Variable Stiffness Characteristics Research Articles

An all-position type control strategy of the haptic interactive virtual training system based on cable-driven

The virtual microgravity training system based on cable drive usually uses a force-position hybrid control strategy which has following problems: the force control method is sensitive to load disturbances, variable stiffness characteristics of cables reduce the control accuracy of PID controllers, and the expected tension fluctuations are large. These will affect the control accuracy, and further affect the tactile sensation and training effectiveness of astronauts. For the above problems, an all-position type control strategy is proposed to improve the system control accuracy. This strategy uses a compliant control method. In this method, elastic elements are connected in cables, the conversion model of tension and displacement is established, and the tension control is realized by the displacement control which has characteristics of high control accuracy and strong resistance to load disturbance. The PID controller is replaced by the active disturbance rejection controller. In this controller, the tracking differentiator is used to reduce high frequency noises of the input signal, and the extended state observer is used to estimate and compensate the error caused by the change of the cable stiffness. A tension distribution method is designed to make expected cable tensions approach the average tension to reduce the tension fluctuation. The experimental results show that compared with the force-position hybrid control strategy, the all-position type control strategy reduces the tension error and speed error by about 51% and 33% respectively.

Research on a Biomimetic Flexible Ball Joint With Variable Stiffness for Robots

Abstract The human ball joint is a compact and flexible 3-degree-of-freedom (DOF) composite joint. The ball joints commonly used in robot design lack active driving capability. Ball joints with active drive generally consist of three single-degree-of-freedom joints connected in series, which is a noncompacted structure and easily leads to singular postures. In order to meet the demand for high-performance composite joint modules for service robots, this article designs a flexible biomimetic spherical robot joint with variable stiffness characteristics: the mechanism of muscle parallel antagonistic drive and ligament wrapping constraint is simulated; three parallel branch chains are used to drive three composite degrees-of-freedom; ropes, soft airbags, and series elastic drive gears are used to form a flexible transmission system; the contour of the rope winch has been optimized with the aim of transmission stability; and a pneumatic variable stiffness soft structure has been designed and fabricated. A compliance control algorithm for joints was developed based on the principle of impedance control. The research results indicate that the biomimetic ball-and-socket joint has a compact structure, a wide range of motion and good motion tracking performance, variable stiffness performance, and flexible interaction ability.

Design and Hysteretic Performance Analysis of a Novel Multi-Layer Self-Centering Damper with Shape Memory Alloy

This paper presented the development process of a novel multi-layer self-centering damper utilizing a NiTi shape memory alloy (SMA) with remarkable superelastic properties. The construction and operating principles of the novel damping device were introduced. A model for calculating the restoring force–displacement hysteretic curve of the novel damper was established, and based on this theoretical model, a parameter analysis of the damper’s hysteresis performance was conducted. The effect of SMA pre-strain, SMA diameter, number of layers in the damper, and number of SMA wires per layer on the damper’s stiffness, the unit cycle energy dissipation, and the equivalent viscous damping ratio were investigated, respectively. The results showed that the restoring force–displacement hysteretic curve of the novel SMA damper exhibits a full spindle shape, demonstrating the damper’s excellent energy dissipation capacity, self-centering capability, significant stroke, and unique variable stiffness characteristics (i.e., appropriate initial stiffness, minimal isolation stiffness, and significant limit stiffness). The results also indicated that the SMA pre-strain has a minor impact on the damper’s stiffness but a significant influence on unit cyclic energy dissipation and equivalent damping ratio. As the SMA pre-strain increased from 0.03 to 0.04, 0.05, and 0.06, the maximum stroke of the damper continuously decreases, while the unit cyclic energy dissipation initially increases and then decreases, with the optimal energy dissipation achieved at a pre-strain of 0.04. Increasing the SMA diameter results in a higher damper stiffness and energy dissipation capacity, with no significant change in maximum stroke and equivalent damping ratio. Increasing the number of damper layers leads to an increase in maximum stroke and unit-cycle energy dissipation, accompanied by a decrease in stiffness and almost constant equivalent damping ratio. As the number of SMA wires per layer increased from 8 to 16 and 32, the maximum stroke and equivalent damping ratio presented little variation, but the damper’s stiffness and unit cyclic energy dissipation continuously increased.

