Variable Stiffness Characteristics Research Articles

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.

Online chatter detection in robotic machining based on adaptive variational mode decomposition

Chatter is the main problem that limits the application of industrial robots in the field of machining process. It is critically important to establish an adaptive chatter detection solution for robot machining process and realize the online detection of chatter. However, different from machine tool chatter, the chatter in robotic machining process is more complex to be detected due to the variable stiffness characteristics and weaker stiffness of normal industrial robot, and the existing literature has less research on this problem. This paper presents a comprehensive solution for online chatter detection in robotic machining process. Firstly, in order to detect the chatter in robotic machining process and avoid mode mixing problem in variational mode decomposition (VMD) process, an adaptive variational mode decomposition (AVMD) method based on kurtosis and instantaneous frequency is proposed, which realizes the adaptive selection of the decomposition parameter. Secondly, optimal decomposition parameters are calculated by using genetic algorithm. By optimizing the discrete step length of decomposition parameter, it greatly reduces the optimization time. Last but not least, approximate entropy, energy entropy, and proposed entropy drift coefficient are extracted to distinguish chatter and stable machining state. Simulation and experimental results show that the proposed method can meet the real-time requirements of online detection and detect the occurrence of chatter effectively.

Quantification and Modeling of Ankle Stiffness During Standing Balance.

This study investigates the factors contributing to the modulation of ankle stiffness during standing balance and evaluates the reliability of linear stiffness models. A dual-axis robotic platform and a visual feedback display were used to quantify ankle stiffness in both the sagittal and frontal planes while subjects controlled different levels of ankle muscle co-contraction, center-of-pressure (CoP), and loading on the ankle. Results of 40 subjects demonstrated that ankle stiffness in the sagittal plane linearly increased with the increasing level of these three factors. The linear model relating the change in these factors from the baseline measurements during quiet standing to the change in weight normalized ankle stiffness resulted in high reliability (R2 = 0.83). Ankle stiffness in the frontal plane increased with the increasing ankle muscle co-contraction and ankle loading, but the linearity was less obvious. It also exhibited a clear nonlinear trend when CoP was shifted mediolaterally. Consequently, the reliability of the linear model was low for ankle stiffness in the frontal plane (R2 = 0.37). During standing balance, ankle stiffness in the sagittal plane could be well explained by a linear model if ankle muscle activation, CoP, and ankle loading were collectively considered. However, the linear model cannot capture highly variable and nonlinear ankle stiffness characteristics in the frontal plane. The outcomes of this study could benefit the development of lower-extremity robots and their controllers. Furthermore, the ankle stiffness models could be used as a baseline in developing patient-specific ankle rehabilitation protocols.

Kinematic and quasi-static analysis model of a novel variable stiffness pneumatic artificial muscle

A novel variable stiffness axial expansion pneumatic artificial muscle based on hexagonal origami is proposed. Based on the presented assumptions, a kinematic analysis model of the pneumatic artificial muscles is presented, and the changes in crease angles, air cavity volume and geometric configurations of the pneumatic artificial muscles during the actuation process are obtained. The equivalent elastic modulus of the hyperelastic material is obtained by fitting the stress-strain curve. The stress state of the crease is simplified as the pure bending model of a straight beam, and the rotational stiffness of the crease is formulated. Based on the energy method, a quasi-static characteristic analysis model of the pneumatic artificial muscles is developed. The pressure-displacement curve under the unloading state and the output force-displacement curve under the loading state are calculated. The variable stiffness characteristics of the pneumatic artificial muscles are evaluated. Compared with the experimental and numerical simulation results, the analysis models are verified. The work will provide analysis models for the mechanical design and force-displacement control of this type of pneumatic artificial muscles.

