Compliant Cantilever Research Articles

Effect of additively manufactured polymeric inserts on impact response of construction safety helmets

Purpose Struck-by accidents (i.e. being hit by a falling object) are a leading cause of traumatic brain injuries in the construction industry. Despite the critical role of hard hats in minimizing such injuries, their overall design has not appreciably changed in decades. Therefore, this study aims to explore the potential benefits of modifying commercially available hard hat designs by incorporating a compliant cantilever and a sacrificial, energy-absorbing structure to enhance their protective capabilities against impacts. Design/methodology/approach This study involved conducting experimental impact tests to obtain the head acceleration attenuation using hard hats with a variety of compliant cantilever lattice insert designs. These lattice inserts were additively manufactured using three polymeric materials, including polylactide (PLA), acrylonitrile butadiene styrene, high-impact polystyrene and three porosity levels. A Hybrid III head/neck assembly was fitted with each hard hat design, and experimental drop tests were conducted using a 1.8-kg steel impactor dropped from 1.83 m. The maximum acceleration and head injury criterion (HIC) values were obtained for each test. Findings Analysis of variance revealed that HIC was significantly reduced for all lattices with 56% porosity (p < 0.023) compared to the control (unmodified) hard hat. The most effective insert was found to be a PLA insert with 56% porosity, which reduced the HIC value by 38% compared to the control (unmodified) hard hat, with a statistically significant p-value of 0.018. Originality/value The data present in this study reveals that simple and inexpensive modifications can be made to existing hard hat designs to reduce injury risk from overhead impacts.

Design of Microfabricated Mechanically Interlocking Metamaterials for Reworkable Heterogeneous Integration

Abstract Next-generation interconnects utilizing mechanically interlocking structures enable permanent and reworkable joints between micro-electronic devices. Mechanical metamaterials, specifically dry adhesives, are an active area of research which allows for the joining of objects without traditional fasteners or adhesives, and in the case of chip integration, without solder. This paper focuses on reworkable joints that enable chips to be removed from their substrates to support reusable device prototyping and packaging, creating the possibility for eventual pick-and-place mechanical bonding of chips with no additional bonding steps required. Analytical models are presented and are verified through finite element analysis (FEA) assuming pure elastic behavior. Sliding contact conditions in FEA simplify consideration of several design variations but contribute ∼10% uncertainty relative to experiment, analysis, and point-loaded FEA. Two designs are presented; arrays of flat cantilevers have a bond strength of 6.3 kPa, and nonflat cantilevers have a strength of 29 kPa. Interlocking designs present self-aligning in-plane forces that emerge from translational perturbation from perfect alignment. Stresses exceeding the material yield stress during adhesion operations present a greater concern for repeatable operation of compliant interlocking joints and will require further study quantifying and accommodating plastic deformation. Designs joining a rigid array with a complementary compliant cantilever array preserve the condition of reworkability for the surface presenting the rigid array. Eventual realization of interconnect technology based on this study will provide a great improvement of functionality and adaptability in heterogeneous integration and microdevice packaging.

Dynamic analysis of a hybrid compliant mechanism with flexible central chain and cantilever beam

Membrane peeling in retinal and cataractous surgery is a challenging task due to physiological hand tremors and delicate tissue. To relieve this problem, we proposed a hybrid compliant mechanism with a flexible central chain and a cantilever beam to suppress hand tremors and vibrate along peeling direction since the vibration can reduce peeling force. The particularly designed mass block makes the axial deformation of central chain and cantilever beam negligible in dynamic modeling. We then studied the dynamic response of the proposed hybrid compliant mechanism. The pseudo-rigid-body model (PRBM) of compliant links, central chain and cantilever beam is given. The relationship between the moving platform and parallel kinematic chains is derived. Next, the full dynamic model is established using the Lagrange equation. Furthermore, the dimension of the full dynamic model is reduced by the proper orthogonal decomposition (POD) method. Simulation results show that the reduced-order model is about 9.0 times faster than the full dynamic model. Experimental results show that the average relative errors of the full dynamic model and the reduced-order model are 2.12% and 1.93%, respectively.

