‐aware function, and the monitoring accuracy is within 5%. At the same time, this article utilizes the liquid metal's resistive thermal effect to realize heating function, so that the robot no longer needs heating systems such as heating wires and can realize the phase transition by energizing itself. Based on this design, the robot arm can realize the transition between maximum and minimum stiffness within 240 s.

Research on the dynamic variation law of the discontinuous characteristics of the curvic coupling of aero-engine rotors under working conditions

For the design of advanced aero-engine rotor systems under ultra-high rotational speeds, this paper undertakes a comprehensive investigation into the contact stiffness of curvic couplings, which are the key connection mechanism of modern aero-engine rotors, and explores the dynamic variations in the contact stiffness of curvic couplings under working conditions. Firstly, the impact of dynamic loads of aero-engine rotors under working conditions on the curvic coupling is studied; Then, the contact stiffness analytical model of curvic couplings considering three-dimensional geometric features is proposed with the effects of dynamic loads; Finally, based on the established stiffness model, the dynamic loss laws of contact stiffness of curvic couplings under different dynamic loads are investigated, and the established model is experimentally validated. The results show that the dynamic loss law of contact stiffness varies with different dynamic loads. In comparison to the contact stiffness under the static condition, dynamic loads significantly reduce the contact stiffness of curvic couplings under working conditions, which in turn leads to changes in the dynamic characteristics of the rotor with curvic couplings. For the safe integration of the discontinuous rotor system under ultra-high rotational speeds, it is essential to carefully design and regulate the operating speed, transmission torque, unbalanced mass, and preload.

Understanding the role of chain stiffness in the mechanical response of cross-linked polymer: Flexible vs. semi-flexible chains

Cross-linked polymers are widely used in structural, engineering, and biomedical applications due to their lightweight and superior properties. Although chain bending stiffness has been recognized to play an essential role in their thermodynamical and mechanical properties, how it influences these properties of cross-linked polymers with flexible or semi-flexible chains remains under debate. Here, we systematically explore its influences utilizing coarse-grained (CG) molecular dynamics (MD) simulations based on a bead-spring CG model. It is found that with chain bending stiffness increasing, both density and elastic moduli (i.e., shear modulus and tensile modulus) of cross-linked polymers first decrease slightly and then decrease significantly followed by a gradual increase, along with the polymer transition from a dense cross-linked thermoset to a highly porous fibrous network. The moduli of cross-linked polymers with flexible and semi-flexible chains exhibit distinct scaling laws with the density. For cross-linked polymers with flexible chains, their moduli increase significantly with increasing strain rate, which correlates to the change in potential energy of interchain interaction during deformation. However, the moduli display slight dependence on strain rate for porous cross-linked polymers with sufficiently stiff chains, where the intrachain interactions (i.e., bond stretching and angle bending energies) become dominant and independent of strain rate. Moreover, the elastic moduli exhibit scaling laws with Debye-Waller factor for both dense cross-linked thermosets with flexible chains and highly porous networks with stiff backbones. Our work facilitates a better understanding for mechanical properties and deformation mechanism of cross-linked polymers with variable chain bending stiffness at molecular level, shedding light on tailoring mechanical properties of cross-linked polymers via chain engineering.