Fixed-guided Beam Research Articles

Simulation and Investigation of Si-Based Piezoelectric Micromachined Ultrasonic Transducer (PMUT) Performances

Micro-electromechanical system (MEMS) based piezoelectric ultrasonic transducers for acoustic imaging of the surroundings are known as piezoelectric micromachined ultrasonic transducers (PMUTs). This research proposes a structural design of the PMUT with four fixed-guided beams. The beam is subjected to lateral loads, with vectors that are perpendicular to the longitudinal axis. This project simulated Piezoelectric Micromachined Ultrasonic Transducer (PMUT) with three different material properties i.e. Aluminium Nitride (AlN), Lead zirconate titanate (PZT) and Zinc Oxide (ZnO). Based on the study, it was found that reducing the beam dimensions and increasing the plate size will result in the first mode frequency reduction from 1.33x107 Hz to 3.74x106 Hz. Other than that, it was found that AlN PMUT experienced the maximum deflection of 6.3413 to 6.3478 μm when the loads applied in the range of 50 to 200 μN/m2. When the piezoelectric material changed to PZT, we obtained the maximum deflections of 0.3771 to 0.3786 μm when the same loads range applied to the PMUT. As for the ZnO PMUT, the maximum deflections obtained were in between 0.1702 μm to 0.1772 μm with the loads are maintained as in the loads applied to the AlN and PZT. This study proved the significant impact of altering the structural dimensions and material properties of PMUTs on their operational characteristics, specifically the first mode frequency and deflection behavior.

Design of Passive Constant-Force End-Effector for Robotic Polishing of Optical Reflective Mirrors

Polishing plays an indispensable role in optical processing, especially for large-aperture optical reflective mirrors with freeform surfaces. Robotic polishing requires effective control of the contact force between the robot and the mirror during processing. In order to maintain a constant contact force during polishing, traditional polishing robots rely on closed-loop control of air cylinders, whose performances heavily rely on high-fidelity force sensing and real-time control. This paper proposes to employ a compliant constant-force mechanism in the end-effector of a polishing robot to passively maintain a constant force between the robot and the mirror, thus eliminating the requirement for force sensing and closed-loop control. The compliant constant force mechanism utilizing the second bending mode of fixed-guided compliant beams is adopted and elaborated for the passive end-effector. An end-effector providing a constant contact force of 40 N is designed and prototyped. The polishing experiment shows that the passive constant-force end-effector provides stable contact force between the robot and the mirror with fluctuation within 3.43 N, and achieves RMS (Root Mean Square) lower than λ/10 (λ = 632.8 nm) of the polished surface of the large-aperture optical reflective mirror. It is concluded that the constant-force compliant mechanism provides a low-cost and reliable solution for force control in robotic polishing.

Design of quasi-zero stiffness compliant shock isolator under strong shock excitation

The quasi-zero stiffness (QZS) mechanism can rely on the combination of negative and positive stiffness elements to achieve very low dynamic stiffness while obtaining high static stiffness to support the isolated payload. It is a nonlinear shock isolation method with good shock isolation performance. In this paper, a new QZS compliant shock isolator is designed for shock isolation under strong acceleration shock excitation(>1000g), by paralleling a fixed-guided beam with negative stiffness and a Roberts configuration compliant beam with positive stiffness. The force-displacement characteristics of the QZS compliant shock isolator is analyzed and calculated theoretically using an elliptic integration method, and are verified by comparison using finite element simulation. The dynamic time-domain response characteristics of the QZS compliant shock isolator under the excitation of ideal shock excitation with different amplitudes, different periods, different payloads, and actual shock excitation are calculated, and compared with the performance of a general positive stiffness compliant shock isolator under the same excitation. The results show that the proposed QZS compliant shock isolator can be applied to shock isolation under strong shock excitation, and exhibits good constant force characteristics in the whole stroke during the shock isolation process, and is less affected by the amplitude and period of shock excitation. Compared with the general positive stiffness compliant shock isolator, the proposed QZS compliant shock isolator can significantly reduce the peak of the shock, reduce the maximum acceleration ratio and improve the shock isolation performance. It can provide some theoretical guidance for the design of the QZS compliant shock isolator under strong shock excitation.