A Heterogeneous Integrated MEMS Inertial Switch With Compliant Cantilevers Fixed Electrode and Electrostatic Locking to Realize Stable On-State

A novel heterogeneous integrated inertial micro-switch has been designed with adjustable acceleration threshold and a stable ‘on’-state due to a predefined bias voltage. The bias voltage is applied onto the large-area parallel-plate electrodes, which endows the movable proof-mass with electrostatic forces. With an external excitation acceleration, the movable electrode moves to the fixed electrode and it can be locked by the electrostatic force onto the compliant electrical contacts, which are composed of micro-cantilever array to eliminate the contact rebound during electrostatic pull-in process. Both the dynamic response of the proof-mass and the relationship between the bias voltage and the inertial excitation acceleration were analyzed using theoretical model and finite element simulation. A unique heterogeneous integration process including both the silicon-based and non-silicon surface micromachining processes was adopted to fabricate the switch. The tests using a standard dropping hammer system demonstrated that the switch could keep a stable switch-on at the 57 g excitation acceleration and 38 V bias voltage. As wide as 52% adjustment range of the acceleration threshold was obtained when the applied bias voltage was from 38 V to 44 V. The tested relationship between the bias voltage and the external acceleration was very consistent with the simulated relationship. [2019-0038]

An Explicit Solution to Continuum Compliant Cantilever Beam Problem with Various Variational Iteration Algorithms

The geometric nonlinearity resulting from large deformation of compliant members has continued to be an interesting research topic in nonlinear mechanics. In this study, two standard variational iteration algorithms, VIM-I and VIM-III are employed to investigate the large deformation of the continuum compliant beam under point load. The VIM is an efficient technique that bypasses the linearization process and proffers solutions to nonlinear problems. The horizontal and vertical displacements of the continuum compliant cantilever beam free end are expressed in explicit analytical forms. Numerical experiment and simulations were carried out to validate the efficacy and applicability of the semi-analytical method. The VIM-I was split into two; VIM-I(A) and VIM-I(B), with the difference being the initial approximations. The results from the VIM-I(A), VIM-I(B) and VIM-III algorithms were compared with the experimental and exact solution. The outcomes reveal that both algorithms correlated well with the analytical solution and experimental result.

Pseudo-Rigid-Body Dynamic Models for Design of Compliant Members

Abstract Movement in compliant mechanisms is achieved, at least in part, via deformable flexible members, rather than using articulating joints. These flexible members are traditionally modeled using finite element analysis (FEA)-based models. In this article, an alternative strategy for modeling compliant cantilever beams is developed with the objectives of reducing computational expense and providing accuracy with respect to design optimization solutions. The method involves approximating the response of a flexible beam with an n-link/m-joint pseudo-rigid-body dynamic model (PRBDM). Traditionally, static pseudo-rigid-body models (PRBMs) have shown an approximation of compliant elements using two or three revolute joints (2R/3R-PRBM). In this study, a more general nR-PRBDM model is developed. The first n resonant frequencies of the PRBDM are matched to exact or FEA solutions to approximate the response of the compliant system and compared with existing PRBMs. PRBDMs can be used for co-design studies of flexible structural members and are capable of modeling large deflections of compliant elements. We demonstrate PRBDMs that show dynamically accurate response for a random geometry cantilever beam by matching the steady-state and frequency response, with dynamical response accuracies up to 10% using a 5R-PRBDM.

