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This activity gives students the opportunity to design an experiment, collect data, and solve for the spring constant of different springs. The use of low-cost materials and the inquiry-based structure makes it more accessible for teachers and more engaging for students. It can be scaffolded in several different ways, so that each teacher can differentiate according to the needs of their physics students. Some common student misconceptions are also addressed to assist teachers in their preparation for leading this activity. [ABSTRACT FROM AUTHOR]

We present an experimental study demonstrating the ability to control the spring constant of helical mechanical springs using a magnetic field, achieved by embedding ferrimagnetic Fe3O4 nanoparticles within in a silicone polymer matrix. The composite material, in its gel form, was injected into a 3D-printed mold featuring a helical-spring-shaped cavity. An external magnetic field applied perpendicular to the coil axis of the spring allows the aligmment of the magnetic nanoparticle assemblies (chain axis) in the field direction. This alignment process determines the preferred magnetization orientation of the particle assembly chain, thereby balancing the magnetic force between the magnetic anisotropy field and the Zeeman field under a given external field. When the spring is subjected to compression or stretching loads under an externally applied magnetic field, these two magnetic fields modify the effective spring constant of the helical spring magnets (HSMs) by ∼31%, incresing it from 8.7 N m−1 (under no field) to 11.5 N m−1 at 300 mT. Analytical modeling using a simplified rod geometry aptly explains the experimental results, demonstrating that the spring constant linearly increases with the field strength up to 300 mT. Such composite HSMs could be utilized as active vibration absorbers or isolators due to their field-controllable elasticity. [ABSTRACT FROM AUTHOR]

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We present a mathematical model that considers the formation of an ice layer with expansion in a container with a moving boundary. The displacement represents the strain of the tank when the solidifying water expands. The results show that the ice and liquid fractions inside the tank depend on the spring constant and dimensions of the tank. If the spring constant tends to infinity, the ice and liquid fractions are those corresponding to an isochoric process. For each temperature, there is a threshold value of the spring constant, below which all the contents of the tank become ice and above which a smaller fraction does so. The threshold value of the spring constant relates to the degree to which water expands as it freezes. Structural design of a tank shows that the process departs from isochoric. Keeping the process completely isochoric requires oversizing the tank with corresponding increases in manufacturing costs and transportation weight. • We model formation of ice in a self pressurizing elastic tank for freezing temperatures. • The model calculates ice fraction as a function of freezing temperature and elastic constant. • The solution includes as a special case the isochoric freezing process. • The model determines the modified spring constant below which all the water becomes ice. • Structural design of a spherical tank shows the process may depart from the isochoric case. [ABSTRACT FROM AUTHOR]

Simple harmonic motion experiments have been conducted using a smartphone-based spring-mass system with the Phyphox application. This research aims to investigate the relationship between the mass of an object and the period and frequency of oscillations and determine the spring constant using smartphone-based experimental equipment. The method uses the "spring" feature in the Phyphox application to visualize oscillatory movements in real-time and measure the period and frequency of oscillations. The experimental results show that the spring constant obtained from the smartphone-based experiment is 9.51 N/m, with a difference of 1.25% compared to the Hooke's Law experimental setup with the conventional method. This shows that using a smartphone-based experimental setup can be a better alternative for conducting physics experiments requiring high accuracy.

In nature, living organisms move in a collective state of aggregation, this collective motion is influenced by the nature of the environment, the obstacles refocused during the movement and the local interaction between individuals, this interaction is responsible for avoiding collision between each individual. In this paper, we study numerically the collective motion of self-organized organisms by expanding the Langevin dynamics, in which we have modeled the interaction between individuals by an elastic force. Modeling the interaction between individuals using an elastic force gives remarkable results. This interaction has an important effect if the individuals are dispersed a lot in space, but if a certain number of particles N is exceeded, this force is of no importance and the saturation velocity becomes constant. The results of the numerical simulation show that the average velocity of the individuals goes through a transient regime before reaching the permanent regime. Moreover, the results show that the system represents a transition from a nonequilibrium state to an equilibrium state, which is similar to a second-phase transition (paramagnetic/ferromagnetic) in the absence of the magnetic field; this phase transition is observable if the distance between two individuals is greater than a critical radius noted R c . [ABSTRACT FROM AUTHOR]

