Variable Stiffness Structure Research Articles

Experimental and numerical studies on buckling and post-buckling behavior of T-stiffened variable stiffness panels

Currently, experimental research on variable stiffness design mainly focuses on laminates. To ensure adaptability in practical application, it is imperative to conduct a systematic study on stiffened variable stiffness structures, including design, manufacture, experiment, and simulation. Based on the minimum curvature radius and process schemes, two types of T-stiffened panels were designed and manufactured. Uniaxial compression tests have been carried out and the results indicate that the buckling load of variable stiffness specimens is increased by 26.0%, while the failure load is decreased by 19.6%. The influence mechanism of variable stiffness design on the buckling and failure behavior of T-stiffened panels was explicated by numerical analysis. The primary reason for the reduced strength is the significantly increased load bearing ratio of stiffeners. As experimental investigations of stiffened variable stiffness structures are very rare, this study can be considered a reference for future work.

Modelling and characterisation of a magnetically coupled piezoelectric beam for energy harvesting gear meshing motion

Gear transmission systems are crucial components for transmitting power and motion in a host of engineering applications. Recently, the potential to embed sensors into transmission components has attracted significant attention for accurate condition monitoring of system health. As a result, embedded sensors must operate in a safe and stable manner, whilst being able to provide a continuous power-supply and ensure operational autonomy. In this work, a magnetically coupled beam-type piezoelectric energy harvester is developed for energy harvesting of rotational centrifugal forces and individual gear meshing excitation events. A new coupled electromechanical dynamic model is developed to explain the working principle and response of the harvester when excited by a combination of gear meshing excitation events, a centrifugal force, and a magnetic force. Since gear meshing events are observed to lead to an increased hardening nonlinearity of the energy harvester, and a decrease in power output, a novel variable-section cantilever structure was developed. Our detailed theoretical analysis demonstrates that the novel variable stiffness structure improves both the power output and bandwidth, with excellent agreement with experimental measurements. This work provides new theoretical insights into the application of magnetically coupled piezoelectric energy harvesters for self-powered sensing systems for critical gear transmission systems.

A variable stiffness design method for soft robotic fingers based on grasping force compensation and linearization

Abstract Soft fingers play an increasingly important role in robotic grippers to achieve adaptive grasping with variable stiffness features. Previous studies of soft finger design have primarily focused on the optimization of the structural parameters of existing finger structures, but limited efforts have been put into the design methodology from fundamental grasping mechanisms to finger structures with desired grasping force features. To this aim, a fundamental architecture of soft fingers is proposed for analyzing common soft finger features and the influence of the internal structures on the overall grasping performance. In addition, three general performance metrics are introduced to evaluate the grasping performance of soft finger designs. Then, a novel method is proposed to combine the variable stiffness structure with the fundamental architecture to compensate for the grasping force of the finger and linearization. Subsequently, an embodiment design is proposed with a cantilever spring-based variable stiffness (CSVS) mechanism based on the method, and a multi-objective optimization method is employed to optimize the design. Besides, the CSVS features are analyzed through finite element analysis (FEA), and by comparing the grasping performance between the V-shape finger and the CSVS finger, it is demonstrated that the design method can effectively shorten the pre-grasp stage and linearize the grasping force in the post-grasp stage while reducing the likelihood of sliding friction between the finger and the grasped object. Finally, experiments are conducted to validate the accuracy of the FEA model, the effectiveness of the design methodology, and the adaptability of the CSVS finger.

Optimization design and 3D printing of curvilinear fiber reinforced variable stiffness composites based on polar coordinate sweeping

The 3D printing of curvilinear fiber reinforced variable stiffness structures (CFRVSSs) provides new opportunities for innovative design and fabrication of complex components in response to rising demand for high-performance and lightweight components in aerospace, railway, and other fields. In this paper, we get rid of the limitations of existing research on the structure of open-hole plates and aim to investigate complex structures with large curvature. Considering the characteristics of 3D printing and service load, an optimization design method based on polar coordinate sweeping was proposed for CFRVSSs. The consistency factors between the fiber distribution (direction, content) and stress distribution (direction, magnitude) were established. Through quantitative analysis, the directional consistency factor between the optimized local fibers and stresses was enhanced by a factor of 3.69, and the correspondence factor between the fiber content and the stress magnitude was enhanced by a factor of 3.8. Furthermore, the calculation method for curve spacing and curve arc length based on polar coordinate sweeping were proposed to minimize the forming errors caused by CFRVSSs 3D printing. The design and fabrication of a high-speed rail tie rod structure were carried out using the optimization design method and 3D printing process in current research. As a result, the ultimate tensile strength of the optimized curvilinear fiber reinforced tie rod structure increased by 156 % compared to the unoptimized straight-line fiber reinforced tie rod structure. The method proposed in this study has a wide range of applications for the design and fabrication of complex components with large curvature in the engineering field.