Minimizing tip-sample forces and enhancing sensitivity in atomic force microscopy with dynamically compliant cantilevers

Due to the harmonic motion of the cantilever in Tapping Mode Atomic Force Microscopy, it is seemingly impossible to estimate the tip-sample interactions from the motion of the cantilever. Not directly observing the interaction force, it is possible to damage the surface or the tip by applying an excessive mechanical load. The tip-sample interactions scale with the effective stiffness of the probe. Thus, the reduction of the mechanical load is usually limited by the manufacturability of low stiffness probes. However, the one-to-one relationship between spring constant and applied force only holds when higher modes of the cantilever are not excited. In this paper, it is shown that, by passively tuning higher modes of the cantilever, it is possible to reduce the peak repulsive force. These tuned probes can be dynamically more compliant than conventional probes with the same static spring constant. Both theoretical and experimental results show that a proper tuning of dynamic modes of cantilevers reduces the contact load and increases the sensitivity considerably. Moreover, due to the contribution of higher modes, the tuned cantilevers provide more information on the tip-sample interaction. This extra information from the higher harmonics can be used for mapping and possibly identification of material properties of samples.

A surface-micromachining-based inertial micro-switch with compliant cantilever beam as movable electrode for enduring high shock and prolonging contact time

A novel laterally-driven inertial micro-switch with two L-shaped elastic cantilever beams as the movable electrode, which is attached to the proof mass, is proposed in this paper. The advantage of this design is that the contact time of the inertial micro-switch can be prolonged. Meanwhile, the micro-switch can withstand a higher shock than the traditional designs whose cantilever beams are attached to the fixed electrode. The designed inertial micro-switch was simulated and optimized with ANSYS software and fabricated on a quartz substrate by surface micromachining technology. The simulated result demonstrates that the threshold acceleration (aths) under stable switch-on state is about 288g and the contact time is about 198μs when the pulse width of acceleration loads is 1ms. At the same time, it indicates that the threshold acceleration, the response time and the contact time of designed micro-switch all increase with the pulse width of acceleration loads. The simulation of impact process in non-sensitive direction shows that the introduced constraint sleeve structure in the novel inertial micro-switch can lower the off-axis sensitivity. The fabricated micro-switch prototype has been tested by a standard dropping hammer system under shock accelerations with various amplitudes and pulse widths. The experimental measurements show that the contact time is about 150μs when the threshold acceleration is about 288g. It also indicates that the response time and the contact time both increase with the pulse width, which is consistent with the simulation ones.

Adaptive Quasi-Static Modelling of Needle Deflection During Steering in Soft Tissue

In this letter, we present a model for needle deflection estimation in soft tissue. The needle is modelled as a vibrating compliant cantilever beam that experiences forces applied by the tissue as it is inserted. Each of the assumed vibration modes are associated with a weighting coefficient whose magnitude is calculated using the minimum potential energy method. The model only requires as input the tissue stiffness and needle-tissue cutting force. Contributions of this letter include the estimation of needle-tissue contact forces as a function of the tissue displacement along the needle shaft, while allowing for multiple bends of the needle. The model is combined with partial ultrasound image feedback in order to adaptively calculate the needle-tissue cutting force as the needle is inserted. The image feedback is obtained by an ultrasound probe that follows the needle tip and stops at an appropriate position to avoid further tissue displacement. Images obtained during early stages of the insertion are used to predict the deflection of the needle further along the insertion process. Experimental results in biological and phantom tissue show an average error in predicting needle deflection of 0.36 mm.

Contact resonance force microscopy with higher-eigenmode for nanoscale viscoelasticity measurements

Nanoscale viscoelastic properties are essential for polymeric materials in their wide applications in nanotechnology. Here we proposed a contact resonance force microscopy (CRFM) method for viscoelasticity measurements by utilizing a cantilever's higher-eigenmode (n > 3). Numerical analysis results show that, compared to its lower eigenmodes, a cantilever's higher eigenmode is more sensitive to contact damping and less affected by contact stiffness variations. This tendency is then verified by nanoscale viscoelasticity mapping on a polystyrene (PS)/polymethyl methacrylate (PMMA) copolymer thin film using a compliant cantilever's different eigenmodes. Results show that higher-eigenmode CRFM can provide better imaging contrast and is thus suggested for viscoelasticity measurements.