The aim of this work is to create a new type of gravimeter that can function effectively in the challenging conditions of space, specifically on the surfaces of planets and moons. The proposed device, called a diamagnetically stabilized magnetically levitated gravimeter (DSMLG), uses magnetic forces to balance a test mass against the force of gravity, allowing for accurate measurements. A diamagnetically stabilized levitation structure comprises a floating magnet, diamagnetic material, and a lifting magnet. The floating magnet levitates between two diamagnetic plates without the need for external energy input due to the interaction between the magnetic forces of the floating magnet and the stabilizing force of the diamagnetic material. This structure allows for stable levitation of the floating magnet without requiring additional energy. The goal is to design a gravimeter that is lightweight, requires minimal power, can withstand extreme temperatures and shocks, and has a low data rate. The authors envision this gravimeter being used on various robotic spacecraft, such as landers and rovers, to study the interiors of rocky and icy celestial bodies. This paper reports on the results of a finite element model analysis of the DSMLG and the strength of the resulting diamagnetic spring. The findings contribute to the understanding of the levitation characteristics of diamagnetically stabilized structures and provide valuable insights for their practical applications, including in the development of the proposed DSMLG. [ABSTRACT FROM AUTHOR]

In this paper, a mass-spring system is considered. The system is modelled using a second-order homogeneous linear (ODE) with constant coefficients. Using this model, the behaviour of the system is studied. The most significant factor, the value of the damping, determines whether the case occurs: no damping, underdamping, critical damping, or overdamping. Each case is mathematically analysed to get parameters that impact how the motion system performs. The obtained solution, which demonstrates the behaviour of the system in a diagram plot of a displacement-time graph and a phase plane graph, is graphically presented in MATLAB software. [ABSTRACT FROM AUTHOR]

This study advances a STEM teaching proposal and aims to determine spring constant of a spring pendulum by means of an Arduino microprocessor. The measurements are managed by simply letting the spring pendulum to oscillate freely and recording the distance perceived by the distance sensor-Arduino system as a function of time. The mean periods are estimated by using displacement-time plots of the harmonic motion and the results are used to estimate the spring constant. The spring constant is also determined conventionally by employing Hooke's law a number of times. The relative error rate between the two results is found to be about % 6.00 which is pretty acceptable. This approach is important in the sense that it is inexpensive and also encourages students to learn how to use the Arduino microprocessor. The approach adds to physics education efforts due to creating an enjoyable and beneficial teaching-learning environment.

As spectral resolution increases, the dimension of the Doppler Asymmetric Spatial Heterodyne (DASH) interferometer increases. The existing approach for stably mounting the interferometer is limited to mounting a normal-sized DASH interferometer. In this study, a novel and stable structure is proposed, with its effecti1veness exemplified for a near-infrared (NIR) DASH interferometer. The mathematical model of a flexible structure was established. The parameters of the support structure were optimized by requiring the mechanical stress of the flexible structure and shear stress at the bonding surface to be less than the strength value. The spring constants were optimally designed to adjust natural frequency and minimize stress. The finite element analysis (FEA) results show that the maximum mechanical stress was 65.56 MPa. The maximum shear stress was 3.4 MPa. All stress values had a high safety margin. The mechanical material and adhesive area were optimally designed. Therefore, the thermal resistance of the structure was improved by 7.5 times. The test results indicate that the proposed flexible support structure could satisfy the requirements of the launch environment. The results from FEA and vibration tests were consistent with the model calculation results. Compared to existing structures, the mechanical performance and thermal resistance were improved. [ABSTRACT FROM AUTHOR]

Atomic force microscopes (AFMs) have emerged as the principal enabling tool for nanotechnology research. They are used ubiquitously in a wide range of fields: from 2D materials, semiconductors, ferroelectrics, and batteries to biomolecules, polymers, and cell biology. As the name implies, AFMs are microscopes. However, rather than using focused light or electrons to magnify sample features, AFMs scan a mechanical probe with a very sharp tip over the surface to create a high-resolution 3D topographical image. Further, by modifying the probe composition or structure, other material properties (electrical, mechanical, magnetic, etc.) can be simultaneously measured and mapped onto the topographic image for precise structure/property correlation. Clearly, the probe is key to unlocking the power of the AFM, thus, choosing the right probe is critical. In this article, we will provide novice and experienced users with basic information and guidelines to simplify the AFM probe selection process. [ABSTRACT FROM AUTHOR]

