Variable Stiffness Structure Research Articles

Investigation of buckling characteristics of cracked variable stiffness composite plates by an eXtended Ritz approach

Variable Angle Tow (VAT) composite plates are characterized by in-plane variable stiffness properties, which opens to new concepts of stiffness tailoring and optimization to achieve higher structural performance for advanced lightweight structures where damage tolerance consideration are often mandatory. In this paper, a single-domain eXtended Ritz formulation is proposed to study the buckling behaviour of variable stiffness laminated cracked plates. The plate behaviour is described by the first order shear deformation theory whose generalized displacements, namely reference plane translations and rotations, are expressed via suitable admissible trial functions. These consist of a set of regular terms, built using orthogonal polynomials, augmented with special functions able to describe the crack opening and the singular behaviour at the crack tips; boundary functions are used to ensure the required homogeneous essential boundary conditions. Governing equations are inferred via the stationarity of the energy functional an solved to carry out an extensive study on the buckling behaviour of variable angle tow homogeneous and layered composite plates. The results obtained for homogeneous plates evidence that the crack presence strongly influences the buckling behaviour depending on its length and inclination and plate boundary conditions with a meaningful variability with respect to the fibre paths configuration, which can arrange for better performances with respect to the straight fibre case. Also for cracked laminates the results show that there are several fibre path able to provide higher buckling loads and higher overall axial stiffness with respect to the straight fibre case. In the framework of damage tolerant engineering applications, this allows to select fibre paths that guarantee predefined design levels of buckling load and axial stiffness even in presence of cracks. Finally, this study highlights the potential of the proposed approach for the analysis of the buckling behaviour of cracked composite variable stiffness plates, which provides an efficient analysis tool for the damage tolerant design and optimization of advanced variable stiffness structures.

Bio‐Inspired Conformable and Helical Soft Fabric Gripper with Variable Stiffness and Touch Sensing

AbstractThere are many instances in nature where continuum, helical manipulators are used to efficiently grasp different objects with various shapes and sizes. Inspired by nature, this paper introduces a continuum, flat, scalable, helical soft‐fabric robotic gripper that is thin and lightweight with stiffness tunability and sensory feedback. The gripper is fabricated by a facile method of simple insertion using a computerized technique from apparel engineering and controlled by a miniature hydraulic source to grasp different objects at different scales and weights. It uses a thermally activated variable stiffness structure (VSS) for high load capacity that can complete a softening‐stiffening cycle within 24 s, which is among the fastest results reported so far. In addition, a highly stretchable liquid metal‐based soft sensor with an enhanced sensing sensitivity (15 times more sensitive compared to conventional designs) is embedded into the gripper to provide real‐time touch sensing. The gripper successfully grasped various objects of different geometries and weights (up to 220 times of its mass) and retrieved them from confined hollow spaces. Its excellent performance and versatility make it an ideal candidate for various domains, including industry, exploration, rescue, and other applications in confined and hazardous environments such as gas/oil or drainage sectors.

An element-free study of variable stiffness composite plates with cutouts for enhanced buckling and post-buckling performance

In this paper, an efficient element-free modeling framework for variable stiffness composite laminates with cutouts is developed. In comparison with other numerical methods or semi-analytical methods, element-free meshless methods offer many advantages in modeling variable stiffness materials and structures, e.g. complex geometries with cut-outs, providing accurate stress computations and stable nonlinear behavior modeling. In this study, an element-free Galerkin (EFG) method based modeling framework is developed to model variable stiffness composite plates containing circular holes, specifically for buckling and post-buckling analysis. Weighted orthogonal basis functions are used to further reduce the computational costs of the meshless method. Modeling accuracy for variable stiffness composite structures using node-based fiber angle definitions in this element-free framework are validated against FEM results obtained from ABAQUS. The critical buckling loads of linearly varying fiber composite laminates with different sizes of central circular holes are then computed. Based on the proposed element-free modeling scheme, nonlinear post-buckling equilibrium paths of variable stiffness composite plates are traced using an incremental loading step control method, which enables efficient post-buckling analysis. Changes in both critical buckling loads and nonlinear post-buckling performance with respect to hole size and the linear variation of fiber angles are investigated with the results presented in the form of parametric studies. The numerical results show that stress redistribution remains the major factor driving improvements in the buckling and post-buckling performance of variable stiffness composite plates with cut-outs. The research work presented in this paper for composite plates with linearly varying stiffness provides a basis for the analysis of general variable stiffness soft materials in the future.