Preparation of superhydrophobic shape memory composites with uniform wettability and morphing performance

Superhydrophobic shape memory surfaces have attracted much attention in recent years, as they can intelligently control surface wettability. However, less research has focused on the development of superhydrophobic shape memory materials that can maintain uniform wettability in any morphing shape. It is common in nature that species such as lotus leaves and kingfisher show good superhydrophobicity in any movement under/on water. Based on this inspiration, this work presents a novel superhydrophobic shape memory composite (SSMC) by coupling superhydrophobic coatings and shape memory epoxy composites. The SSMC exhibits excellent water repellency and self-cleaning performance regardless of how it is bent. In addition, its good shape memory effect and variable stiffness characteristics enable it to be potentially used as deployable marine structures and morphing skin of aquatic unmanned aerial vehicles. On the other hand, the SSMC also offers good anti-icing properties and mechanical/chemical robustness that enhance long-term service performance all year round. This research provides a fresh idea for the design of new smart superhydrophobic materials and expands applications in the field of marine and aviation facilities.

Design and optimization of the magnetic field-driven spherical gripper with adjustable stiffness

This paper presents a new gripping technique that merges the variable stiffness characteristics of conventional magnet-controlled and negative-pressure spherical grippers to produce a spherical gripper capable of securely grasping large and structurally diverse objects. The proposed method incorporates the smart rheological material from magnet-controlled grippers with the particle-jamming smart structure used in negative-pressure grippers. The gripper comprises a magnetic control device and a spherical variable stiffness body. Simulation analysis was used to optimize its structure and enhance the efficiency ratio of the magnetic control device. The flexible variable stiffness body was initially designed to be cylindrical to increase interlocking with objects. Experiments were conducted to evaluate the gripping efficiency and adaptability of the magnetron spherical gripper, which were designed to simulate real-world application requirements. These results suggest that the magnetically controlled spherical gripper can achieve a gripping efficiency of approximately five and securely grasp objects with a relative bladder diameter ranging from 20 % to 130 %. Furthermore, it can stably grip objects up to an offset distance of 15 mm without requiring sensor assistance. The enhanced magnetic field-powered spherical gripper exhibits superior adaptability and efficiency in gripping compared to its counterpart. In addition, it boasts robust resistance against environmental interference.

An analytical solution for thermomechanical buckling of variable angle tow composite laminates with elastically restrained edges

The inherent anisotropy and variable stiffness characteristics exhibited by Variable Angle Tow (VAT) composite materials offer significant possibilities for enhancing the performance of corresponding structures. Through appropriate selection of the curved fiber paths, it becomes feasible to design structures that are both lightweight and efficient. However, conducting mechanical analysis on VAT composite structures is of considerable challenges, particularly in seeking analytical solutions. In view of this, this paper aims to investigate the thermomechanical buckling behavior of VAT composite laminates with elastically restrained edges and presents an analytical solution for the studied problem. The analysis is based on the assumption that the fiber orientation angle of each lamina varies linearly or nonlinearly along the x direction, and the fundamental equations for thermomechanical buckling of VAT laminates are derived using the classical laminated plate theory. The analytical solution is obtained through the combined utilization of Taylor series and Frobenius series. Furthermore, a comprehensive parameter analysis is conducted to assess the impact of different factors, such as fiber paths and elastic support stiffness, on the critical thermomechanical buckling load and mode of VAT laminates. The resulting findings serve as a valuable reference for VAT laminate design, while the proposed analytical solution can be employed as a benchmark for validating other numerical results.

Bioinspired Rigid-Flexible Coupled Adaptive Compliant Motion Control of Robot Gecko for Space Stations.

This paper presents a study on bioinspired rigid-flexible coupling adaptive compliant motion control of a robot gecko with hybrid actuation for space stations. The biomimetic robot gecko is made of a rigid trunk, four motor-driven active legs with dual-degree-of-freedom shoulder joints, and four pneumatic flexible pleated active attachment-detachment feet. The adaptive impedance model consists of four input parameters: the inertia coefficient, stiffness coefficient, damping coefficient, and segmented expected plantar force. The robot gecko is equipped with four force sensors mounted on its four feet, from which the normal force of each foot can be sensed in real-time. Based on the sensor signal, the variable stiffness characteristics of the feet in different states are analyzed. Furthermore, an adaptive active compliance control strategy with whole-body rigidity-flexibility-force feedback coupling is proposed for the robot gecko. Four sets of experiments are presented, including open-loop motion control, static anti-interference experiment, segmented variable stiffness experiment, and adaptative compliant motion control, both in a microgravity environment. The experiment results indicated that the presented control strategy worked well and the robot gecko demonstrates the capability of stable attachment and compliant detachment, thereby normal impact and microgravity instability are avoided. It achieves position tracking and force tracking while exhibiting strong robustness for external disturbances.