Commonly, the columns and beams of glass panels are frequently subjected to in-plane loading, in which their joints will transfer the in-plane forces. Therefore, it is necessary to investigate the spring constants of the joints of these glass panels for the mechanical analysis of the structures. However, few issues were published on this subject, so estimating the spring constants of glass structure joints is important. Devote themselves to proposing methods to evaluate the spring constants of the joints of structural glass panels. This study tests two types of glass panels with thicknesses of 12 mm and 19 mm based on static and cycling loading. In addition, two types of Cushions: (1) aluminum and (2) rubber with a hardness of 65 and 90 degrees, are set between steel bolt(s) and glass panel(s) for the experiments. The spring constants are determined by the ratios of measured loads and the displacements between the glass panels and bolts. In addition, the authors proposed an equation to evaluate the bending spring constant from its axial spring constant determined by the loading tests. The experimental results showed that the joints with the aluminum cushion appear exactly non-linear elasticity while loading and unloading. Also, the pin junction within the central region (no Curve) is 0.6 mm. It is also determined that aluminum (cushion) slides of approximately ±0.3 mm under compression and tension. While loading (Tension/compression) is incremental, rubber acts nonlinearly but linear as unloaded. [ABSTRACT FROM AUTHOR]

RF MEMS switch is an actuator which can be used to make or break a signal path in RF Communications. The proposed switch is an electrostatically actuated dual channel switch whose actuating beam has varying cross-section. This letter focuses on developing a mathematical model for the spring constant of a varying section fixed-fixed beam and validating it with simulation results. Unit load method and Moment area method are used in modeling of the beam. The theoretical and simulated results are matching closely and the difference is not more than 16%. Further, the effects of spring constant on the switch parameters like Pull-in Voltage, Switching time, Switching speed and restoring force are studied. The results and relations obtained are presented. [ABSTRACT FROM AUTHOR]

Diamagnetic levitation is applied to attain the smallest possible effective spring constant suitable for detection of weak and continuous forces relevant to various phenomena including biological ones. A Nd-Fe-B permanent magnet was suspended under aerial conditions with lifting force from a multi-layered solenoid and stabilized horizontally via repulsive interaction with a diamagnetic substance. The effective spring constant of the suspensions was analyzed via a ringdown measurement of the electromotive force caused by oscillation while changing the magnitude of the DC current in the solenoid. Measured minimum spring constant beyond which the potential energy minima along plumb direction vanishes was 26 mN/m for a ∅1.5 mm x 1.5 mm cylindrical permanent magnet in a Bi cylindrical diamagnetic pore. A variable-sized diamagnetic cavity composed of four mobile graphite slabs adaptable to cubic permanent magnets of arbitrary size was introduced to attain a smaller spring constant. The measured minimum spring constant for a 1 mm cubic permanent magnet levitated in this cavity was approximately 6 mN/m. Although the spring constant for a smaller 0.5 mm cubic magnet was not detectable with the present ringdown setup, its minimum possible value was evaluated from its volume to be below 1 mN/m, which can lead to the detection of a force below 1 nN if combined with an adequate optical displacement detection method. The measured spring constants were compared with the calculated results.

Simple configuration and has good efficiency, make a moving mass stabilizer one of the options that can be applied to reduce roll motion on a small vessel. This stabilizer however has a limitation in dealing with the ship’s hydrostatic changes while on duty especially when the stabilizer is designed to be passive. The purpose of this research is to improve the ability of the stabilizer to be able to adapt the change in ship hydrostatics. A Tsunami 22’ fishermen vessel model was selected to be used for this research. By conducting roll decay experiments, natural frequency data from the vessel is then used to design calculations for the device on two different load conditions. Moving mass stabilizer frequency is dependent on two parts that are the spring coefficient “k” and the weight of the mass moving. In this Research, Spring adjustment is selected to make the stabilizer able to change frequency following change on the vessel. It is found that the best frequency ratio between the frequency of stabilizer and vessel is 1. Adjusting the spring of the stabilizer turned out to give an increase in device performance by 8.9 % when compared to adjusting the mass. The results obtained in this research indicate the moving mass stabilizer has good potential to reduce the roll motion.