Realization of a Simultaneous Position-Stiffness Controllable Antagonistic Joint Driven by Twisted-Coiled Polymer Actuators Using Model Predictive Control

Stiffness adjustability is one of the key characteristics that help humans achieve safe and reliable motions. This paper aims to realize the simultaneous position-stiffness control of an antagonistic joint driven by a type of super-coiled polymer (SCP) artificial muscles, made from a combination of Spandex and nylon fibers. A nonlinear model that can exhibit the variable stiffness characteristics of the actuator is first proposed. The model, whose parameters are identified and verified experimentally, is suitable for estimating the actuator's stiffness as a function of the length and temperature. Based on a linearized model of the antagonistic joint system, a model predictive control (MPC) is applied to control joint angle and stiffness simultaneously. By controlling both actuators' temperatures, simultaneous position-stiffness control is realized. Our contribution also includes enhancement of MPC control by incorporating time delay estimation to estimate model variations and external disturbances. The control performance is verified with both step command and sinusoidal reference with composite frequencies of 0.02Hz to 0.1Hz. Experimental results show that the system can achieve high accuracy of joint position control performance with the maximum position error of 0.42 degrees while varying joint stiffness 46.5%.

Study on trunk posture support device utilizing variable stiffness characteristics by pneumatic soft actuator

Study on trunk posture support device utilizing variable stiffness characteristics by pneumatic soft actuator

A variable stiffness composite mixed with pneumatic muscle fibers and elastomer

Pneumatic muscle fibers (PMFs) are a type of pneumatic artificial muscles (PAMs) with millimeter-scale diameter, which show great power to be a soft actuator under injecting the compressed fluid into its bladder. In this paper, the pressurized PMF was considered and investigated as a spring system due to the active contraction capability. The stiffness and variable stiffness characteristics of pressurized PMFs were theoretically investigated by utilizing a non-linear quasi-static model. Experiments were conducted to validate the theoretical model, and the experimental results have good agreement with the model predictions. A variable stiffness composite which was embedded with PMFs into the soft elastomer was presented and experimented to explore the potential adaptive shape-changing behaviors. The composite presented in this paper consists of 16 PMFs with the linear array distribution and two rectangular plates were used to support the PMFs. By taking advantage of the variable stiffness characteristics of pressurized PMFs, the presented composite shows the capability of varying stiffness partly and the shapes of the presented composite can change flexibly.

Novel Design and Modeling of a Soft Pneumatic Actuator Based on Antagonism Mechanism

The soft actuator possesses the characteristics of flexibility, environmental adaptability, and human–machine interaction. Firstly, aiming to resolve the limitation of variable stiffness performance of a traditional pneumatic artificial muscle (PAM) actuator, based on the antagonistic mechanism of extensor and contractor muscles, a novel pneumatic soft actuator coupled of extensor and contractor muscles is proposed in this paper. The actuator can perform the compound action of elongation/contraction, and the stiffness of it can be controlled by adjusting the elongation and contraction forces. Secondly, based on the deformation principle of woven and elastic fabric layers, the mechanical characteristics model of the actuator is established and simulated. The mechanical properties of the actuator are tested under different pressures and deformation displacement and the variable stiffness characteristics of the actuator are verified. Finally, actuators are utilized to manufacture a soft mechanical manipulator, which can achieve variable stiffness in a fixed bending attitude.

Elastic Actuator Design Based on Bending of Cylindrical Beam for Robotic Applications

The lack of suitable actuators has hampered the development of high-performance machines or robots that can compete with living organisms in terms of motion, safety, and energy efficiency. The adaptation properties of biological systems to environmental variables—for example, the control performance of biological muscle with variable stiffness properties—exceeds the performance of mechanical devices. The variable stiffness characteristics of elastic actuators are different from the operating principle of conventional solids. Although there has been a lot of work on the design of elastic actuators in recent years, a low-cost and compact elastic actuator that can be used in place of standard rigid servo actuators is not yet available. In this study, a standard servo motor has been transformed into an elastic actuator by an elastic coupling attached to the gear system. The elastic coupling consists of four small steel beams with a cylindrical cross section placed on the circular disk, and the stiffness of the actuator is adjusted by varying the clutch length of the cylindrical beams. In this study, this innovative design is explained, then the equations expressing the variation of the torsional stiffness of the cylindrical beams with the coupling length and solutions of these equations are given. The experimental results are presented to show the ability of the proposed actuator to control position and regulate the stiffness independently.