Ultra-low wide bandwidth vibrational energy harvesting using a statically balanced compliant mechanism

Structure design of ultra-low wide bandwidth vibrational energy harvesters remains an open issue. In this research, a statically balanced compliant mechanism (SBCM) is proposed, dynamically modelled, and experimentally demonstrated to address this need. This SBCM is designed based on the concept of stiffness compensation between a linear component with positive-stiffness (two double parallelograms in parallel) and a nonlinear component with negative-stiffness (two sets of post-buckled fixed-guided compliant beams in parallel). A design guideline of the SBCM starting from using rapid-design stiffness compensation equation is provided for reasonably approximate and accurate results. Subsequently, a dynamic analytical model of the displacement response of the SBCM to harmonic base excitation has been derived based on the averaging method. The nonlinear force-displacement relationship of the system was obtained through nonlinear finite element analysis (FEA) simulations in this regard and a 5th order polynomial fit was chosen taking only odd terms into account. The accuracy of this analytical model is confirmed by numerical analysis. Next, a prototype of the SBCM was fabricated and its applicability to piezoelectric vibrational energy harvesters (PVEHs) was demonstrated by integrating piezoelectric capacitors made of PVDF films with compliant beams of the SBCM to generate electric outputs in response to the bending of the beams. Static balancing is achieved over a continuous displacement range of 2 mm around the origin. Bi-stability and mono-stability were observed with the same prototype by adjusting the length of the positive-stiffness beams. Under static-balancing condition, the SBCM is able to respond to a wide range of ultra-low frequencies with low accelerations, which has been established experimentally, analytically and numerically. In dynamic experiments, the steady-state relative displacement amplitude H is 2.9 mm under an excitation condition of 6 Hz and 0.1g (1g=9.8 m/s2), and it reaches a maximum of 9.4 mm under 12.75 Hz and 0.25 g. A 30%-Hmax frequency bandwidth is introduced to assess the nonlinear dynamic performance of the SBCM from a mechanical perspective. The maximum experimental 30%-Hmax bandwidth of the structure is 6.75 Hz (from 6 Hz to 12.75 Hz) at 0.25 g and the corresponding theoretical value is 8.73 Hz (from 3.34 Hz to 12.07 Hz). Under the same excitation condition, it is shown that the maximum relative displacement amplitude deceases as the jump-down frequency increases. In addition, super-harmonic and sub-harmonic oscillations are observed in the dynamic experiments. The SBCM can provide a practical structural solution for harvesting energy from a range of vibrational scenarios (e.g. ocean waves, human motions and bridge vibrations) with ultra-low wide bandwidth frequencies and weak accelerations. The concept of SBCM is suitable to be combined with various energy conversion principles and is not limited to piezoelectric sources alone. When miniaturized, the SBCM concept can be of particular interest to researchers active in energy harvesting for microelectromechanical systems (MEMS) technology.

Design and Analysis of a Novel Compliant Tensile Testing Module Based on Buckled Fixed-Guided Beam

The need to accurately measure the mechanical properties of freestanding thin films such as carbon nanotube reinforced nanocomposite thin films and various buckypaper is increasingly urgent. This paper presents the design and control of a novel compliant tensile testing module based on buckled fixed-guided beams aimed at accurately measuring the mechanical properties of freestanding thin films. The piezoelectric stack actuator that can provide high resolution for the output displacement is chosen to actuate the tensile testing module. The advantages of the module are its compactness, no friction, no wear, low cost and good repeatability. The performance is further evaluated by the established analytical model using the elliptic integral approach and the nonlinear finite-element analysis (FEA). A metal prototype of the tensile testing design has been fabricated and the performance of the fabricated prototype is investigated through open-loop displacement response experiments. Experimental results demonstrate the effectiveness of the proposed ideas for the mechanism. The design holds great potential applications in measuring mechanical properties of freestanding thin-film materials such as carbon nanotube reinforced nanocomposite thin films and various buckypaper as well as other freestanding thin-film materials.

Statics Analysis and Optimization Design for a Fixed-Guided Beam Flexure

The ratchet mechanism has been used to ensure moving in one direction of rotation, i.e. either clockwise or counterclockwise. This mechanism is designed based on fixed-guided beam flexures to reduce friction and improves accuracy compared to the traditional mechanism. This paper presents a static analysis and parameter optimization for the fixed-guided beam flexures via using the pseudo-rigid-body model and a fmincon algorithm. The Finite Element Method (FEM) of the fixed-guided beam also has been used to verify the maximum stress and the x-direction displacement. Modified pseudorigid-body model (M-PRBM) is also applied to significantly enhance the accuracy of the maximum stress value. The results show that the averaged errors of maximum stress between MPRBM and FEM are 3.48% for aluminum, and less than 10.9% for titanium, carbon steel, and alloy steel. From the obtained results, the MPRBM is good for prototype design and fabrication of the ratchet mechanism in the future. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Design and Testing of a New Force-Sensing Cell Microinjector Based on Soft Flexure Mechanism