Influence of applied acceleration loads on contact time and threshold in an inertial microswitch with flexible contact-enhanced structure

An inertial microswitch with flexible contact-enhanced structure to prolong contact time has been designed and fabricated by surface micromachining technology. The flexible structure is an L-shaped compliant cantilever beam, which can realize elastic deformation during contact process when the movable electrode impacts to the stationary electrode. The influence of applied acceleration loads on contact time and threshold was analyzed, simulated and evaluated. The analysis results indicate that the stiffness of inertial system, amplitude and pulse width of acceleration loads are important influence factors for the contact time: the contact time will be increased along with the increase of acceleration amplitude and the decrease of inertial system stiffness. The broadening of pulse width of acceleration loads will result in a greater value of threshold acceleration and contact time. The simulated results demonstrate that the dynamic properties of designed inertial micro-switch are in agreement with the analytical ones. The fabricated microswitch has been tested by dropping hammer system, the test results indicate that the threshold acceleration is about 110g and the corresponding contact time is about 42μs when the pulse width is about 1.7ms. Meanwhile, the contact time increases with the broadening of pulse width. Finally, the fabricated inertial microswitch device has been also tested under applied half-sine wave acceleration with different amplitudes and pulse widths. It is indicated that the contact time does not increase after reaching to a maximum (75μs under 259g applied acceleration load). From the analysis in the present work, the influence of applied shock loads on contact time and threshold level in an inertial microswitch with flexible contact-enhanced structure is revealed. The conclusions reached in this study provide guidance for future research into the design and fabrication of inertial microswitches.

A laterally-driven micromachined inertial switch with a compliant cantilever beam as the stationary electrode for prolonging contact time

A novel micro-electromechanical systems inertial switch based on non-silicon surface micromachining technology has been designed, fabricated and characterized in the present work. Compared with the traditional inertial switch, a compliant cantilever beam as a stationary electrode has been proposed to prolong the contact time, which can realize sufficient elastic deformation during the contact between the electrodes. The dynamic contact process is analyzed theoretically and the corresponding mechanical impact mechanism is also explained. To investigate the contact-enhancing mechanism of the cantilever beam, the switch applied half-sine acceleration with various amplitudes in the sensitive direction is simulated with ANSYS software. The dynamic simulation results confirm the contact-enhancing mechanism described by the theoretical analysis and it is shown that the contact time (i.e., the switch-on time) can be prolonged effectively by utilizing the elastic deformation of the cantilever beam and increased with the applied accelerations. The inertial switch is successfully fabricated by electroplating and sacrificial layer processes technologies. The prototype has been characterized by dropping hammer experiment. The test results indicate that the contact effect is improved significantly and the contact time is ∼80 µs under the 297 g acceleration, and the maximum value is ∼410 µs for the 672 g acceleration amplitude, which is in general accordance with the simulated results. The mechanical contact between the cantilever beam and the proof mass is evaluated following thousands of impacts. The scanning electron micrographs of the contact surfaces indicate that the all-metal switch still keeps a good mechanical property after suffering the hot contact, and the contact resistance is also stable.

Hydrodynamic coupling of two sharp-edged beams vibrating in a viscous fluid

In this paper, we study flexural vibrations of two thin beams that are coupled through an otherwise quiescent viscous fluid. While most of the research has focused on isolated beams immersed in placid fluids, inertial and viscous hydrodynamic coupling is ubiquitous across a multitude of engineering and natural systems comprising arrays of flexible structures. In these cases, the distributed hydrodynamic loading experienced by each oscillating structure is not only related to its absolute motion but is also influenced by its relative motion with respect to the neighbouring structures. Here, we focus on linear vibrations of two identical beams for low Knudsen, Keulegan-Carpenter and squeeze numbers. Thus, we describe the fluid flow using unsteady Stokes hydrodynamics and we propose a boundary integral formulation to compute pertinent hydrodynamic functions to study the fluid effect. We validate the proposed theoretical approach through experiments on centimetre-size compliant cantilevers that are subjected to underwater base-excitation. We consider different geometric arrangements, beam interdistances and excitation frequencies to ascertain the model accuracy in terms of the relevant non-dimensional parameters.