The continuum and discrete phase interaction could significantly affect the inhaled particle's transport behaviour. The accurate analysis of continuum and discrete phase interaction needs computational fluid dynamics (CFD) and Discrete Element Method (DEM) simulation, which is computationally expensive. Therefore, this study aims to develop a novel machine learning (ML) prediction model from CFD-DEM data to predict pharmaceutical aerosol transport in airways accurately. This study uses the CFD model for the continuum and DEM for the discrete phases. A soft sphere approach was used to calculate the overlap of the colliding particles. Proper validation was performed to ensure the accuracy of the present model. The CFD-DEM model analysed the particle transport in an idealised and realistic airway model, and different methods were used to analyse the transport behaviour. As the flow rate increased from 15 to 60 lpm, the deposition efficiency (DE) significantly improved due to particle interaction, rising from 20 % to 42 % without interaction and from 50 % to a remarkable 76 % with interaction, demonstrating the critical role of particle interaction in enhancing DE across varying flow rates. During the particle-particle interaction, a stagnation point and a high-pressure zone were observed at the airway model's carinal angle. Finally, a ML prediction model is developed from CFD-DEM data, which accurately predicts the pharmaceutical aerosol deposition in airways. The ML prediction model predicts the deposition pattern for different flow rates and particle sizes without CFD-DEM simulations. The present findings and more case-specific investigation would advance the knowledge of aerosol transport in airways and benefit more efficient targeted drug delivery devices. [Display omitted] • An advanced CFD-DEM-ML model for particle transport in airways; • Spring constant significantly influences the flow fields; • Deposition efficiency increases with the flow rate and particle diameter; • Particle-particle interaction significantly increase with the spring constant; • Deposition efficiency is significantly higher at the upper part of the airway. [ABSTRACT FROM AUTHOR]

Alcohols are used in the life sciences because they can condense and precipitate DNA. Alcohol consumption has been linked to many diseases and can alter genetic activity. In the present report, we carried out experiments to make clear how alcohols affect the efficiency of transcription-translation (TX-TL) and translation (TL) by adapting cell-free gene expression systems with plasmid DNA and RNA templates, respectively. In addition, we quantitatively analyzed intrachain fluctuations of single giant DNA molecules based on the fluctuation-dissipation theorem to gain insight into how alcohols affect the dynamical property of a DNA molecule. Ethanol (2–3%) increased gene expression levels four to five times higher than the control in the TX-TL reaction. A similar level of enhancement was observed with 2-propanol, in contrast to the inhibitory effect of 1-propanol. Similar alcohol effects were observed for the TL reaction. Intrachain fluctuation analysis through single DNA observation showed that 1-propanol markedly increased both the spring and damping constants of single DNA in contrast to the weak effects observed with ethanol, whereas 2-propanol exhibits an intermediate effect. This study indicates that the activation/inhibition effects of alcohol isomers on gene expression correlate with the changes in the viscoelastic mechanical properties of DNA molecules. [ABSTRACT FROM AUTHOR]

As spectral resolution increases, the dimension of the Doppler Asymmetric Spatial Heterodyne (DASH) interferometer increases. The existing approach for stably mounting the interferometer is limited to mounting a normal-sized DASH interferometer. In this study, a novel and stable structure is proposed, with its effecti1veness exemplified for a near-infrared (NIR) DASH interferometer. The mathematical model of a flexible structure was established. The parameters of the support structure were optimized by requiring the mechanical stress of the flexible structure and shear stress at the bonding surface to be less than the strength value. The spring constants were optimally designed to adjust natural frequency and minimize stress. The finite element analysis (FEA) results show that the maximum mechanical stress was 65.56 MPa. The maximum shear stress was 3.4 MPa. All stress values had a high safety margin. The mechanical material and adhesive area were optimally designed. Therefore, the thermal resistance of the structure was improved by 7.5 times. The test results indicate that the proposed flexible support structure could satisfy the requirements of the launch environment. The results from FEA and vibration tests were consistent with the model calculation results. Compared to existing structures, the mechanical performance and thermal resistance were improved.