Cell microinjection plays an important role in biological and medical fields. As compared with manual cell microinjection and position-based robotic cell microinjection, force-assisted robotic cell microinjection can improve the success rate and survival rate of the injected cells. In this paper, a novel force-sensing cell microinjector is proposed with a piezoresistive force sensor embedded in soft-material-based flexure mechanism. The soft flexures act as fixed-guided beams, which are introduced to achieve the force measurement with high sensitivity in pure one-degree-of-freedom direction. The microinjector is developed by considering the installation and replacement issues of the micropipette and the connection between the micropipette and the tube of compressed air. Four different prototypes of the cell microinjector with force sensor are fabricated, calibrated, and compared. Results show that the resolution and measurement ranges of an embedded force sensor are 0.65 mN and 16.5 mN, respectively. Experimental study on microinjection of crab eggs is conducted to validate the performance of the fabricated microinjector in practice.

A modified pseudo-rigid-body modeling approach for compliant mechanisms with fixed-guided beam flexures

Abstract. In the present paper, we investigate a modified pseudo-rigid-body (MPRB) modeling approach for compliant mechanisms with fixed-guided beam flexures by considering the nonlinear effects of center-shifting and load-stiffening. In particular, a fixed-guided compliant beam is modeled as a pair of fixed-free compliant beams jointed at the inflection point, where each fixed-free beam flexure is further modeled by a rigid link connected with an extension spring by a torsion spring, based on the beam constraint model (BCM). Meanwhile, the characteristic parameters of the proposed MPRB model are no longer constant values, but affected by the applied general tip load, especially the axial force. The developed MPRB modeling method is then applied to the analysis of three common compliant mechanisms (i.e. compound parallelogram mechanisms, bistable mechanisms and 1-DOF translational mechanisms), which is further verified by the finite element analysis (FEA) results. The proposed MPRB model provides a more accurate method to predict the performance characteristics such as deformation capability, stiffness variation, as well as error motions of complaint mechanisms with fixed-guided beam flexures, and offers a new look into the design and optimization of beam-based compliant mechanisms.

Design of a PVDF-MFC Force Sensor for Robot-Assisted Single Cell Microinjection

Robot-assisted cell microinjection is an important approach to modern biological applications. Micro-force sensor is a crucial device to facilitate a precise injection of biological cells. Majority of existing film-based force sensors are designed as a cantilever structure for cell injection application. However, such kind of force sensor has inherent disadvantages in terms of unstable transmission of injection force, bigger puncturing wound, and operation inaccuracy. In this paper, a novel 1-D force sensor is designed by using polyvinylidene fluoride (PVDF) and macro fiber composite (MFC) films as fixed-guided beams to construct a multistage compound parallelogram flexure mechanism. It enables both capabilities of force sensing and stable cell holding. A prototype is fabricated, calibrated, and applied to crab egg embryo injection. The transverse strain effect of the fixed-guided sensing beams has been quantitatively measured by experiments. Comparison investigation reveals the great potential of MFC film over PVDF film for force sensing in cell microinjection application. The MFC force sensor offers the resolution, sensitivity, and measuring range of 0.80 mN, 1.23 mV/mN, and 100 mN, respectively. Microinjection experiments demonstrate that the developed force sensor faithfully reveals the process of cell injection and measures the puncturing force of 27 mN for crab eggs in real time.

Design and Control of a Novel Compliant Constant-Force Gripper Based on Buckled Fixed-Guided Beams

This paper presents the design and control of a novel gripper device with a passive type of compliant constant-force mechanism. The function of constant-force output is achieved by using the combination of a positive-stiffness and a negative-stiffness mechanism. The negative stiffness is generated by a bistable buckled fixed-guided beam. Conventionally, when gripping a target-object using a high-stiffness gripper, both the displacement control and force control are required to prevent the damage of the object. The uniqueness of the developed constant-force gripper is that it can eliminate the dependence on force control while keeping the force constant via its mechanical structure. The gripper performance is evaluated by the established analytical model and nonlinear finite-element analysis, and validated through experimental study on a fabricated prototype. To achieve a precise position output of the gripper jaw, a discrete-time variable structure control strategy based on a nonswitching type of reaching law is realized. The effectiveness of the gripper system is verified by conducting experimental studies on grasp-hold-release operations of a micro copper wire.