Phase Changing Materials-Based Variable-Stiffness Tensegrity Structures.

Soft robots leverage deformable bodies to achieve different types of locomotion, improve transportability, and safely navigate cluttered environments. In this context, variable-stiffness structures provide soft robots with additional properties, such as the ability to increase forces transmitted to the environment, to lock into different body configurations, and to reduce the number of actuators required for morphological change. Tensegrity structures have been recently proposed as a biologically inspired design principle for soft robots. However, the few examples of tensegrity structures with variable stiffness displayed relatively small stiffness change (i.e., by a factor of 3) or resorted to multiple and bulky actuators. In this article, we describe a novel design approach to variable-stiffness tensegrity structures (VSTSs) that relies on the use of variable-stiffness cables (VSCs). As an example, we describe the design and implementation of a three-strut tensegrity structure with VSCs made of low melting point alloys. The resulting VSTS displays unprecedented stiffness changes by a factor of 28 in compression and 13 in bending. We show the capabilities of the proposed VSTS in three validation scenarios with different tensegrity architectures: (1) a beam with tunable load-bearing capability, (2) a structure that can self-deploy and lock its shape in both deployed and undeployed states, and (3) a joint with underactuated shape deformations.

State space modelling of variation propagation in multistage machining processes for variable stiffness structure workpieces

Satisfying the quality requirement of products in multistage machining processes (MMPs) is significant and challenging nowadays. In spite of the success of the stream of variation (SoV) theory in variation propagation modelling for MMPs, the absence of elastic deformation variations could be an important factor that limits its application in variable stiffness structure (VSS) workpieces. To this end, a generic variation propagation framework in MMPs for VSS workpieces is established, incorporating the induction and propagation of elastic deformation variations. Region division strategy is adopted according to the characteristics of VSS workpieces, and the analytic solutions of elastic deformation in different regions are solved by contact theory and elastic theory. The effectiveness and accuracy of the proposed model are verified by a six-stage machining process on a four-cylinder engine block, and the proposed model is compared with the conventional SoV model resulting in a significant improvement on quality prediction.

Theoretical and Experimental Investigation of Variable Stiffness Finger Seal

A finger seal is a flexible and dynamic contact seal, and many researches and experiments have proved its application potential in aviation engines, gas turbines, and other equipment. However, the contradiction between hysteresis leakage and wear life in the design and initial installation condition of finger seals seriously affects the integrated performance design effect. A variable stiffness finger seal is investigated in the present study to resolve the aforementioned problems, and the influence of initial installation condition is considered. First, a theoretical model of the finger seal is established to calculate the hysteresis characteristic and contact pressure between finger feet and rotor. The performances of the variable stiffness finger seal and traditional involute curved finger seal are compared to confirm the advantages of the variable stiffness finger seal. The results show that the initial conditions such as rotor structure and support bearing clearance have an important influence on the accuracy of finger sealing performance calculation. In addition, the variable stiffness structure improves the hysteresis characteristic of the finger seal with virtually no loss of wear life under low pressure differential and reduces the hysteresis rate by more than 50%. Under high pressure differential, the variable stiffness structure reduces the average contact pressure by more than 25%. Therefore, the leakage and wear performance of the finger seal are simultaneously improved by the variable stiffness structure. This characteristic does not change with an increase in rotor excitation. This indicates that the variable stiffness finger seal provides good synthetic performance and high dynamic adaptability to random operating conditions.

On the integrated design of curvilinearly grid-stiffened panel with non-uniform distribution and variable stiffener profile

In this paper, the integrated design of curvilinearly grid-stiffened panels is investigated, including stiffener layout design and profile design. The layout design includes the curvilinear path and non-uniform distribution of stiffeners. Firstly, the path of curvilinear stiffeners is defined by the piecewise linear function, and the non-uniform distribution of curvilinear stiffener cluster is described by the proposed representation method based on the PCHIP interpolation function. In addition to the layout design, the variable profile design method of grid-stiffened structures is also proposed in this paper. The variations of the thickness and height of stiffeners are represented by curves respectively. Similarly, the variable profile design of stiffeners is realized by designing the curves. On this basis, various novel configuration of curvilinearly grid-stiffened panels can be obtained by the integrated layout and profile design. The effectiveness of the proposed integrated design framework is validated by numerical examples. Compared with the initial design, the final integrated design improves the critical buckling factor of the grid-stiffened panel by 73.09%, which shows a great design potential of this kind of variable-stiffness structure compared to constant-stiffness structures.