Shape Programmable and Multifunctional Soft Textile Muscles for Wearable and Soft Robotics

Textiles are promising candidates for use in soft robots and wearable devices due to their inherent compliance, high versatility, and skin comfort. Planar fluidic textile‐based actuators exhibit low profile and high conformability, and can seamlessly integrate additional components (e.g., soft sensors or variable stiffness structures [VSSs]) to create advanced, multifunctional smart textile actuators. In this article, a new class of programmable, fluidic soft textile muscles (STMs) that incorporate multilayered silicone sheets with embedded fluidic channels is introduced. The STMs are scalable and fabricated by apparel engineering techniques, offering a fabrication approach able to create large‐scaled multilayered structures that can be challenging for current microfluidic bonding methods. They are also highly automation compatible due to no manual insertion of elastic tubes/bladders into textile structures. Liquid metal is employed for creating fluidic channels. It is not only used for actuation but also used as channels for additional features such as soft piezoresistive sensors with enhanced sensitivity to STMs’ pressure‐induced elongation, or VSSs of either low‐melting‐point alloys or a new thermo‐responsive epoxy with low viscosity and transition temperature. The STMs hold promising prospects for soft robotic and wearable applications, which is demonstrated by an example of a textile‐based wearable 3D skin‐stretch haptic interface.

Muscle-inspired stiffness-tunable flexible fiber jamming structure for wearable robots *

Soft robotics have found their tremendous application prospects in wearable robots due to the inherent compliance of soft materials when interacting with human bodies. However, the limited load-bearing and output capabilities impeded their application in real world. Variable stiffness design contributes to tackling this problem by enhancing the overall structural rigidity. Nevertheless, most of current jamming-based variable stiffness structures realize their stiffness enhancement by squeezing discrete rigid elements, resulting in the loss of structural compliance in the high stiffness state, which could significantly reduce the deformability and even injure the individuals when utilized in wearable robots. In this paper, we propose a muscle-inspired stiffness-continuously-adjustable flexible fiber jamming (FFJ) structure for soft wearable robots. The FFJ structure can achieve continuous stiffness-variation by controlling the fiber overlapping length, which maintains stretchability even in the high stiffness state. We provide a theoretical model to analyze the mechanical performance of the proposed FFJ structure with different design parameters, and verify the model experimentally. The preliminary results show that we achieved 9 times of stiffness enhancement of the proposed FFJ structure by controlling the vacuum pressure, and the maximum tensile stiffness is 4.1 N mm−1. We further demonstrated the effectiveness of the proposed FFJ structure on wearable robots in three different working scenarios: active finger rehabilitation, active elbow rehabilitation, and passive trunk support. The results show that the FFJ structure was able to provide controllable impedance force for active finger/elbow rehabilitation, and help support the human body during long-term labor. This work broadens the frontiers of soft wearable robots and leads a way to the future design of soft and strong robots and devices.

Intelligent design and buckling experiment of curvilinearly stiffened thin-walled structures

Curvilinearly stiffened variable-stiffness structures offer excellent load-bearing capacities and design flexibility, particularly for thin-walled structures with cutouts. Nevertheless, the complex combination of numerous variables, buckling failure modes, and unclear load-carrying mechanisms present significant challenges to structural analysis and optimization. Hence, a unified characterization method for nonuniform layouts and variable thicknesses is proposed and an intelligent optimization framework based on structural image learning is established. Buckling experiments on two stiffened panels and a corresponding numerical analysis are performed to verify the effectiveness of the method under axial compressive loading. Results show that the curvilinearly stiffened panel exhibits a superior load-bearing capacity of 28.8% compared with an orthogonally stiffened panel. Specifically, the curvilinearly stiffened panel efficiently transfers axial loads to a broader region and avoids interruptions in the force transmission path by cutouts, thereby resulting in material and buckling failures simultaneously.