A novel gardenia-shaped structure materials with variable stiffness under elastic tension

Nature's creatures often have unique behaviors that have inspired humans to create many bionic structures to meet engineering needs. In previous work, we reported a Gardenia-shaped structure (GSS) materials. Then an optimal GSS materials is developed in this paper. The optimal GSS materials shows its easily available variable stiffness characteristics from the testing in the homemade experimental bench. The variable stiffness characteristics of the optimal GSS materials were investigated by using both experimental and finite element methods in this paper. The experimental results show good agreement with the numerical results. The excellent performance of the optimal GSS materials has the potential for engineering applications to meet multi-stiffness requirements.

Magnetorheological Fluid-Filled Origami Joints With Variable Stiffness Characteristics

Origami technology has applications in diverse areas, such as metamaterials, space structures, and haptic interfaces due to the low-cost manufacturing, rapid assembly, and compact structures. Existing origami robots, however, often lack variable stiffness due to the intrinsic properties of conventional origami structures made of rigid facets and flexible joints. In this article, we present a design of magnetorheological (MR) fluid-filled origami joints with variable stiffness characteristics. Compared with existing approaches to realize controllable origami joints stiffness, our proposed method has the advantage of magnetically remote control. To predict the joint stiffness under different magnetic flux densities, we derive a theoretical model and calibrate it by test. Subsequently, to demonstrate MR fluid-filled origami joints can apply in more complex origami structures, we design a modified thick Yoshimura structure and a Kresling structure that can achieve stiffness enhancement of 59.2 and 83.6%, respectively. Also, we introduce jamming behavior into the joint to achieve the same capability of variable stiffness while utilizing a relatively weak magnetic setup. Additionally, we fill MR fluid into the origami facets to develop an origami robot that can carry loads while crawling on flat ground and climbing on an inclined surface.

A Versatile Semiactive Electrically Interconnected Suspension With Heave-Roll Vibration Decoupling Control

This paper develops a versatile electrically interconnected suspension (EIS) system with variable inertance and variable damping (VIVD) in the heave direction and variable stiffness (VS) in the roll direction for vehicles to improve ride comfort. The conventional hydraulicly interconnected suspensions have been utilized to improve ride comfort and prevent rollover, while such a hydraulic system results in more design complexity, maintenance, and cost. The EIS can achieve the suspension interconnection electrically and offer more design flexibility, energy efficiency, and faster system response. The proposed EIS comprises two electromagnetic dampers (EMDs), which are interconnected by an electrical network (EN) with controllable resistors, capacitors, and inductors, enabling the suspension to generate VIVD and VS characteristics in heave and roll, respectively. The system only requires energy for controlling electronic switches, which is low and efficient. Then, a decoupling semi-active control strategy based on <inline-formula><tex-math notation="LaTeX">${\mathbf{H}}_\infty $</tex-math></inline-formula> controller is proposed to mitigate the heave and roll vibration. Moreover, a half-car test rig is developed to evaluate the vibration control performance of the proposed EIS system by conducting a series of comprehensive tests. As a result, the EIS has a significant improvement in performance than a passive suspension. The versatile EIS has reduced the resonance by 13.0&#x0025; compared to non-versatile EIS. The proposed versatile EIS system has great potential in practical application.

Research on variable stiffness characteristics of turntable bearing under heavy load condition based on FEM

Based on ANSYS finite element analysis software, a method of extracting stiffness matrix of four-point contact ball bearing was proposed. The finite element model of four-point contact ball bearing was established, the stress and strain of the bearing under different loads were calculated, and the relationship between load and stress and strain was analyzed, The global stiffness matrices of turntable bearing with steel and aluminum as inner ring materials are extracted and compared, and the causes of large changes in the matrix are analyzed.

Modeling and control system design of 6-DOF bionic parallel mechanism with compliant modules

Quadrupeds are capable of dynamic movements such as fast running and long-distance jumping due to their flexible and elastic torso structures. In this paper, a compliant parallel mechanism is proposed as a bionic torso to simulate the diversified behaviors and agile locomotion of the tetrapod torso. The spring module is incorporated into the limb of the parallel mechanism to absorb external shocks, cushion, and dampen vibrations, thus improving the compliance performance of the bionic torso. For the compliant parallel mechanism, its kinematics and kinetics are analyzed, and the overall electromechanical system and control framework are devised. The multidimensional damping dynamic characteristics of the proposed mechanism are qualitatively analyzed by simplifying the limb into a spring–mass damping system. The parallel mechanism with compliant spring modules absorbs external forces to different degrees with different stiffness coefficients to avoid damage to the structure by external impacts. The parallel mechanism with different initial positions exhibits the inherent variable stiffness characteristics of the mechanism. The parallel mechanism simulates the diverse behavior of the animal torso, with independent and synthesized locomotor behavior of the six underlying motion patterns. Simulations and experiments demonstrated that the compliant parallel mechanism is effective in vibration damping and cushioning, with a rapid response and small steady-state error. The motion of the compliant parallel mechanism in one direction and the motion of the integrated multi-degree of freedom (DOF) are confirmed and exhibited in the behavioral experiment.