Cell force measurements in 3D microfabricated environments based on compliant cantilevers

We report the fabrication, functionalization and testing of microdevices for cell culture and cell traction force measurements in three-dimensions (3D). The devices are composed of bent cantilevers patterned with cell-adhesive spots not lying on the same plane, and thus suspending cells in 3D. The cantilevers are soft enough to undergo micrometric deflections when cells pull on them, allowing cell forces to be measured by means of optical microscopy. Since individual cantilevers are mechanically independent of each other, cell traction forces are determined directly from cantilever deflections. This proves the potential of these new devices as a tool for the quantification of cell mechanics in a system with well-defined 3D geometry and mechanical properties.

A method to measure nanomechanical properties of biological objects

We postulate that one will be able to quantitatively infer changes in the mechanical properties of proteins, cells, and other biological objects (BO) by measuring the shifts of several thermally excited resonance frequencies of atomic force microscopy cantilevers in contact with BOs. Here, we provide a method to extract spring constants and molecular damping factors of BOs in biologically relevant phosphate buffered saline medium and using compliant AFM cantilevers with a small aspect ratio (a ratio of length to width).

Accurate spring constant calibration for very stiff atomic force microscopy cantilevers

There are many atomic force microscopy (AFM) applications that rely on quantifying the force between the AFM cantilever tip and the sample. The AFM does not explicitly measure force, however, so in such cases knowledge of the cantilever stiffness is required. In most cases, the forces of interest are very small, thus compliant cantilevers are used. A number of methods have been developed that are well suited to measuring low stiffness values. However, in some cases a cantilever with much greater stiffness is required. Thus, a direct, traceable method for calibrating very stiff (approximately 200 N/m) cantilevers is presented here. The method uses an instrumented and calibrated nanoindenter to determine the stiffness of a reference cantilever. This reference cantilever is then used to measure the stiffness of a number of AFM test cantilevers. This method is shown to have much smaller uncertainty than previously proposed methods. An example application to fracture testing of nanoscale silicon beam specimens is included.

Modeling and experimental characterization of the stress, strain, and resistance of shape memory alloy actuator wires with controlled power input

Recently, a novel power controller has been presented that simultaneously controls electric power input and measures resistance of a commercially available Flexinol shape memory alloy wire. This work exploits the new power controller by plotting shape memory alloy stress, strain, and resistance versus Joule heating power instead of input voltage or current. Heating power is directly related to shape memory alloy temperature, whereas standard constant voltage or constant current inputs cause more or less heating as the resistance of the wire changes due to phase transformation. A simple experimental setup consisting of a 50-µm-diameter Flexinol wire mounted in series with the tip of a compliant cantilever beam is used to systematically study the shape memory alloy behavior. Actuator performance is reported for a range of prestress values and actuation frequencies. All the experimental data are compared with simulated behavior that is derived from a free energy–based numerical model for shape memory alloy material. Additionally, a new resistance model based on the simulated wire temperature and phase fractions is introduced and compared to experimental data. Exploiting a multifunctional power controller and an improved understanding of the resistance change during phase transformation will help enable the use of shape memory alloy wires in simultaneous sensing and actuating applications.