We performed a time-lapse imaging with atomic force microscopy (AFM) of the motion of eukaryotic CRFK (Crandell-Rees Feline Kidney) cells adhered onto a glass surface and anchored to other cells in culture medium at 37 °C. The main finding is a gradient in the spring constant of the actomyosin cortex along the cells axis. The rigidity increases at the rear of the cells during motion. This observation as well as a dramatic decrease of the volume suggests that cells may organize a dissymmetry in the skeleton network to expulse water and drive actively the rear edge. [ABSTRACT FROM AUTHOR]

Intro: Force measurements of the nucleus, the strongest organelle, have propelled the field of mechanobiology to understand the basic mechanical components of the nucleus and how these components properly support nuclear morphology and function. Micromanipulation force measurement provides separation of the relative roles of nuclear mechanical components chromatin and lamin A. Methods: To provide access to this technique, we have developed a universal micromanipulation apparatus for inverted microscopes. We outline how to engineer and utilize this apparatus through dual micromanipulators, fashion and calibrate micropipettes, and flow systems to isolate a nucleus and provide force vs. extensions measurements. This force measurement approach provides the unique ability to measure the separate contributions of chromatin at short extensions and lamin A strain stiffening at long extensions. We then investigated the apparatus' controllable and programmable micromanipulators through compression, isolation, and extension in conjunction with fluorescence to develop new assays for nuclear mechanobiology. Results: Using this methodology, we provide the first rebuilding of the micromanipulation setup outside of its lab of origin and recapitulate many key findings including spring constant of the nucleus and strain stiffening across many cell types. Furthermore, we have developed new micromanipulation-based techniques to compress nuclei inducing nuclear deformation and/or rupture, track nuclear shape post-isolation, and fluorescence imaging during micromanipulation force measurements. Conclusion: We provide the workflow to build and use a micromanipulation apparatus with any inverted microscope to perform nucleus isolation, force measurements, and various other biophysical techniques. [ABSTRACT FROM AUTHOR]

The research purpose is explored the effect of guided inquiry learning with digital spring for science generics skills. The subject of research are 70 student in XI MIPA SMAN 11 Semarang consisting of 35 students in the experimental group and 35 students in the control group. Design study uses Quasy Experiment Design, the type to be used is Nonequivalent Control Group Design. Data collection techniques through observation and questionnaire with a Likert scale. The results of data analysis from observation sheet on average experiment class = 3,22 and the average control class = 2,93. This study uses independent sample t-test show tcount ttable that is 3,76 1,99 interpreted tcount ttable then Ho rejected Ho and accepted Ha. Based on the result of this research, it can be concluded that guided inquiry learning digital spring constant give positive influence to science generic skill student in SMAN 11 Semarang. Students' generic science skills were better after the implementation of guided inquiry learning assisted with teaching aids.

Abstract In this study, the spring constant of an accelerometer with a liquid-type proof mass was analyzed. Unlike a general solid-type microelectromechanical system accelerometer, the Laplace pressure is considered a restoring force in the analyzed accelerometer. Using a base excitation mathematical model, the sensor output could be estimated for a specific spring constant. Although the estimated sensor output data fit well with the experimental results, the spring constant of the device could also be determined dynamically (for oscillations below 5 Hz). Moreover, the damping constants could be inferred depending on whether sandblasting treatment was performed. Finally, the effects of the oscillation, surface condition, and volume of liquid metal droplets on the spring constant were analyzed.

In a parking house with KOMA TOWER computer-controlled automated parking system it happens that a control system is locked out of service after a pallet has failed to reach the required position during the shifting of pallets, loaded with cars, into rack cells.