Bi-BCM: A Closed-Form Solution for Fixed-Guided Beams in Compliant Mechanisms

A fixed-guided beam, with one end is fixed while the other is guided in that the angle of that end does not change, is one of the most commonly used flexible segments in compliant mechanisms such as bistable mechanisms, compliant parallelogram mechanisms, compound compliant parallelogram mechanisms, and thermomechanical in-plane microactuators. In this paper, we split a fixed-guided beam into two elements, formulate each element using the beam constraint model (BCM) equations, and then assemble the two elements' equations to obtain the final solution for the load–deflection relations. Interestingly, the resulting load–deflection solution (referred to as Bi-BCM) is closed-form, in which the tip loads are expressed as functions of the tip deflections. The maximum allowable axial force of Bi-BCM is the quadruple of that of BCM. Bi-BCM also extends the capability of BCM for predicting the second mode bending of fixed-guided beams. Besides, the boundary line between the first and the second modes bending of fixed-guided beams can be easily obtained using a closed-form equation. Bi-BCM can be immediately used for quick design calculations of compliant mechanisms utilizing fixed-guided beams as their flexible segments (generally no iteration is required). Different examples are analyzed to illustrate the usage of Bi-BCM, and the results show the effectiveness of the closed-form solution.

Nonlinear Dynamics of Axially Loaded Piezoelectric Energy Harvester

In the present work nonlinear dynamics of axially loaded energy harvester which is modeled as a fixed-guided beam with tip mass having piezoelectric patch has been investigated. The system is subjected to a base excitation and periodic axial load. The governing equation of motion of the system is developed using Lagrange principle. A closed form solution has been developed to find out the response and generated voltage using method of multiple scales (MMS). Frequency response of the system is obtained for superharmonic and subharmonic resonance conditions and parametric study has been carried out in order to investigate the variation of output voltage with different system parameters.

On the modeling of tilted fixed-guided flexible beams under tension

We derive explicit solutions for a fixed-guided slender suspension beam that is initially straight and tilted with respect to the moving direction of its sliding end. The beam experiences substantial axial forces during the tension, resulting in a nonlinear boundary value problem. We consider sliding end displacements in the direction that cause longitudinal tension along the beam. We first propose an exact approach, leading to analytical solutions for various physical variables such as the transverse force and deflection profile, in terms of the axial force and the positive real solution of a third-order algebraic equation. We also propose an alternative approximate solution based on a second-order equation, which provides closed-form analytical solutions for the physical variables. We also introduce analytical validation techniques for the underlying assumptions. Consistency with nonlinear finite-element analysis is also addressed. Moreover, the results of the approximate method are represented by dimensionless formulas, generating charts to predict solutions for arbitrarily assigned beam parameters. Magnitudes of the normal and shear stress values are also included to consider the effects of yield and shear strengths as the limiting factors at large deflection conditions.

A nonlinear multi-mode wideband piezoelectric vibration-based energy harvester using compliant orthoplanar spring

In this paper, a nonlinear wideband multi-mode piezoelectric vibration-based energy harvester (PVEH) is proposed based on a compliant orthoplanar spring (COPS), which has an advantage of providing multiple vibration modes at relatively low frequencies. The PVEH is made of a tri-leg COPS flexible structure, where three fixed-guided beams are capable of generating strong nonlinear oscillations under certain base excitation. A prototype harvester was fabricated and investigated through both finite-element analysis and experiments. The frequency response shows multiple resonance which corresponds to a hardening type of nonlinear resonance. By adding masses at different locations on the COPS structure, the first three vibration modes are brought close to each other, where the three hardening nonlinear resonances provide a wide bandwidth for the PVEH. The proposed PVEH has enhanced performance of the energy harvester in terms of a wide frequency bandwidth and a high-voltage output under base excitations.

Analysis of a Fixed-Guided Compliant Beam With an Inflection Point Using the Pseudo-Rigid-Body Model Concept

This paper provides an efficient method of analysis for a fixed-guided compliant beam with an inflection point, subjected to beam end load or displacement boundary conditions, or a combination thereof. To enable this, such a beam is modeled as a pair of well-established pseudo-rigid-body models (PRBMs) for fixed-free compliant beam segments. The analysis procedure relies on the properties of inflection in developing the necessary set of parametric, static equilibrium and compatibility equations for solution. The paper further discusses the multiplicity of possible solutions, including displacement configurations, for any two specified beam end displacement boundary conditions, depending on the locations and types of the effecting loads on the beam to meet these boundary conditions. A unique solution may exist when a third beam end displacement boundary condition is specified; however, this selection is not unconditional. A concept of characteristic deflection domain is proposed to assist with the selection of the third boundary condition to yield a realistic solution. The analysis method is also used to synthesize a simple, fully compliant mechanism utilizing the fixed-guided compliant segments.