In situ quantification of electrical isolation in STM-fabricated TiO x nanostructures

In this Letter, a combination of conductive atomic force microscopy (AFM) and scanning tunnelling microscopy (STM) with a compliant cantilever is used to electrically probe oxidised TiO2−x nanostructures in situ. In STM mode, both the written width and the effective resistivity of material in the written line increase with write bias. At low writing voltages (∼3.5 V), the STM written lines are narrow (30 nm), but they are not resistive enough to allow patterns with a 1–2 µm perimeter to provide electrical isolation above 10 MΩ. Raising the bias to 8.5 V during writing allows similar structures to provide isolation of better than 250 MΩ. The resistivity in the lines written at the latter with high bias is 28 Ω m. From electrical estimates, the oxidation appears to go through the thickness at all voltages, but is more chemically incomplete (larger value of x) at low voltage. The data are not consistent, with a small amount of metallic Ti remaining under the written mark, that is, partial penetration of the oxidation. The thickness of this Ti layer would have to be unphysically small (1 million times smaller than an atomic layer thickness) to allow this interpretation.

Low-force AFM nanomechanics with higher-eigenmode contact resonance spectroscopy **Publication of NIST, an agency of the US government, not subject to copyright.

Atomic force microscopy (AFM) methods for quantitative measurements of elastic modulus on stiff (>10 GPa) materials typically require tip–sample contact forces in the range from hundreds of nanonewtons to a few micronewtons. Such large forces can cause sample damage and preclude direct measurement of ultrathin films or nanofeatures. Here, we present a contact resonance spectroscopy AFM technique that utilizes a cantilever’s higher flexural eigenmodes to enable modulus measurements with contact forces as low as 10 nN, even on stiff materials. Analysis with a simple analytical beam model of spectra for a compliant cantilever’s fourth and fifth flexural eigenmodes in contact yielded good agreement with bulk measurements of modulus on glass samples in the 50–75 GPa range. In contrast, corresponding analysis of the conventionally used first and second eigenmode spectra gave poor agreement under the experimental conditions. We used finite element analysis to understand the dynamic contact response of a cantilever with a physically realistic geometry. Compared to lower eigenmodes, the results from higher modes are less affected by model parameters such as lateral stiffness that are either unknown or not considered in the analytical model. Overall, the technique enables local mechanical characterization of materials previously inaccessible to AFM-based nanomechanics methods.

Multi-material bio-fabrication of hydrogel cantilevers and actuators with stereolithography

Cell-based biohybrid actuators are integrated systems that use biological components including proteins and cells to power material components by converting chemical energy to mechanical energy. The latest progress in cell-based biohybrid actuators has been limited to rigid materials, such as silicon and PDMS, ranging in elastic moduli on the order of mega (10(6)) to giga (10(9)) Pascals. Recent reports in the literature have established a correlation between substrate rigidity and its influence on the contractile behavior of cardiomyocytes (A. J. Engler, C. Carag-Krieger, C. P. Johnson, M. Raab, H. Y. Tang and D. W. Speicher, et al., J. Cell Sci., 2008, 121(Pt 22), 3794-3802, P. Bajaj, X. Tang, T. A. Saif and R. Bashir, J. Biomed. Mater. Res., Part A, 2010, 95(4), 1261-1269). This study explores the fabrication of a more compliant cantilever, similar to that of the native myocardium, with elasticity on the order of kilo (10(3)) Pascals. 3D stereolithographic technology, a layer-by-layer UV polymerizable rapid prototyping system, was used to rapidly fabricate multi-material cantilevers composed of poly(ethylene glycol) diacrylate (PEGDA) and acrylic-PEG-collagen (PC) mixtures. The incorporation of acrylic-PEG-collagen into PEGDA-based materials enhanced cell adhesion, spreading, and organization without altering the ability to vary the elastic modulus through the molecular weight of PEGDA. Cardiomyocytes derived from neonatal rats were seeded on the cantilevers, and the resulting stresses and contractile forces were calculated using finite element simulations validated with classical beam equations. These cantilevers can be used as a mechanical sensor to measure the contractile forces of cardiomyocyte cell sheets, and as an early prototype for the design of optimal cell-based biohybrid actuators.