Deployable, Variable Stiffness, Cable Driven Robot for Minimally Invasive Surgery.

Minimally Invasive Surgery (MIS) imposes a trade-off between non-invasive access and surgical capability. Treatment of early gastric cancers over 20 mm in diameter can be achieved by performing Endoscopic Submucosal Dissection (ESD) with a flexible endoscope; however, this procedure is technically challenging, suffers from extended operation times and requires extensive training. To facilitate the ESD procedure, we have created a deployable cable driven robot that increases the surgical capabilities of the flexible endoscope while attempting to minimize the impact on the access that they offer. Using a low-profile inflatable support structure in the shape of a hollow hexagonal prism, our robot can fold around the flexible endoscope and, when the target site has been reached, achieve a 73.16% increase in volume and increase its radial stiffness. A sheath around the variable stiffness structure delivers a series of force transmission cables that connect to two independent tubular end-effectors through which standard flexible endoscopic instruments can pass and be anchored. Using a simple control scheme based on the length of each cable, the pose of the two instruments can be controlled by haptic controllers in each hand of the user. The forces exerted by a single instrument were measured, and a maximum magnitude of 8.29 N observed along a single axis. The working channels and tip control of the flexible endoscope remain in use in conjunction with our robot and were used during a procedure imitating the demands of ESD was successfully carried out by a novice user. Not only does this robot facilitate difficult surgical techniques, but it can be easily customized and rapidly produced at low cost due to a programmatic design approach.

A soft gripper with variable stiffness inspired by pangolin scales, toothed pneumatic actuator and autonomous controller

Abstract Aiming at combining compliant covering and rigid lifting to the object grasping, this paper presents the design principle of a variable stiffness soft gripper and carries out its structural design, gripper fabrication and controller development. The proposed soft finger is composed of a variable stiffness layer and a pneumatic driven layer. The variable stiffness layer is inspired by the pangolins whose scales are flexible in daily activities and become tough when being threatened by predators. A toothed pneumatic actuator is designed to supply power with increased stiffness. The three-finger soft gripper is fabricated by 3D printing and molding of super elastic material. The tests for verifying grasping capability and variable stiffness are implemented. Experimental results show that the gripper can grasp a large variety of objects and achieve enhanced stiffness. The stiffness of the gripper is more than twice higher than the pneumatic gripper without variable stiffness structure. Finally, the control system for autonomous grasping is developed. The control block is divided into the actuation layer, information processing layer and user interface layer. According to the grasping process, the feedback signals in the information processing layer are collected by sensors. A safe grasping assessment is added to the control scheme for changing the gripper stiffness autonomously, which differs from the traditional soft gripper controller. The proposed soft gripper has variable stiffness, enhanced pneumatic input, autonomous control system. Therefore, it has great potential to be applied in the unstructured environment for effective, adaptable and safe object grasping.

Design of manufacturable fiber path for variable-stiffness panels based on lamination parameters

Compared with traditional composite panels, the modeling, analysis and design of variable-stiffness panels with curvilinear fibers are much more complicated. Although the design flexibility is greatly enhanced, the design of variable-stiffness structures must meet manufacturing constraints to ensure that the designed structures can be fabricated finally. In order to design variable-stiffness composite panels that is very challenging due to its nonlinearity and non-convexity, a novel multi-stage design method for variable-stiffness panels is developed based on lamination parameters. First, lamination parameters are taken as design variables, and the stiffness distribution is obtained efficiently by few iterations. Next, the lamination parameters are transformed into actual layups. Finally, the realistic fiber path is regenerated by considering manufacturing constraints. In addition, the isogeometric analysis, which is more suitable for variable-stiffness structure, is used instead of the traditional finite element analysis to improve the analysis accuracy. Illustrative example demonstrates the high computational efficiency and optimization capacity of proposed method, compared to gradient-based algorithm and evolutionary algorithm.