Soft electroadhesive grippers with variable stiffness and deflection motion capabilities

Soft gripper robots provide superior safety, adaptability, and compliance compared to rigid robots. However, soft grippers must address inadequate stiffness and interference resistance. Soft pneumatic electroadhesion (EA) grippers with variable stiffness are potential options for addressing these difficulties. In this paper, we present a soft bionic gripper (SOBG) that resembles human finger movements, such as bending and deflection, employing pneumatic actuation, and whose stiffness is effectively decoupled from its position through a layer jamming-induced variable stiffness structure. By applying electroadhesive forces, the SOBG can perform complex motion tasks that would typically require a wrist joint, making them simpler to perform than with conventional flexible grippers. In addition, the SOBG can perform one-finger object manipulation to grasp flat, concave, and convex objects. To show the potential for more complex robotic applications, we evaluated each function independently by presenting a demonstration of cap-screwing, a material handling system, and an anti-interference research. The SOBG concept and solution proposed in this study may pave the way for the easy integration of EA into soft robotic systems and promote the wider use of EA technology.

Variable stiffness structure inspired by seashells

Variable stiffness is typically employed in soft robotics to address the trade-off between compliance and the ability to generate stability when required. Among the several approaches investigated, jamming transition systems show remarkable stiffness performance and fast response. Building upon the preliminary study on a seashell bioinspired variable stiffness structure, here we extend the design space through a parametric study supported by a finite element model based on commercially available software. The study allows establishing the relationship between the design parameters and the stiffness performance. Moreover, the optimal configuration in terms of performance to energy consumption is identified and compared to previous similar approaches. Finally, the low computational cost of the finite element model demonstrated to be an effective tool for the analysis of complex geometries, thereby establishing a foundation for the development of cost-effective and lightweight soft robotic devices empowered by variable stiffness capabilities (e.g. a wearable device for assistance).

Design and Experiment Investigation on Soft Grippers with Modular Variable Stiffness Structure.

Soft grippers have good adaptability and flexibility for grasping irregular or fragile objects, and to further enhance their stiffness, soft grippers with variable stiffness have been developed. However, existing soft grippers with variable stiffness have the disadvantages of complex structure and poor interchangeability. Here, a soft gripper with modular variable stiffness is proposed that has flexible Velcro embedded in the bottom layer of the soft actuator and one side of the variable stiffness cavity respectively, and both the general and variable stiffness grasping modes are achieved by separation or combination. First of all, according to the neo-Hookean model and the assumption of constant curvature, a free bending model of the soft actuator is established and optimal structural parameters of the soft actuator are obtained by the Genetic Algorithm. Then, influence of the driving pressure on the soft actuator stiffness is investigated, and a mathematical model of the variable stiffness is established. Finally, correctness of the statics model and the stiffness model were verified by experiments. Experimental results indicate that the proposed soft gripper with modular variable stiffness structure has excellent adaptability and stability to different objects, outstanding load bearing capacity, and stiffness adjustment capability.

Performance Optimization for Bionic Robotic Dolphin with Active Variable Stiffness Control.

Aquatic animals such as fish and cetaceans can actively modulate their body stiffness with muscle to achieve excellent swimming performance under different situations. However, it is still challenging for a robotic swimmer with bionic propulsion mode to dynamically adjust its body stiffness to improve the swimming speed due to the difficulties in designing an effective stiffness adjustment structure. In this paper, based on the special torque mode of a motor, we propose an active variable stiffness control method for a robotic dolphin to pursue better swimming speed. Different from a variable stiffness structure design, a torque control strategy for the caudal motor is employed to imitate the physical property of a torsion spring to act as the variable stiffness component. In addition, we also establish a dynamic model with the Lagrangian method to explore the variable stiffness mechanism. Extensive experiments have validated the dynamic model, and then the relationships between frequency and stiffness on swimming performance are presented. More importantly, through integrating the dynamic model and torque actuation mode-based variable stiffness mechanism, the online performance optimization scheme can be easily realized, providing valuable guidance in coordinating system parameters. Finally, experiments have demonstrated the stiffness adjustment capability of the caudal joint, validating the effectiveness of the proposed control method. The results also reveal that stiffness plays an essential role in swimming motion, and the active stiffness adjustment can significantly contribute to performance improvement in both speed and efficiency. Namely, with the adjustment of stiffness, the maximum speed of our robotic dolphin achieves up to 1.12 body length per second (BL/s) at 2.88 Hz increasing by 0.44 BL/s. Additionally, the efficiency is also improved by 37%. The conducted works will offer some new insights into the stiffness adjustment of robotic swimmers for better swimming performance.