In this paper, the geometry of a frog- shape MEMS microphone is optimized using a particle swarm optimization technique to reduce bias voltage and to increase sensitivity. The PSO algorithm is a population based stochastic optimization technique that inspired by social behavior of bird flocking, which is used to solve complicated design spaces and multi physical problems. The proposed method in this paper can be adapted to a variety of MEMS device designs. This approach shows improvements over previous designs that were generated from the conventional design approach (approximate methods based on trial and error). Considering that the performance of the microphone is studied in different directions, and various design parameters are in a trade off with each other, the definition of a multi-purpose target function is very important. In this work, we define the target function such that all three factors of resonance frequency, mechanical sensitivity and pull-in voltage should be considered, simultaneously. The results show that the designed microphone has a good performance. Actually, only by choosing optimal dimensions for length and width of frog-shape diaphragm arms, the mechanical sensitivity and open circuit sensitivity of the microphone increased approximately 4 and 2 times respectively, and the pull-in voltage decreased to half approximately.

In this paper we introduce the concept, modelling and analysis of triangular and sinusoidal springs intended for large in-plane translational displacements for MEMS-guiding applications. The proposed spring systems combine the advantages of minimal space requirement, low stiffness in the axial direction and high mechanical resistance in off-axis directions. An analytical model for the description of the force-displacement characteristic of triangular springs is derived considering typical mechanical constraints. Based on the model, geometrical parameters of the springs influencing linearity and selectivity with respect to the in- and off-axis stiffness are analyzed. The validity of the models is demonstrated by finite element analysis and experimental verification realized by silicon-on-insulator demonstrators. [2020-0360] [ABSTRACT FROM AUTHOR]

Variations in cell wall composition and biomechanical properties can contribute to the cellular plasticity required during complex processes such as polarized growth and elongation in microbial cells. This study utilizes atomic force microscopy (AFM) to map the cell surface topography of fission yeast, Schizosaccharomyces pombe, at the pole regions and to characterize the biophysical properties within these regions under physiological, hydrated conditions. High‐resolution images acquired from AFM topographic scanning reveal decreased surface roughness at the cell poles. Force extension curves acquired by nanoindentation probing with AFM cantilever tips under low applied force revealed increased cell wall deformation and decreased cellular stiffness (cellular spring constant) at cell poles (17 ± 4 mN/m) relative to the main body of the cell that is not undergoing growth and expansion (44 ± 10 mN/m). These findings suggest that the increased deformation and decreased stiffness at regions of polarized growth at fission yeast cell poles provide the plasticity necessary for cellular extension. This study provides a direct biophysical characterization of the S. pombe cell surface by AFM, and it provides a foundation for future investigation of how the surface topography and local nanomechanical properties vary during different cellular processes. Take away: AFM was utilized to provide high‐resolution surface topography mapping of S. pombe cell surface.Cell poles had decreased cellular stiffness, increased cell wall deformation, and decreased surface rougness compared to the cell body. [ABSTRACT FROM AUTHOR]

The technology for radio frequency micro-electro-mechanical system (RF MEMS) is well established. In the next phase of miniaturization, RF MEMS transforming into RF nano-electro-mechanical system (NEMS) requires scaling laws. For MEMS devices, vertical scaling laws are available in the literature. However, existing scaling laws are isotropic and not valid for the majority of the MEMS devices. Like VLSI technology, the scaling in the MEMS is asymmetric and needs optimization in each direction. In the MEMS, depending upon the working principle, the scaling laws vary from device to device. In the present work, spring constant scaling laws for the electrostatic RF MEMS devices are derived given the device performance. The scaling laws are derived in such a way that existing limitations of the MEMS technology like low switching speed, high pull-in voltage, stiction, etc., are minimized and the response of the switch is improved. [ABSTRACT FROM AUTHOR]

This paper illustrates the design, modeling, and analysis of bridge type structure based capacitive RF MEMS switch with different beam thickness and materials. We have used Ashby's approach to select the best materials in each and every level which helped to improve the overall performance of the switch in terms of mechanical, electrical, and RF properties. Silicon Nitride thin film (εr = 7.8) is used as a dielectric material. The beam structure stiffness is analyzed with different materials, such as gold, titanium, and platinum, within these materials gold with high thermal conductivity and Euler-Young's modulus of 77 GPa is offering the best performance. Incorporation of meanders and perforations to the membrane helped to reduce the pull-in voltage. The proposed switch is offering very low pull-in voltage of 1.9 V. The deflection of beam thickness is tabulated for the three materials among them the 2 ţm thickness is best beam thickness for the switch for X-band applications. The switch offers best return loss (S11) of -21.36 dB, insertion loss (S12) of -0.147 dB, and isolation (S21) of -52.04 dB at 8GHz. The switch presented in this paper is preferable in X-band applications.