Elastic mechanics-based fixturing scheme optimization of variable stiffness structure workpieces for surface quality improvement

The surface quality is quite important for many mechanical products. An improper fixturing scheme (i.e., magnitudes of clamping forces and fixture layout) leads to undesirable deformation of the workpiece, which will seriously affect the final quality of the machined surface, especially for the form accuracy. Current researches on fixturing scheme optimization have been mainly focused on rigid workpieces and flexible workpieces, however, seldom considered variable stiffness structure (VSS) workpieces. Besides, most existing fixturing scheme optimization models are derived based on the finite element method (FEM), which demands considerable time for computation. Therefore, there is a lack of an effective and efficient approach to improve the surface quality for VSS workpieces by fixturing scheme optimization. To this end, a novel systematic approach based on elastic mechanics is proposed in this paper. Firstly, a static cutting force model is developed to obtain the minimum clamping forces needed to maintain the fixturing stability. Secondly, by dividing the VSS workpiece into three kinds of characteristic regions, the analytical solutions of the elastic deformation induced by clamping forces are derived using elasticity theory. Thirdly, the optimization model is solved by the genetic algorithm, so as to minimize the maximum fixturing induced deformation of the surface to be machined. The effectiveness and efficiency of the proposed approach are verified by a face milling experiment on a four-cylinder engine block, and the final quality of the machined surface is improved by 9.1%.

Fast‐Response, Stiffness‐Tunable Soft Actuator by Hybrid Multimaterial 3D Printing

AbstractSoft robots have the appealing advantages of being highly flexible and adaptive to complex environments. However, the low‐stiffness nature of the constituent materials makes soft robotic systems incompetent in tasks requiring relatively high load capacity. Despite recent attempts to develop stiffness‐tunable soft actuators by employing variable stiffness materials and structures, the reported stiffness‐tunable actuators generally suffer from limitations including slow responses, small deformations, and difficulties in fabrication with microfeatures. This work presents a paradigm to design and manufacture fast‐response, stiffness‐tunable (FRST) soft actuators via hybrid multimaterial 3D printing. The integration of a shape memory polymer layer into the fully printed actuator body enhances its stiffness by up to 120 times without sacrificing flexibility and adaptivity. The printed Joule‐heating circuit and fluidic cooling microchannel enable fast heating and cooling rates and allow the FRST actuator to complete a softening–stiffening cycle within 32 s. Numerical simulations are used to optimize the load capacity and thermal rates. The high load capacity and shape adaptivity of the FRST actuator are finally demonstrated by a robotic gripper with three FRST actuators that can grasp and lift objects with arbitrary shapes and various weights spanning from less than 10 g to up to 1.5 kg.

Variable Stiffness Structures Utilizing Pneumatic Artificial Muscles

Pneumatic artificial muscles (PAMs) can offer excellent force-to-weight ratios and act as shape-changing actuator under injecting the actuation fluid into their bladders. PAMs could be easily utilized for morphing structures due to their millimeter-scale diameter. The pressurized PAM can serve not only as artificial muscle actuator which obtains contraction deformation capability but also as a spring system with variable stiffness. In this study, the stiffness behaviors of pressurized PAMs and a variable stiffness structure are investigated. By taking advantage of the designed PAMs which was conducted by the non- linear quasi-static model, significant changes in the spring stiffness can be achieved by air pressure control. A case study is presented to explore the potential behavior of a structure with circular permutation PAMs. The structure used in this case consists of sixteen PAMs with circular homogeneous distribution and a circular supporter with sixteen slide way runners. The stiffness of presented structure can vary flexibly in wide range through controlling the air pressure levels and slide deformation respectively.

3D-Printed Ready-To-Use Variable-Stiffness Structures

Various physical phenomena have been used to develop variable-stiffness (VS) materials and structures, but all have involved some elements of manual fabrication, which limits their applications. In contrast, here we show fully three-dimensional (3D) printed monolithic VS structures that can be used directly from the printer. Thermally responsive polylactic acid (PLA) and conductive graphene PLA (GPLA) are combined in-printer to deliver a new framework for the temperature-controlled 3D VS structures. The embedded GPLA acts as a heating element, and both it and the surrounding PLA can be transitioned from rigid to soft using simple Joule heating because of the glass transition behavior of PLA. The mechanical and electrical properties of printed composite VS structures are studied. The great potential of this technology is demonstrated in a prototype variable-stiffness orthotic for foot drop.