Fascicular module of nylon twisted actuators with large force and variable stiffness

In terms of stunning characteristics of ultra-high power density, large stroke and low hysteresis, nylon twisted actuators are ideal actuators for fusion applications of soft robots and conventional rigid-body robots. However, most of previous studies only used single ply of fiber in the devices like prosthesis hands, leading to inadequate force output. Moreover, the stiffness adjustability which is critical to perform dexterous and safe actions has been neglected. In this work, a fascicular module consisting of nylon twisted actuators in parallel connection was proposed and a structural configuration method aiming to realize variable stiffness function was presented and corroborated. The contraction length at the temperature of 120℃ was from 2.22 % to 9.40 % with a fascicular module while it was from 1.29 % to 6.07 % with a single fiber. Under a load of 300 g the contraction length was 0.85%–9.40% with a fascicular module while it was from 0.04%–6.07% with a single fiber. A stiffness variation range of 60.2 % from 1.498 N mm° to 2.402 N mm° was achieved. The enhanced load capacity and standard interface make it more feasible to utilize nylon twisted actuators in bionic robots, rehabilitation devices, etc. In addition, variable stiffness characteristics ensure that soft-rigid devices function in a more reliable and safer way.

Metal mesh embedded in colorless shape memory polyimide for flexible transparent electric-heater and actuators

The current electroactive shape memory polymer composites (SMPCs) show low electric heating efficiency, and the transparency of the matrix is seriously damaged by the conductive fillers. In this work, transparent metal mesh is used to replace the conductive fillers to construct a conductive network for electrical actuation for the first time. The self-cracking aluminum mesh is embedded in the transparent shape memory polyimide film (Alm@TSMPI) by solution casting. As a new type of flexible and transparent heater, the Alm@TSMPI has advantages of fast response and high steady-state temperature. As an electric actuator, the Alm@TSMPI is active and deformable depending on its variable stiffness characteristics, and reverts to its original shape within 13 s under electric stimulation. This is the first report on an electroactive transparent shape memory polymer while maintaining light transmission. Moreover, the transition temperature of 230 °C is much higher than that of all other reported electroactive SMPCs. Furthermore, the Alm@TSMPI is attached to transparent shape memory polystyrene as a flexible transparent heater, and the deformation is triggered by electric field. According to this strategy, the Alm@TSMPI can be applied for the electrical actuation of other SMPs, extending the applications in the electric actuators.

Conceptual mechanical design of antagonistic variable stiffness joint based on equivalent quadratic torsion spring.

The variable stiffness joint is a kind of flexible actuator with variable stiffness characteristics suitable for physical human-robot interaction applications. In the existing variable stiffness joints, the antagonistic variable stiffness joint has the advantages of simple implementation of variable stiffness mechanism and easy modular design of the nonlinear elastic element. The variable stiffness characteristics of antagonistic variable stiffness joints are realized by the antagonistic actuation of two nonlinear springs. A novel design scheme of the equivalent nonlinear torsion spring with compact structure, large angular displacement range, and desired stiffness characteristics is presented in this article. The design calculation for the equivalent quadratic torsion spring is given as an example, and the actuation characteristics of the antagonistic variable stiffness joint based on the equivalent quadratic torsion spring are illustrated. Based on the design idea of constructing the antagonistic variable stiffness joint with compact structure and high compliance, as well as the different design requirements of the joints at different positions of the multi-degrees of freedom robot arm, nine types of mechanical schemes of antagonistic variable stiffness joint with the open design concept are proposed in this article. Finally, the conceptual joint configuration schemes of the robot arm based on the antagonistic variable stiffness joint show the application scheme of the designed antagonistic variable stiffness joint in the multi-degrees of freedom robot.

Magnetically steerable manipulator with variable stiffness using graphene polylactic acid for minimally invasive surgery

For manipulators used in minimally invasive surgery (MIS), variable stiffness and miniaturization are very important characteristics. However, previously proposed mechanisms are difficult to miniaturize due to large and complex structures; thus, they do not achieve variable stiffness characteristics, consequently being difficult to be applied to manipulators used in MIS. In this study, we proposed a manipulator that can be magnetically steered by a permanent magnet at the end and can have variable stiffness characteristics by a phase transition of graphene polylactic acid (GPLA). Thus, the proposed manipulator is easy to fabricate and miniaturize as a magnetic steering MIS manipulator. To verify the magnetic steering and variable stiffness performances of the proposed manipulator, various basic experiments and analysis simulations were executed. In addition, by applying the discriminating properties of the proposed manipulator (magnetic steering, variable stiffness), we can construct a double-segment manipulator with variable stiffness and verify its implementation in postures which are difficult to achieve in other MIS manipulators.

