Compliant Frame Research Articles

Compliant frame geometry for DEMES-based gripper and flapping wing actuators: A comprehensive design study

Dielectric elastomer minimum energy structures (DEMES) have attracted significant attention in the recent past because of their ability to switch between multiple equilibrium states. The DEMES is formed when a pre-stretched elastomer film adheres to an inextensible frame and is further allowed to attain an equilibrium configuration as a result of energy minimization. While several researchers have investigated; both theoretically and experimentally, the underlying mechanics of DEMES, a majority of them deploy simplistic boundary frames (square/rectangular/circular) to obtain the requisite minimum energy configuration. In this paper, we demonstrate that this seemingly restrictive choice of using simplistic frame geometries can be given away by designing more complex-shaped compliant frames capable of producing useful modes of deformation. To demonstrate this idea, two prototypes; namely, the four-arm gripper actuator and the flapping-wing actuator, are studied numerically and experimentally. In both cases, a single compliant frame is used to realize the respective configuration, thus circumventing the need to assemble multiple MES on a common platform. In tandem, we investigate the role of reinforcements in (a) controlling the warping in MES and (b) maximizing actuation in the desired mode of deformation. Finite element analysis are carried out using the ABAQUS to determine the equilibrium configuration of the actuators, and subsequently their electromechanical behavior. Experimental investigations involve the utilization of the commercially available VHB 4910 acrylic tape in conjunction with PET frames and 3D-printed reinforcements. Excellent qualitative agreement is achieved between the numerical predictions and the experimental observations. Finally, we allude to a few innovative frame architectures leading the MES of engineering interest.

Effect of geometrical parameters on the nonlinear behavior of DE-based minimum energy structures: Numerical modeling and experimental investigation

This work presents a finite element framework for simulating the quasi-static response of dielectric elastomer-based minimum energy structure (DEMES). The DEMES is an actuator formed by combining an inextensible frame and pre-stretched dielectric membrane that exhibits the unique shape-morphing characteristics of the actuator. A continuum strain energy-based model is implemented to investigate the impact of the different geometrical parameters on the performance of the DEMES actuator. Finite element analyses are performed using user-defined element (UEL) in ABAQUS for determining the equilibrium shape of the actuators and further investigating their electromechanical response. Experiments are performed using the commercially available VHB-4910 acrylic tape and the PET frames. 3D-printed reinforcements are used to impart anisotropy in the specimen. The findings of the model solutions provide preliminary insights on the alteration of the initial and final configurations of the DEMES affected by different geometrical parameters. It is observed that the shape of the electrode (rectangular, circular and triangular), compliant frame (rectangular, circular and triangular) and implemented stiffeners appreciably alter the attained initial configuration, final configuration and actuation range of the DEMES actuator. In general, this investigation can find its potential use in designing the futuristic DEMES through topological optimization of the compliant electrode and frame geometry together with material anisotropy of the elastomer.

A continuous broadband electromagnetic energy harvester based on amplitude and phase adjustments

Broadening the bandwidth of vibration energy harvesters is a critical issue for their practical implementations. Although utilizing multi-degree-of-freedoms is a frequently used solution to widen the operating frequency range, the resultant effective bandwidth could consist of discrete peaks (existing local minimum points lower than the half-power level) if the modal amplitudes have large differences at different frequencies. To solve these problems, we designed a new electromagnetic multi-modal energy harvester, which works in a broad and continuous low-frequency bandwidth. This is achieved by attaching the magnet and the coil to a compliant frame integrated with two different kinked beams, respectively. In this way, the voltage can be generated in a continuous and wide frequency range by adjusting the amplitudes and phases of the magnet and the coil in different modes according to a proposed design requirement. Finite element results and experimental results are in good agreement with each other, which validate the performance of the proposed harvester. The experimental results demonstrate that the half-power bandwidth can be achieved in the range of 15.0 Hz and the maximum peak power is 1.56 mW at the center frequency of 40.5 Hz under base excitation of the root-mean-square acceleration of 0.24 g. The broadband and high power density feature are also validated in a random excitation test, so that this harvester has great potential for practical applications.