Curve Decomposition for Large Deflection Analysis of Fixed-Guided Beams With Application to Statically Balanced Compliant Mechanisms

Statically balanced compliant mechanisms require no holding force throughout their range of motion while maintaining the advantages of compliant mechanisms. In this paper, a postbuckled fixed-guided beam is proposed to provide the negative stiffness to balance the positive stiffness of a compliant mechanism. To that end, a curve decomposition modeling method is presented to simplify the large deflection analysis. The modeling method facilitates parametric design insight and elucidates key points on the force–deflection curve. Experimental results validate the analysis. Furthermore, static balancing with fixed-guided beams is demonstrated for a rectilinear proof-of-concept prototype.

Residual strain measurement of piezoelectric multilayers by spiral structure

A new structure is described to measure the residual strain of thin film of piezoelectric multi-layers. The spiral shaped structure consists of the four fixed-guided beams. Piezoelectric multilayers consisting of SiOx/Pt/PZT/Pt on SiNx substrate are used to evaluate the suggested structure. Finite element analysis predicts that the out-of-plane displacement of the spiral structure by residual stress depends linearly on the beam length, but there is little difference depending on the beam width. PZT is prepared by sol-gel method and multilayered spiral structures are released by microfabrication technique. Sensitivity analysis of the spiral structure with various layer stack shows that the high displacement of piezoelectric multilayers can be decreased by the application of SiOx layer with compressive stress over the piezoelectric multilayers.

A building block synthesis approach for precision flexure systems with integrated, strain-based position sensing

Abstract Early stage design of precision flexure systems that utilize strain-based displacement sensing is difficult due to the strong coupling between the mechanical and sensing subsystems. Traditional tools for flexure system and compliant mechanism synthesis are not capable of simultaneously optimizing the mechanical and sensing subsystems. The building block synthesis approach developed in this work is the only tool capable of designing compliant mechanisms with integrated strain based sensing. Building block modeling allows for rapid synthesis and vetting of concepts. This approach also allows the designer to determine concept feasibility, identify performance limits and tradeoffs, and obtain 1st order estimates of flexure geometry. In short, this method enables one to find an optimal design and set first order design parameters. The utility of the building block approach is detailed in a case study detailing the synthesis and modeling of three different one degree-of-freedom translational stages that are all derived from the series and parallel addition of fixed-guided cantilever beam building blocks.

Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms

This paper explores the deflection and buckling of fixed-guided beams used in compliant mechanisms. The paper’s main contributions include the addition of an axial deflection model to existing beam bending models, the exploration of the deflection domain of a fixed-guided beam, and the demonstration that nonlinear finite element models typically incorrectly predict a beam’s buckling mode unless unrealistic constraints are placed on the beam. It uses an analytical model for predicting the reaction forces, moments, and buckling modes of a fixed-guided beam undergoing large deflections. The model for the bending behavior of the beam is found using elliptic integrals. A model for the axial deflection of the buckling beam is also developed. These two models are combined to predict the performance of a beam undergoing large deflections including higher order buckling modes. The force versus displacement predictions of the model are compared to the experimental force versus deflection data of a bistable mechanism and a thermomechanical in-plane microactuator (TIM). The combined models show good agreement with the force versus deflection data for each device.

Transverse Stiffness and Guiding Characteristics Analysis of Compliant Linear Guided Mechanism

This paper presents a novel compliant linear guided mechanism (CLGM) to replace traditional spring and translation joint to transfer motion and force with its advanced guiding characteristics. In view of the incompatible relationship between axial stiffness and transverse stiffness of CLGM, eight kinds of CLGMs were developed by using building block approach based on fixed-guided flexure beam. The finite element analysis (FEA) models of eight CLGMs were built to complete numerical analysis on the force-displacement in axis and off-axis direction with same geometric sizes. The FEA results show that the structure configuration of Type 2-Type 8 can achieve a larger axial travel, Type 2 and Type4 have the advanced guiding characteristic with higher ratio of axial/transverse stiffness. Analysis indicates that the building block approach is an efficient method to complete the conceptual synthesis of compliant mechanism and FEA is effective on the structure optimization for the required compliance and stiffness in axial and transverse direction.