Active and Deformable Organic Electronic Devices based on Conductive Shape Memory Polyimide

Smart, deformable, and transparent electrodes are a significant part of flexible optoelectronic devices. In this work, a novel approach to making highly transparent, smooth, and conductive shape memory polyimide hybrids has been proposed. Colorless shape memory polyimide (CSMPI) with high optical transparency and high heat resistance is served as the substrate for flexible electronic devices for the first time. A hybrid (Au/Ag) metal grid electrode embedded in CSMPI (BMG/CSMPI) is first fabricated via self-cracking template and solution-coating, the advantages of which include ultrasmooth surface, superior mechanical flexibility and durability, strong surface adhesion, and excellent chemical stability due to the unique embedded hybrid structure. The resulting white polymer light emitting diodes (WPLEDs) based on BMG/CSMPI with shape memory effect are active and deformable, and are converted from 2D device into 3D devices depending on its variable stiffness characteristics. The deformed 3D devices could actively recover to the original shape upon heating. Furthermore, ultrathin and flexible 3D optoelectronic devices fabricated using shape memory polymers can promote the development of advanced optoelectronic applications in the future.

Adaptive Variable Stiffness Particle Phalange for Robust and Durable Robotic Grasping.

Grasping is an important characteristic of robots in interacting with humans and the environment. Due to the inherent compliance of soft grippers, they can easily adapt to novel objects and operate safely in a human-centered environment. However, soft hands suffer from poor grasping robustness and operation durability, especially for heavy objects or objects with sharp spikes, mainly due to their fragile material and low structural stiffness of the soft actuators. Thus, the widespread use of soft hands in daily applications is still limited. Existing works have shown a promising direction to enhance grasping performance by solving the contradiction between inherent compliance/adaptability and loading capacity. It is known that the stiffness of the robotic phalange is highly related to the performance of robotic hands. In this article, we propose a novel variable stiffness particle phalange, called VSPP here. The proposed VSPP exhibits variable stiffness characteristics without the need for dedicated actuation by utilizing passive particle jamming resulted from forces in interacting with the environment. The VSPP can cooperate with any kind of actuators, soft or rigid, to function as a compliant and robust robotic hand. A prototype robotic hand based on VSPP could maintain reliable grasping even when pierced by sharp objects such as a needle, a cactus, and a durian. This durability is effective both in air and underwater, thus presents new possibilities for the soft robotic hand to work in a harsh environment. The inherent multidirectional compliance of the VSPP makes safety in human/robot interaction guaranteed. The design and modeling presented in this research will provide useful guidance in VSPP applications. A prototype gripper, VSPP-3, composed of three 2-segments VSPP fingers and pneumatic joints, has been built for demonstrations in reliable and robust grasping of daily objects. The sample grasping has shown that the proposed VSPP has great potential for a robust and durable soft robotic hand or gripper design.

Experimental Testing of Variable Stiffness Bracing System for Reinforced Concrete Structure under Dynamic Load

ABSTRACT This study reports the development of variable stiffness bracing (VSB) system as the lateral resisting element for RC-framed structures subjected to dynamic load. This device can enhance the lateral stability of structures against dynamic loading. The developed VSB device includes a nonlinear leaf spring, which provides variable stiffness characteristics to the system and can be considered a passive structural control system because it is independent of any external power source. A new design for the VSB of structures is proposed, and a prototype is fabricated and installed in an RC frame subjected to dynamic experimental tests. The effect of VSB implementation in an RC frame under dynamic loading is evaluated and compared with a bare frame. Furthermore, the numerical study includes pushover and time history analyses to assess the seismic performance of the developed VSB device. The results of the experimental test and numerical simulation confirmed the efficiency of the developed VSB device as a resisting/retrofitting technique for RC-framed structures. The ductility trend, overall stiffness, and final capacity of the frame improved when the VSB was implemented in the frame. Given that the VSB device can be simply fabricated and installed in an RC frame, the VSB device can also be used as an alternative for increased lateral stability and energy dissipation tendency in new RC-framed buildings. Furthermore, this device can be used as a rapid retrofitting strategy for existing RC buildings.