Effect of viscoelasticity on the nonlinear dynamic behavior of dielectric elastomer minimum energy structures

Dielectric elastomer minimum energy structure (DEMES) formed by clinging a pre-stretched dielectric elastomer (DE) membrane to the compliant frame possess both material and geometrical nonlinearity. The viscous and hyperelastic nature of the DE membrane and coupling between the compliant frame and membrane forms the basis of these nonlinearities. Practically, DE membrane based DEMES actuator executes the transient motion which is significantly affected by the viscoelastic behavior of the DE membrane. Hence, for an efficient design of such devices, it is very important to analyse the effect of membrane viscoelasticity on the dynamic response of DEMES. In the present work, we have developed an analytical model to analyse the viscoelastic effect of DE membrane on the nonlinear dynamic behavior of the DEMES. In order to incorporate the viscous effect, the Zener rheological model consisting of a spring element connected in parallel to a Maxwell element is employed. The neo-Hookean material model based on the additive decomposition of the isotropic strain energy density into equilibrium and viscous parts is considered. The governing differential equation representing the dynamic behavior of DEMES actuator is derived using Euler–Lagrange equation of motion for non-conservative system. The isotropic viscous stretch is obtained by using the thermodynamically consistent evolution equation. The developed dynamic model predicts the initial shape, DC and AC response, periodicity of the DEMES for different values of viscosity parameter. The result reveals that the onset of equilibrium state delays as viscosity parameter increases. Further, the bending angle of DEMES actuator is significantly affected by the applied electric field and viscoelastic behavior of the DE membrane. Poincaré maps along with phase diagrams are presented to analyse the periodicity of nonlinear oscillation of the system. Further, the structure executes a stability transition (stable-unstable-stable) as the value of viscosity parameter increases. The obtained results can help in robust and efficient designing of DEMES based actuators subjected to dynamic loading.

Integrated Design of Actuation and Mechanism of Dielectric Elastomers Using Topology Optimization Based on Fat Bezier Curves.

Soft actuation technology has attracted considerable interest in recent decades, with the light weight, high response speed, and large deformation of dielectric elastomer actuators (DEAs) showing particular promise. DEAs composed of compliant frames and prestrained dielectric elastomers (DEs) can be considered as a soft actuation system, which is termed minimum-energy structure. Most existing DEAs come from a well-known design with a simple configuration but complex design process. In this article, we propose an integrated design method for the actuation and mechanism of DEs based on topology optimization using fat Bezier curves. In this method, the compliant frame is represented by fat Bezier curves, and the prestrained DE is distributed in the region bounded by the curves. This article first describes the theoretical modeling process, and then presents three design examples that validate the optimization algorithm. Finite element analysis (FEA) and experiments are conducted to assess the performance of the optimized configurations. The FEA simulations and experimental results show that the topology optimization algorithm results in DEAs that exhibit the desired motion.

A simple and easy-to-build optoelectronics force sensor based on light fork: Design comparison and experimental evaluation

In this paper, the design and the implementation of a force sensor based on a commercial optoelectronic component called light fork and characterized by the simple construction process is presented. The proposed sensor implementation is designed to measures the force applied by a cable-based actuation by detecting the deformation of a properly designed compliant structure integrated into the actuation module. Despite this, the design method here presented allows to adapt the sensor to a large set of robotic applications, thanks to its simplicity in the construction and low cost. The main advantages of the proposed sensor consist in the use of a very compact commercial optoelectronic component, called light fork, as sensing element. This solution allows a very simple assembly procedure together with a good sensor response in terms of sensitivity, linearity and noise rejection to be achieved using an extremely simple electronics, thereby obtaining in this way a reliable and very cheap sensor that can be easily integrated in actuation modules for robots and can easily adapted to a wide application set.The paper presents the basic sensor working principle and the compliant frame design. An analytic model of the compliant frame deformation is proposed and verified both by finite element analysis and by experimental measures performed on four different sensor specimens manufactured by 3D printing and CNC milling, and the results have been compared. Moreover, the sensor specimens calibration and the experimental validation have been performed both in static and dynamic conditions.

Ideal shear banding in metallic glass

As the most fundamental deformation mechanism in metallic glasses (MGs), the shear banding has attracted a lot of attention and interest over the years. However, the intrinsic properties of the shear band are affected and even substantially changed by the influence of non-rigid testing machine that cannot be completely removed in real compression tests. In particular, the duration of the shear banding event is prolonged due to the recovery of the stressed compliant frame of testing machine and therefore the temperature rise at the operating shear band is, more or less, underestimated in previous literatures. In this study, we propose a model for the ‘ideal’ shear banding in metallic glass. The compliance of the testing machine is eliminated, and the intrinsic shear banding process is extracted and investigated. Two important physical parameters, the sliding speed and the temperature of shear band, are calculated and analysed on the basis of the thermo-mechanical coupling. Strain-rate hardening is proposed to compensate thermal softening and stabilise the shear band. The maximum value of the sliding speed is found to be on the order of 10 m/s at least, and the critical temperature at which strain-rate hardening begins to take effect should reach as high as 0.9Tg (Tg is the glass transition temperature) for a stable shear banding event in metallic glass according to the early experimental data. This model can help to understand and control the shear banding and therefore the deformation in MGs.