A high load capacity and efficient-transporting inchworm-like crawling robot with bistable structure and pneumatic networks actuator

Although pneumatic soft crawling robots have made great progress, there are still several difficulties hindering their practical progress, the most important of which is the insufficient stiffness and the insufficient load capacity under large deformations. An inchworm-like soft crawling robot with load capacity and deformability is proposed in this paper. Bistable composite structures are typically smart morphing variable stiffness structures with lightweight, good stiffness under large deformations and possessing two stable configurations. Instead of traditional materials with high Young’s modular, the inchworm-like crawling robot, which consists of a stiffness-enhancing hybrid actuator integrating a bistable shell with a soft pneumatic actuator for the main body and two bristle structures for the feet, has lightweight, flexibility, and high stiffness under large deformations. By controlling the stiffness-enhanced hybrid actuator, the robot is capable of achieving crawling and reversing motions like an inchworm. Experimental results show that the tip output force of the inchworm-like deformed trunk was five times larger than a single pneumatic actuator, which means that the inchworm-like robot owns excellent driving performance and flexibility. The collapse of an inchworm-like deformed trunk with 100 g load is less than the collapse of a single pneumatic networks actuator. This also demonstrates that the bistable structure exactly improves the load capacity of the crawling robot. The periodic bending-flattening motion of the actuator is transformed into the unidirectional crawling motion of the robot by installing feet on both sides of the actuator. The crawling robot also can perform well in environments with different angles, heights, and surfaces, which is verified by experiments. The inchworm-like crawling robot provides a method to improve the load capacity while maintaining the flexibility of soft robots and demonstrating huge practicability in field exploration and goods transportation.

Buckling stability of variable stiffness composite cylinder shell based on automated fiber placement technology

Automated fiber placement technology (AFP) is the key technology to realize variable-stiffness design that have fiber orientation variation across its in-plane. However, defects such as fiber angle deviation and overlap are inevitable during AFP manufacturing. A finite element model has been developed for variable-stiffness cylinder shell that can investigate the effect of the overlap areas and fiber angle deviation on the buckling stability of variable stiffness cylinder shell. Furthermore, the influence of the design parameters of the curved fiber path and the process parameters such as the tow width, the number of tow feeding, and the overlapping strategies on the buckling performance of the structure was studied by parametric analysis. The results showed under the condition of compression-bending coupling, the buckling performance is improved by the variable stiffness design in which the fiber angle varies along the circumferential direction, the maximum critical buckling load factor of optimal variable-stiffness design [0 /〈30|80〉/ 90 /−〈30|80〉] s is 10771, which is 21.1% higher than that of the optimal normal stiffness design. It is found that increasing the course width reduces the buckling performance of the variable stiffness structure, when the tow width is kept constant. When the course width is kept constant, the buckling performance of the variable stiffness structure increases with the increase of the tow width.

Design and analysis of a novel flexible variable stiffness damping mechanism for grinding electric spindle

The purpose of this research is to design a flexible variable stiffness damping mechanism to solve the load impact problem in the grinding process of permanent magnet electric spindle. Firstly, combined with the structure and usage scene of the grinding permanent magnet electric spindle, according to the design principles and technical indicators, a novel flexible variable stiffness vibration damping joint is proposed. Then the stiffness and energy storage model of the flexible variable stiffness damping mechanism is established, and the stiffness and energy storage characteristics of the mechanism are analyzed. The strength and dynamic characteristics of the flexible variable stiffness mechanism are analyzed by Ansys and Adams, respectively. Finally, an experimental platform for the comprehensive performance verification of the flexible variable stiffness damping mechanism is built to verify the dynamic characteristics and damping effect of the mechanism. The research results show that the designed flexible variable stiffness structure has better vibration damping effect and can improve the grinding performance of the permanent magnet electric spindle.