Soft Gripper using Variable Stiffness Mechanism and Its Application

Soft robots have advantages such as low weight and compact size compared to rigid robots. Variable stiffness is one of the key methods of improving the performance of a soft robot. The soft gripper grasps objects of various shapes or sizes based on the variable stiffness. In a previous study, we validated the variable stiffness mechanism where flexible and rigid segments were connected alternately in series. This paper presents a soft variable stiffness gripper that can be used to control the stiffness by pulling tendons. The soft gripper has three variable stiffness structures acting as fingers and the stiffness can be controlled using two motors by winding tendons. To understand the tendency of the stiffness variation and determine the design parameters, a compliant mechanism was developed using a pseudo-rigid-body model (PRBM). The experimental results show that the difference between the lowest and highest stiffness values of the fabricated variable stiffness gripper was 5.6 times the original. Similarly, the difference in the gripping weight was 19 times. Using the experimental results, the variable stiffness gripper can be designed and manufactured based on the required stiffness and used to grip various types of objects.

A novel variable stiffness mechanism for dielectric elastomer actuators

In this paper, a novel variable stiffness mechanism is proposed for the design of a variable stiffness dielectric elastomer actuator (VSDEA) which combines a flexible strip with a DEA in a dielectric elastomer minimum energy structure. The DEA induces an analog tuning of the transverse curvature of the strip, thus conveniently providing a voltage-controllable flexural rigidity. The VSDEA tends to be a fully flexible and compact structure with the advantages of simplicity and fast response. Both experimental and theoretical investigations are carried out to reveal the variable stiffness performances of the VSDEA. The effect of the clamped location on the bending stiffness of the VSDEA is analyzed, and then effects of the lengths, the loading points and the applied voltages on the bending stiffness are experimentally investigated. An analytical model is developed to verify the availability of this variable stiffness mechanism, and the theoretical results demonstrate that the bending stiffness of the VSDEA decreases as the applied voltage increases, which agree well with the experimental data. Moreover, the experimental results show that the maximum change of the relative stiffness can reach about 88.80%. It can be useful for the design and optimization of active variable stiffness structures and DEAs for soft robots, vibration control, and morphing applications.

JammJoint: A Variable Stiffness Device Based on Granular Jamming for Wearable Joint Support

In robotics, controlling the stiffness of the joints that contribute to the robots’ degree of freedom dictates the adaptability, versatility, and safety of the whole system. We can achieve variable stiffness or impedance in a robotic system purely by the control or by introducing new material or mechanisms to address cases that require innate safety through system compliancy. This paper presents JammJoint, a compliant and flexible wearable robot, which uses jamming of granular media to vary its stiffness. It consists of a silicone sleeve with hollow sections that are filled with cubic rubber granules and subjected to different levels of vacuum pressure. Unlike contemporary vacuum-based actuators or systems, JammJoint is wearable, portable, and autonomous: It uses a powerful miniature vacuum pump, a small battery, and bluetooth-enabled electronics. Experiments revolving around bending and torsional stiffness show that the system is able to achieve up to a fourfold increase in spring stiffness. Further measurements of individual variable stiffness structures indicate that for other modes of deformation, including simply supported bending or compression for alternative linear applications, higher changes in stiffness over a factor of seven are possible. These aspects make mobile jamming-based stiffness variation as wearable joint assistance promising for future applications such as rehabilitation after injuries and joint support in challenging working conditions.

Adaptive Morphology: A Design Principle for Multimodal and Multifunctional Robots

Morphology plays an important role in behavioral and locomotion strategies of living and artificial systems. There is biological evidence that adaptive morphological changes can not only extend dynamic performances by reducing tradeoffs during locomotion but also provide new functionalities. In this article, we show that adaptive morphology is an emerging design principle in robotics that benefits from a new generation of soft, variable-stiffness, and functional materials and structures. When moving within a given environment or when transitioning between different substrates, adaptive morphology allows accommodation of opposing dynamic requirements (e.g., maneuverability, stability, efficiency, and speed). Adaptive morphology is also a viable solution to endow robots with additional functionalities, such as transportability, protection, and variable gearing. We identify important research and technological questions, such as variable-stiffness structures, in silico design tools, and adaptive control systems to fully leverage adaptive morphology in robotic systems.