Seismic collapse evaluation of steel moment resisting frames with superelastic viscous damper

This study investigates the seismic collapse resistance of steel moment resisting frames equipped with superelastic viscous dampers (SVD) through incremental dynamic analysis (IDA). The SVD is a hybrid passive control device that strategically combines a viscoelastic device and shape memory alloy cables in parallel. The hybrid device exhibits improved re-centering and energy dissipating capabilities compared to only viscoelastic or only SMA-based devices. First, the design and mechanical behavior of SVDs are described. A nine-story steel frame building is selected for the numerical analyses. The building is first designed as a conventional special moment resisting frame (SMRF) to meet the strength and stiffness requirements of the design codes. Then, a reduced strength version of the fully code compliant frame is developed and upgraded with either SVDs or buckling restrained brace (BRB) system. Analytical models of the steel building for each configuration are developed to simulate global frame behavior by considering both geometric nonlinearities and cyclic strength and stiffness deterioration of structural steel components under dynamic loads. Incremental dynamic analysis is employed to assess the seismic resistance of steel frame structures up to collapse using 44 ground motion records. A sensitivity analysis is also performed to evaluate the influence of SVD design parameters on the seismic response of the frame. The results indicate that the steel frame designed with SVDs has the largest median collapse capacity and minimal residual drifts under various seismic hazard levels.

Realization of point planar elastic behaviors using revolute joint serial mechanisms having specified link lengths

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having only revolute joints, each with selectable compliance. The link lengths of the mechanism and the location of the compliant frame relative to the mechanism base are arbitrary but specified. The realizability of a given compliant behavior is investigated, and necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. These realization conditions are interpreted in terms of geometric relationships among the joints. We show that, for an appropriately sized 3R serial mechanism, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. Requirements on mechanism geometry to realize every particle planar elastic behavior at a given location just by changing the mechanism configuration are also identified.

An Optical Torque Sensor for Robotic Applications

In this article, the design and the experimental evaluation of a torque sensor based on optoelectronic components integrated in a suitably designed plastic compliant frame are reported. The sensing principle is based on the variation of the photocurrent flowing through a PhotoDetector (PD) as a consequence of the variation of its relative position, with respect of a Light Emitting Diode (LED), caused by the deformation of the sensor frame under the effect of the torque to be measured. The sensor frame has been designed as a planar structure that shows preferential deformation along a rotation axis normal to the symmetry plane. This article reports the sensor basic working principle, the compliant frame design and verification, the calibration of the sensor, and the experimental evaluation of its sensitivity and frequency response.

A miniaturized optical force sensor for tendon-driven mechatronic systems: Design and experimental evaluation

In this paper, an innovative sensor for the control of a tendon-driven mechatronic system is presented. The proposed sensor measures the tendon tension using optoelectronic components properly selected and mounted on a suitably designed compliant frame. This solution presents several advantages mainly in terms of simplicity and compactness with respect to force sensors based on strain-gauge or Bragg-grating. By exploiting the properties of optoelectronic components with a narrow angle of view and by means of a very simple conditioning electronics, the very small deformation of the compliant frame caused by the tendon force can be measured. Moreover, the compliant frame has been designed to allow the sensor to be mounted in any position along the tendon. The sensor working principle, an optimal design procedure and the results of an experimental testbench where two of the proposed sensors are used for the feedback control of a tendon-driven mechatronic system are reported in the paper. The experimental verification of a contact force estimation algorithm useful for grasping and manipulation purposes in which the data collected by the optoelectronic tendon force sensors are exploited is also reported in the paper.