Ultra-low frequency vibration isolation of a novel click-beetle-inspired structure with large quasi-zero stiffness region

Inspired by the three postures of a click beetle, a novel passive click-beetle-inspired structure (CBIS) with variable asymmetric stiffness characteristics is proposed and systematically investigated for stiffness tunning and low-frequency vibration isolation. The main structure of CBIS is consisted of three rods and two springs but the geometrical nonlinearity and stiffness properties are abundant. Based on the Lagrange principle, the stiffness properties of CBIS is analyzed comprehensively for the unbending posture, down-bending posture and up-bending posture, respectively. The corresponding displacement transmissibility derived with the harmonic balance method. The hardening and softening stiffness phenomenon may occur by tuning geometric parameters. The stiffness can be tuned easily among negative, quasi-zero, zero, small positive by the initial assembly angle, length ratio and linear stiffness ratio. The zero stiffness (ZS) or quasi-zero stiffness (QZS) region can be extremely huge under some special parameters, which can broaden the working range of CBIS and benefit to large-deflection vibration isolation. The peak transmissibility can be reduced to 7 dB or even 0 dB and the resonant frequency can be smaller than 2 Hz, which is conductive to ultra-low frequency vibration isolation. The proposed CBIS opens a new route towards tunning asymmetric stiffness for low frequency vibration isolation.

Development of a long-period vertical base isolation device with variable stiffness for steel frame structures

The current isolation technology is mainly developed for seismic response control of structures in horizontal direction. Seismic records and shaking table test results show that there is a strong need to mitigate the vertical responses of structures. This paper proposes a three-dimensional (3D) isolation device that consists of a traditional horizontal bearing and a newly developed long-period vertical isolation device with variable stiffness (LVIVS). The LVIVS includes three layers of springs and two of them are prestressed. With the aid of displacement constraint components, the non-prestressed springs work independently or in series with the prestressed springs at different loading stages to realize variable stiffness characteristic. As designed, the LVIVS has large vertical stiffness in the normal stage to restrain the displacement under live loads and ground motions with small amplitudes, small vertical stiffness in the isolation stage to prolong the vertical period of the base isolation system, and large vertical stiffness in the limit stage to restrain large vertical displacement at extreme events. The prestress of the springs leads to a self-centering feature of the device. Also, the variable stiffness characteristic shortens the deformation demand of the device under self-weight which enhances the stability of the device significantly and thus it is easier to achieve a long isolation period in the isolation stage. The hysteretic model for the LVIVS is derived, and sinusoidal excitation tests are conducted to verify the proposed hysteretic model of the LVIVS and its variable stiffness mechanism. The experimental results show that the variable stiffness characteristics of the LVIVS can be achieved, and the isolation period reaches 0.95 s. Finite element simulations are also conducted for a steel frame structure to verify the isolation effect of the proposed 3D isolation device.

Design and analysis of passive variable stiffness device based on shear stiffening gel

Shear thickening materials are utilized as the core of variable stiffness devices in various engineering applications in recent years. However, due to the used materials being liquid, most of these devices are suffered from the problem of liquid leakage and coagulation. To address this issue, this paper proposes a design method of a passive variable stiffness device based on shear stiffening gel (SSG), which integrates the core SSG and spring into a compact structure to obtain well stability. The used SSG can affect the force transfer within the device, thereby influencing the system’s stiffness dynamically over the external impact load. Due to the core SSG being good shear stiffening properties, the device is highly sensitive to frequency and shows variable stiffness characteristics. When the frequency of external load increased from 0.1 Hz to 5 Hz, the equivalent stiffness of the device could be increased by 105.74%. An equivalent nonlinear model is used to represent the overall stiffness of the device as a function of the frequency and displacement amplitude of the load. The output of the equivalent nonlinear model agrees well with the experimental data. The cross-validation also proves the accuracy of the model fitting, which provides a quantitative description of the dynamic performance of the variable stiffness device. By combining different types of SSGs and springs with different stiffness, the design principle of the variable stiffness device proposed in this paper can be utilized in various impact-loading applications, such as designing the exoskeletal load carriage supporting mechanism and vehicle suspension systems. The work of this paper has guiding significance for the design of adaptive variable stiffness devices.