Research on a Variable-Stiffness Joint and Its Application in Actuators

Variable-stiffness actuators can flexibly adjust the overall or local stiffness of a structure, thus enabling reconstruction, adaptation, and locking capabilities that can meet a wide range of task requirements. However, the programmable design and manufacture of three-dimensional (3D) variable-stiffness actuators has become a challenge. In this paper, we present a method to develop the 3D structure of variable-stiffness actuators that combines variable-stiffness joints with 3D printing technology. The variable-stiffness joints were obtained by arranging steel needles wrapped with enameled copper wire inside the grooves of a polylactic acid (PLA) structure and bonding the three components with silicone glue. First, a variable-stiffness joint was used as a variable-stiffness node and subjected to 3D printing to realize multiple 3D variable-stiffness designs and manufacture a programmable structure. Then, using the repulsive force between paired magnets, we developed a driving actuator for the 3D variable-stiffness structure, enabling the expansion and deployment functions of the structure. In addition, an electromagnetically driven mechanical gripper was designed based on variable-stiffness joints to effectively decrease the driving energy in applications where objects are held for extended periods using variable-stiffness control. Our study provides practical solutions and guidance for the development of 3D variable-stiffness actuators, contributing to the achievement of more innovative and practical actuators.

Isogeometric degenerated shell formulation for post-buckling analysis of composite variable-stiffness shells

Variable-stiffness (VS) laminated shells with curved fibers have gradually become a promising lightweight structural concept in the aerospace field. However, as the complexity of the shell geometry and the fiber angle increases, the traditional finite element method (FEM) requires mesh refinement to guarantee accurate discretization, which significantly increases the computational cost, especially in the post-buckling analysis with multiple solving requirements. In this study, a non-uniform rational B-Splines (NURBS)-based degenerated solid shell formulation in the total Lagrangian framework is proposed for the post-buckling analysis of VS laminated shells. Since the nonlinear function related to the rotational degrees of freedom (DOFs) is additionally introduced into the displacement field expression, the restriction on the magnitude of the nodal rotations is effectively eliminated. In addition, the paper adopts the NURBS surface reconstruction technology based on the point-line-surface features to build B-spline CAD models from the point cloud with geometric imperfect features. Then, an integrated modeling-analysis framework for predicting the post-buckling behavior of VS structures with geometric imperfections is proposed. A series of numerical examples systematically demonstrate that the framework can effectively conduct the post-buckling analysis of shell structures with geometric imperfections. Meanwhile, the accuracy and robustness of the solutions by IGA are proved to be better than FEM.

Dynamic Performance of Hygrothermal Mechanically Preloaded Variable-Stiffness Composite Fairing Structures

Since the introduction of variable-stiffness composites, the design philosophy for high-performance lightweight composite structures has broadened greatly. Indeed, variable-stiffness composites have been shown to increase buckling performance and dynamic stability, as well as to modify the dynamic response by tailoring stiffness distributions. Thus, efficient linear analysis tools play a significant role in the early design of variable-stiffness structures, allowing designers to identify many viable solutions when considering preloaded dynamically excited aerospace components. To address this need, a Ritz-based method for eigenfrequency and dynamic instability analysis of hygrothermal and mechanically prestressed variable-stiffness laminated doubly curved payload fairing structures is presented. Flexibility in modeling and design is achieved using Sanders–Koiter-based shell kinematics that allow general orthogonal surfaces to be modeled without further assumptions on the shallowness or on the thinness of the structure. The efficiency of the proposed Ritz method is enabled by using Legendre orthogonal polynomials as displacement trial functions. By comparing the present approach with finite element solutions for variable-curvature, variable-angle tow fairing shell geometries, excellent accuracy is shown, accompanied by an order-of-magnitude reduction in variables by the present method. Original solutions are presented comparing the dynamic behavior of prestressed constant and variable-stiffness composite shell structures, showcasing the viability of the variable-stiffness concept to significantly increase the structural performance of critical doubly curved variable-curvature components such as launch vehicle payload fairings.