Dynamic modeling and experimental evaluation of a constant-force dielectric elastomer actuator

Constant-force actuators based on dielectric elastomers can be obtained by coupling a dielectric elastomer film with particular compliant frames whose structural properties must be carefully designed. In any case, the practical achievement of a desired force profile can be quite a challenging task owing to the time-dependent phenomena, which affect the dielectric elastomer’s electromechanical response. Within this scenario, a hyperviscoelastic model of a rectangular constant-force actuator is reported. The model, based on the bond graph formalism, can be used as an engineering tool when designing and/or controlling actuators that are expected to work under given nominal conditions. Simulations and experimental results are provided, which predict the system response to fast changes in activation voltage and actuator position as imposed by an external user.

Time-lapse acoustic, transport, and NMR measurements to characterize microstructural changes of carbonate rocks during injection of CO2-rich water

We investigated how changes induced in the microstructure of carbonate rocks by the injection of [Formula: see text]-rich water affect pore-network properties. In particular, we investigated from multiple perspectives the microstructural changes and types of porosity that alter the observable geophysical properties. We thereby refined our understanding of induced modification of the pore network. Our experimental protocol included a suite of time-lapse acoustic, transport, and nuclear magnetic resonance (NMR) measurements, along with scanning electron microscopy (SEM) and CT-scan images; these gave us complementary sensitivity to changes in different properties of the pore space. Induced porosity variations were smaller than in previous reported results because of chemomechanical compaction resulting from dissolution under pressure. No porosity enhancements larger than 0.8 pu were observed. Results indicated that dissolution occured primarily in the grain-coating cement and the microporosity of the micritic phase. Both caused the formation of cracklike pores around larger grains leading to a more compliant frame, causing both velocity reductions and an increased sensitivity of velocity to pressure. Chalky micritic facies exhibited velocity reductions of [Formula: see text], whereas micritic limestones, less prone to compaction and grain sliding, experienced smaller velocity reductions ([Formula: see text]). Because porosity enhancement was minimal, we hypothesized that the reductions were due to injection-induced reduction of grain-contact stiffness. Dissolution-induced compaction played an integral role also in the permeability response during injection. Compaction in pressure-sensitive chalky facies strongly counteracted the effects of dissolution, leading to negligible permeability and NMR response changes. In contrast, stiff micritic limestones with little dissolution-induced compaction exhibited larger permeability increases ([Formula: see text]). This work demonstrated the advantages of utilizing a suite of concurrent and independent measurements to build a more comprehensive interpretation of microstructure changes induced by injecting fluids that are in chemical disequilibrium with the host formation.

Scaling of Performance, Weight, and Actuation of a 2-D Compliant Cellular Frame Structure for a Morphing Wing

A typical mission profile for a fixed-wing aircraft consists of several idealized phases: takeoff, climb, cruise, dash, loiter, descent, and landing. Corresponding to each phase of flight and associated weight is a specific wing configuration that yields optimal performance. Conventional aircraft employ a single fixed structure (with movable control surfaces), one that is necessarily a compromise. Morphing structures technology provides the possibility of making large global changes to the wing shape, ideally enabling optimum performance over a larger range of flight conditions. Although structural and actuator weights necessarily increase with morphing capability, overall performance gains can offset these subsystem weight increases with fuel savings or by enabling new aircraft missions. A 2-D compliant cellular truss structure was designed to replace the fixed internal structure of a wing; this structure is able to achieve large changes in span and thus planform area and aspect ratio. The capability of this design was determined for aircraft of varying scale. At RC model scale, approximately 0.5—5 kg (1—10 lb), the wing structure is capable of an 85% decrease in the planform area with a structural weight of 2.9% of the gross weight. As the gross weight of the aircraft increases, the achievable span reduction decreases while the structural weight fraction increases. For 50 and 500 kg (100 and 1000 lb) aircraft, the decrease in planform area is 74% and 48%, respectively. At 50 kg (100 lb), the wing structure comprises 7.4% of the gross weight, while at 500 kg (1000 lb), this increases to 8.9%. The difference between the weight of the morphing structure and a similar passive structure is a weight penalty: the trade-off required for the ability to morph. Actuation systems, including a single actuator and a system of parallel actuators, were also considered for their ability to deform the structure. The weight fraction of the actuators required to deform the structure was found to increase with increasing gross weight. A system of parallel actuators was found to have a significant advantage over a single actuator, especially at higher gross weights. The benefit of morphing increases with gross weight but structural morphing capability decreases with gross weight. This suggests, for a given structural paradigm, that there is a gross weight for which morphing is most advantageous and practical.