Robust Tracking Control of Variable Stiffness Joint Based on Feedback Linearization and Disturbance Observer With Estimation Error Compensation

The variable stiffness joint (VSJ) has the characteristics of independent and controllable position and stiffness. The variable stiffness characteristics and inherent flexibility make the VSJ suitable to be used as the actuation joint of the physical human-robot interaction application robot, so as to improve the task adaptability of the robot and physical human-robot interaction safety. The VSJ based on equivalent lever mechanism has the advantages of low energy consumption in stiffness adjustment, so there are many researches on this type of VSJ. The tracking control of output link angular position and joint output stiffness are two basic control targets of the VSJ. For the system dynamic model of the VSJ based on equivalent lever mechanism, considering the unknown parametric perturbations, the unknown friction torques acting on the drive units, the unknown external disturbance acting on the output link and the control input saturation constraints, a robust tracking controller based on feedback linearization, disturbance observer with anti-windup measures, sliding mode control and estimation error compensator is designed to improve the tracking control accuracy of the position and stiffness of the VSJ. The simultaneous tracking control of position and stiffness of the VSJ can be achieved by the designed controller, and the simulation results show the effectiveness and robustness of the proposed controller. Moreover, the simulation results show that the proposed estimation error compensator for the disturbance observer with fixed preset observation gain can effectively reduce the system output tracking error and improve the anti-disturbance characteristics of the controller.

Milling stability prediction of a hybrid machine tool considering low-frequency dynamic characteristics

Stability lobe diagram (SLD) is an important tool to select the spindle speed and axial cutting depth to avoid chatter vibration. For a parallel or hybrid machine tool, the low-frequency dynamic characteristics have a great impact on the SLD and need to be taken into account. One of the major issues related to dynamics analysis is the effective dynamic model of parallel mechanisms, since the stiffness of passive joints varies at different orientations and the structures of components are complex. This paper presents a method to establish an accurate dynamic model and considers the low-frequency characteristics to predict SLD. In this paper, an approach is put forward to get the stiffness and mass matrices of components with variable cross-sections and a structural dynamic model of the parallel mechanism is developed, which innovatively considers the variable stiffness characteristics of the passive joint under different loads. Based on the structural dynamic model, the frequency response function (FRF) of the moving platform is obtained and the results are validated through comparison with those of the hammer test. Using receptance coupling substructure analysis (RCSA) method, the machine-spindle-holder-tool system is divided reasonably and the FRFs at the tool tip are obtained to predict the SLD. It is shown that the low-frequency dynamic characteristics of hybrid machine tools have a great influence on the stability boundary of machine tools, mainly at the low speed region.

A vertical isolation device with variable stiffness for long-span spatial structures

A vertical isolation device with variable stiffness (VIVS) is developed using multiple hydraulic cylinders, which can form a three dimensional (3D) isolation device with a horizontal rubber bearing. The components and control mechanism of the VIVS are explained in detail. A prototype of the VIVS is fabricated to verify its performance by sinusoidal motion tests and shaking table tests. The experimental results show that the variable stiffness characteristics of the VIVS can be achieved, and the isolation period reaches 1.2 s. The shaking table test also verifies the effectiveness of the VIVS in controlling the acceleration. A theoretical model for the VIVS is proposed and validated, and a 60 m single-layer reticulated dome is simulated based on the model. The results indicate that the axial force and acceleration of the structures with VIVS are effectively mitigated with reduced height and displacement of the VIVS.

Theoretical and numerical analysis of stepped disk spring

Disk springs have been widely used in machine tools, aerospace vehicles, and automobiles. Pioneering work by Almen -Laszlo has inspired a deeper understanding of the nonlinear behavior over the last eight decades. There is a need for extending the analysis for stepped section disk springs. In this paper, we report the effect of the stepped section on the force-deflection and variable stiffness characteristics. A simplified method for predicting load deflection of the stepped disk spring has been developed incorporating the geometric non-linearity. Extending the work of Almen-Laszlo, Curti, and Rosa, we present a theoretical analysis that predicts the force deflection characteristic as function of the geometric parameter and the theoretical model is verified using finite element results.