Programmable Design and Fabrication of 3D Variable–Stiffness Structure Based on Patterned Graphene‐Heating Network

The 3D variable–stiffness structure can realize shape programming, reconstruction, adaptation, and locking, and therefore, it has a wide design creation space. Accurate local stiffness control is of considerable significance to the design and application of 3D variable–stiffness structures although it is challenging. Herein, a 3D variable–stiffness structure realization scheme based on a patterned heating network is introduced. The laser‐engraving and 3D‐printing technologies are combined to obtain a 3D variable–stiffness structure composed of a patterned graphene‐heating network (PGHN) and polylactic acid (PLA). The proposed scheme uses PGHN to accurately control the local stiffness of 3D PLA and realize programmable design and fabrication of 3D variable–stiffness structures. The “torsional structure,” “hexagonal structure,” and “spring” cases are used to elaborate the designability, excellent deformation and reconstruction capacity, and reasonable load bearing capacity of the PGHN/PLA variable–stiffness structure. A pneumatic disc, which is used as a reference for studies on shape control of PGHN/PLA variable–stiffness structures, is designed. Also, a pneumatic robot is designed based on the local stiffness control and shape‐locking function of PGHN/PLA to achieve multimode motion control using a single air source. The PGHN/PLA variable–stiffness structure has potential applications in multimode robots, wearable devices, and deployable structures.

On variable stiffness of flexible parallel electroadhesive structures

Electrostatic layer jamming represents a lightweight, low energy consumption, electrically tunable, and cost-effective variable stiffness structure. Flexible parallel electroadhesive structures are the simplest form of electrostatic layer jamming. There is a lack of comprehensive and experimentally validated theoretical variable stiffness models of flexible parallel electroadhesive structures. Here we present the first variable stiffness model of flexible parallel electroadhesive structures under three-point bending, cantilever beam bending subjected to tip concentrated forces, and cantilever beam bending subjected to uniformly distributed forces, using the Euler–Bernoulli beam theory and considering friction and slip between layers by integrating the Maxwell stress tensor into the model. We find that: (1) three-point bending and cantilever beam bending under tip concentrated forces only have pre-slip and full-slip, whereas cantilever beam bending under uniformly distributed forces has an additional partial-slip which can be used for stiffness modulation; (2) the stiffness during the pre-slip stage is four times larger than the stiffness in the full-slip stage; and (3) increasing the voltage, dielectric permittivity, and coefficient of friction can elongate the pre-slip stage, thus enhancing the structural load capability. A customized three-point bending and a cantilever beam bending experimental setup were developed and the experimental deflection–force curve agreed relatively well with the theoretical one. The model, which considered electrode thickness and Young’s modulus, and the results presented in this work are useful insights for understanding the variable stiffness mechanism of electroadhesive layer jamming and are helpful for their structural optimization towards practical applications.

Sizing optimization and experimental characterization of a variable stiffness shape memory polymer filled honeycomb composite

Variable stiffness structures and materials have been considered for many applications, including active vibration control and shape morphing. With regards to shape morphing, variable stiffness materials and composites have been considered for reconfigurable skin materials in aerospace vehicles. Of the many concepts that have been developed for such applications, shape memory polymers (SMPs) are one such promising materials for shape morphing. SMPs exhibit both high modulus ratios and recoverable strains but suffer from a low overall modulus and often require reinforcements, such as honeycomb. This work investigates the design space of such honeycomb reinforced SMPs as variable stiffness materials. Unit cell finite element models are developed for the material, and parametric studies are completed for varying honeycomb cell geometries. A multiobjective, constrained Pareto front optimization is completed for two honeycomb material models and in two loading directions using selected sizing design variables. Pareto fronts are established, and cell geometries are selected and fabricated to experimentally verify the optimized model predictions. The results both predict and demonstrate the advantages of using honeycomb reinforcements for SMPs. Effective in-plane moduli as high as 45 GPa are predicted while achieving a change in modulus of 450X. Compared to existing reinforcement strategies for shape memory polymers, these composites exhibit favorable combinations of both high stiffness and high changes in stiffness with a high degree of tailorability through the honeycomb cell geometry and predicted performances that meet and exceed the state of the art.