Membrane-type metamaterials: Transmission loss of multi-celled arrays

Acoustic metamaterials with negative dynamic mass density have been shown to demonstrate a five-fold increase in transmission loss (TL) over mass law predictions for a narrowband (100 Hz) at low frequencies (100–1000 Hz). The present work focuses on the scale-up of this effect by examining the behavior of multiple elements arranged in arrays. Single membranes were stretched over rigid frame supports and masses were attached to the center of each divided cell. The TL behavior was measured for multiple configurations with different magnitudes of mass distributed across each of the cell membranes in the array resulting in a multipeak TL profile. To better understand scale-up issues, the effect of the frame structure compliance was evaluated, and more compliant frames resulted in a reduction in the TL peak frequency bandwidth. In addition, displacement measurements of frames and membranes were performed using a laser vibrometer. Finally, the measured TL of the multi-celled structure was compared with the TL behavior predicted by finite element analysis to understand the role of nonuniform mass distribution and frame compliance.

Optimal Synthesis of Conically Shaped Dielectric Elastomer Linear Actuators: Design Methodology and Experimental Validation

An analytical model and an operational procedure are presented, which make it possible to optimize conically shaped dielectric-elastomer linear actuators for known materials and desired force/stroke requirements. The actuators are obtained by coupling a dielectric elastomer film with a compliant frame which is sized by means of a pseudorigid body model. Depending on the frame design, the actuators can work monodirectionally or bidirectionally. Simulation and experimental results are provided which demonstrate the efficacy of the proposed design procedure and show that well-behaved conically shaped actuators can be conceived and produced.

Force sensor based on discrete optoelectronic components and compliant frames

In this paper, a novel force sensor based on commercial discrete optoelectronic components mounted on a compliant frame is described. The compliant frame has been designed through an optimization procedure to achieve a desired relation between the applied force and the angular displacement of the optical axes of the optoelectronic components. The narrow-angle characteristics of Light Emitting Diode (LED) and PhotoDetector (PD) couples have been exploited for the generation of a signal proportional to very limited deformation of the compliant frame caused by the external traction force. This sensor is suitable for applications in the field of tendon driven robots, and in particular the use of this sensor for the measurement of the actuator side tendon force in a robotic hand is reported. The design procedure of the sensor is presented together with the sensor prototype, the experimental verification of the calibration curve and of the frame deformation and the testing in a force feedback control system. The main advantages of this sensor are the simplified conditioning electronics, the very high noise-to-signal ratio and the immunity to electromagnetic fields.

Coordinated Kinematic Control of Compliantly Coupled Multirobot Systems in an Array Format

This paper presents coordinated kinematic control of compliantly coupled multirobot systems for payload transportation. In the robot, unicycle-type axles are connected to a moving platform in an array format using compliant frames. A coordinate system is attached to an ideal center point on the platform to establish robot kinematics. In order to drive the system along a reference trajectory, we coordinate axle velocity commands, while considering frame compliance, nonholonomic constraints, and rigid body kinematics, respectively. These commands are further coordinated to consider configuration stability and physical limitations. Simulation and experimental results evaluate the coordination algorithms for various trajectories.

Optimal Design of Lozenge-shaped Dielectric Elastomer Linear Actuators: Mathematical Procedure and Experimental Validation

A novel mathematical procedure is presented, which makes it possible to optimize lozenge-shaped dielectric-elastomer-based linear actuators for known materials and desired force/stroke requirements. Simulation and experimental results are provided which both demonstrate the efficacy of the proposed optimization procedure with respect to traditional design approaches and show that simpler, cheaper, lighter, and better-behaved lozenge-shaped actuators can be conceived, which do not require any integration of compliant frame elements.

Distributed Kinematic Motion Control of Multi-Robot Coordination Subject to Physical Constraints

This paper presents a kinematic motion control strategy for an n-axle Compliant Framed Modular wheeled Mobile Robot (CFMMR). This robot is essentially a passive-joint active-wheel snake robot where coordinated motion of the robot modules is critical for maximizing mobility and minimizing traction forces. A distributed master—slave kinematic motion control structure is proposed where the front axle module of the robot is the master and subsequent axle modules are slaves. An existing path manifold based controller is used to guide the motion of the master. Two steering algorithms with different specializations are then proposed for the slave modules. Performance of the steering algorithms is characterized based upon their capability to reduce traction forces, control final robot posture, and maneuver in a limited space. It is shown that these algorithms satisfy the physical constraints of the robot, which are characterized by path curvature and velocity limitations. Simulation and experimental results validate and characterize the performance of the algorithms.