Damage behavior analysis of unidirectional fiber reinforced shape memory polymer composites

Shape memory polymer composites (SMPCs) are gradually being used in space deployable structures due to their unique shape memory properties and variable stiffness characteristics. Currently, the damage behavior of SMPC has not been systematically investigated, which affects its structural design and application. In this study, the damage behavior analysis of unidirectional fiber-reinforced SMPCs was investigated. The buckling deformation and damage modes of SMPC were analyzed theoretically. The strain energy of the matrix cracking and fiber fracture damage system was developed considering the compressive strain of the matrix. Additionally, the analytical expressions of the key parameters during bending were determined and the law of evolution was revealed. The damage mode analysis showed that decreasing fiber volume content and increasing thickness were more likely to result in matrix cracking damage. The fiber fracture would occur in the stretching region if the fiber volume content was less than a certain value. Finally, the experiment was performed to demonstrate the validity of the theoretical method. This work is significant for the design and optimization of the SMPC-based structure.

Design and performance research of a hydro-pneumatic suspension with variable damping and stiffness characteristics

Design and performance research of a hydro-pneumatic suspension with variable damping and stiffness characteristics

A universal dynamical model of dual-chamber air springs with experimental validation

Experimentally and theoretically, this paper combines thermodynamics, aerodynamics and structural dynamics to give a universal dynamical model of dual-chamber air springs, with physical meanings of each stiffness and damping term. An indicator experiment was designed to verify the theory proposed in this paper. The experimental results show that the dynamic stiffness model can well reflect the hysteresis characteristics and the variable stiffness characteristics of the dual-chamber air spring. It can also clearly reveal the frequency dependence of the dynamic stiffness. Finally, based on the derived model, the influence regulation of each parameter term on the dynamic stiffness amplitude and hysteresis phase angle is given numerically. The results show that each term can influence different dynamic characteristic of the dual-chamber air springs. The conclusions of this article can provide positive guidance for the vehicle dynamics matching and design of air springs.

A novel crank inerter with simple realization: Constitutive model, experimental investigation and effectiveness assessment

The inerter-based device is of increasing interest to scholars in the field of structural vibration control, which is characterized by apparent mass and negative stiffness effects. With this regard, it is potential to develop variable negative stiffness characteristics with the technology of inerter, which is promising to provide improved performance for structural vibration isolation and vibration suppression. In this study, the theoretical analysis and experimental investigation of a novel inerter element, named crank inerter, is performed. The presented crank inerter is proposed to generate a variable negative stiffness effect, which is realized on the basis of a crank mechanism. A constitutive model of crank inerter is developed to predict its mechanical behavior. For an in-depth understanding of the inertial property of the crank inerter, a parametric analysis is conducted on the inertia force calculation of the crank inerter. A prototype crank inerter is fabricated and tested under sinusoidal excitations to verify the proposed constitutive model. A variable negative stiffness of the crank inerter is reflected from the proposed constitutive model. The theoretical results calculated with the proposed constitutive model match well with the experimental data, which verifies that the proposed model can predict the mechanical behavior of the crank inerter. The dynamic analysis of a vibration isolator with a crank inerter is conducted to illustrate its effectiveness using the proposed constitutive model. The analysis results preliminarily show that the isolator with crank inerter can improve the structural performances regarding the peak force transmissibility and frequency band. Based on the presented investigations, a crank inerter with a simple configuration is summarized to be effective for providing an apparent mass effect and variable negative stiffness.

An electrical heating shape memory polymer composite incorporated with conductive elastic fabric

Shape memory polymers (SMPs) are a class of smart materials with large deformation performance and variable stiffness characteristics, and have exhibited great potential in morphing skins. The thermal stimulation of SMPs is one of the hotspots in recent years. Shape memory polymer composites (SMPC) filled with conductive materials are activated by Joule heating without external heating facilities. The existing electro-induced SMPCs filled with conductive materials would limit large tension deformation, cannot be heated in a large area, or damage the heating circuit under cyclic loading. These aspects restrict the application of SMPC for morphing skins. In this work, an electro-induced SMP composite was fabricated by the styrene-based SMP incorporated with conductive elastic fabric (CEF) to remove the limiting factors as much as possible. The thermos-mechanical properties and electro-active characteristics of CEF/SMP composite were systematically investigated. The maximum strain at break of CEF/SMP composites reached 206% at 80°C, exhibiting excellent deformation performance. The resistance remained relatively stable after 50 cycles under 40% tensile strain. Furthermore, the CEF/SMP composite with a dimension of 160×160×3 mm3 was successfully heated above the glass transition temperature, demonstrating the actuating ability with a relatively large region. In general, the CEF/SMP composite is promising for the application of morphing skins.