변수변화에 따른 가변강성 메커니즘의 강성변화 경향성에 관한 연구

일반적으로 시스템을 강성체로 설계할 경우 시스템의 구조적 안정성을 확보할 수 있으나 유리잔을 잡거나 작은 수술용 도구로 사용하는 등의 사용용도에 따라 활용성이 제한될 수 있다. 이러한 문제를 해결하기 위하여 유연한 재질을 사용하여 강성조절이 가능한 메커니즘에 대한 연구가 다양하게 이루어져 왔다. 기존에 연구했던 강성체와 연성체의 연속구조로 이루어진 모델에 텐던을 삽입한 구조를 이용한 가변강성 메커니즘을 통하여 가변강성 구조체에 대한 가능성을 확인하였다. 그러나 필요로 하는 가변강성을 충족하기 위한 구조체의 설계 변수에 대한 연구가 필요하였다. 따라서 본 연구에서는 가변강성 메커니즘의 다양한 변수 변화에 따른 강성변화 실험을 통해 강성의 경향성을 파악하고자 하였다. 실험 결과 지름이 클수록 강성은 증가하며 강성의 증가폭 또한 늘어난다. 또한 연성체 길이가 짧을수록 강성이 증가하며 텐던을 당겨 연성체를 압착할 경우 강성값은 비선형적으로 증가하였다. 동일 조건에서 연성체 길이변화에 따른 강성 증가폭과 강성체의 길이 변화에 따른 강성 증가폭을 비교하였을 때 연성체 길이 변화가 강성체 길이 변화 보다 강성값 변화에 영향을 미친다는 것을 확인하였다. 또한, 해석값이 실험값에 비하여 정확성은 낮지만, 가변강성의 경향성을 확인하기 위하여 해석적인 방법을 통한 강성을 예측해보았다. 이러한 변수변화 실험 결과는 필요로 하는 강성값을 충족하는 가변강성 메커니즘 설계에 활용할 수 있을 것이다. In general, a system can be stable when it is designed with a rigid material. However, the use of a rigid system can be limited, such as grasping a glass or using a small surgical instrument. To resolve this limitation, a variable stiffness mechanism was developed using a flexible material. Previous research verified the variable stiffness mechanism where flexible segments and rigid segments were connected alternately in series. However, research into the design parameters of the variable stiffness structure is needed to satisfy the desired stiffness. Therefore, a variable stiffness structure was tested by varying the design parameters to confirm the trend of the stiffness variation. When the radius of the structure becomes larger, the stiffness increases. The stiffness increased with decreasing length of the flexible segments. Under the same design parameters, the length of the flexible segments had a greater effect on the stiffness than the length of the rigid segments. In addition, the stiffness was estimated using the pseudo rigid body model and was compared with the experimental results. This parametric study can be used as a design guideline for designing the variable stiffness mechanism to satisfy the desired stiffness.

Dynamically variable negative stiffness structures.

Variable stiffness structures that enable a wide range of efficient load-bearing and dexterous activity are ubiquitous in mammalian musculoskeletal systems but are rare in engineered systems because of their complexity, power, and cost. We present a new negative stiffness-based load-bearing structure with dynamically tunable stiffness. Negative stiffness, traditionally used to achieve novel response from passive structures, is a powerful tool to achieve dynamic stiffness changes when configured with an active component. Using relatively simple hardware and low-power, low-frequency actuation, we show an assembly capable of fast (<10 ms) and useful (>100×) dynamic stiffness control. This approach mitigates limitations of conventional tunable stiffness structures that exhibit either small (<30%) stiffness change, high friction, poor load/torque transmission at low stiffness, or high power active control at the frequencies of interest. We experimentally demonstrate actively tunable vibration isolation and stiffness tuning independent of supported loads, enhancing applications such as humanoid robotic limbs and lightweight adaptive vibration isolators.