The main objective of this paper is to design a passive toe for Surena ||| humanoid robot which is designed and fabricated at the center of advanced systems and technologies of the University of Tehran (CAST). To this end, a 2D model of robot has been adopted. The first step is to design the trajectory of joints neglecting the toe joints. The second step is to investigate the motion stability of the humanoid robot which has equipped with a passive toe using zero moment point criteria. For this purpose, angles of the passive toe during motion is needed which is obtained using vibrational equations. Afterward, the dynamic model of the robot is derived. Constraint-relaxation method is used to determine the reaction forces on the robot, then calculating generalized force vector which contains all joint torques and reaction forces for different phases of motion. To validate the derived dynamic model, the position of the zero moment point is calculated again using reaction forces. Therefore, the position of the zero moment point has been calculated using two different methods. The first one is according to the kinematic of the robot and the second is based on the dynamic of the robot. Finally, the spring constant and the damping coefficient parameters have been changed to investigate how these parameters affect on the angle of passive toe and a parametric analysis has been adopted to inspect the effects of the aforementioned parameters on joint powers and joint torques.

A finite element solution was used to analyse a vertically vibrating footing supported on two-layered soils as well as a footing with a different depth of embedment. Variables considered were the thickness of the top layer, properties of each layer and the depth of embedment. Correction charts were then developed in comparison to a footing on the ground surface and supported by a homogeneous soil layer. The charts can provide an understanding of the effect of different parameters affecting the footing vibration behaviour and will be useful in the preliminary stage of the footing design process. [ABSTRACT FROM AUTHOR]

Atomic force microscopy (AFM) is a powerful tool to investigate interaction forces at the micro and nanoscale. Cantilever stiffness, dimensions and geometry of the tip can be chosen according to the requirements of the specific application, in terms of spatial resolution and force sensitivity. Colloidal probes (CPs), obtained by attaching a spherical particle to a tipless (TL) cantilever, offer several advantages for accurate force measurements: tunable and well‐characterisable radius; higher averaging capabilities (at the expense of spatial resolution) and sensitivity to weak interactions; a well‐defined interaction geometry (sphere on flat), which allows accurate and reliable data fitting by means of analytical models. The dynamics of standard AFM probes has been widely investigated, and protocols have been developed for the calibration of the cantilever spring constant. Nevertheless, the dynamics of CPs, and in particular of large CPs, with radius well above 10 μm and mass comparable, or larger, than the cantilever mass, is at present still poorly characterized. Here we describe the fabrication and calibration of (large) CPs. We describe and discuss the peculiar dynamical behaviour of CPs, and present an alternative protocol for the accurate calibration of the spring constant. [ABSTRACT FROM AUTHOR]

This study aims to establish a test method to obtain the dynamic characteristics of hydraulic-pneumatic semi-active suspensions used in tractor cabins. Because dynamic characteristics are utilized in simulation models for developing suspension control logic and must be secured to improve control performance, an accurate test method must be established. The dynamic characteristics of the suspension, i.e., the spring constant and damping coefficient, were obtained by changing the current and velocity conditions. An exciter was used as a test device to control the displacement and velocity of the hydraulic cylinder. In order to derive the spring constant of the suspension, a low-speed reciprocating motion test was performed to obtain the force-displacement diagram and to derive the damping coefficient; 48 tests were performed under 6 velocity conditions and 8 current conditions to obtain a force-velocity diagram for each result. The spring constant of the suspension was confirmed using the slope of the trend line in the force-displacement diagram obtained through the low-speed reciprocating motion test of the suspension. In addition, the damping coefficient was calculated using the force-velocity diagram obtained through the reciprocating motion test of the suspension under various current and velocity conditions. [ABSTRACT FROM AUTHOR]

In this study, the spring constant of an accelerometer with a liquid-type proof mass was analyzed. Unlike a general solid-type microelectromechanical system accelerometer, the Laplace pressure is considered a restoring force in the analyzed accelerometer. Using a base excitation mathematical model, the sensor output could be estimated for a specific spring constant. Although the estimated sensor output data fit well with the experimental results, the spring constant of the device could also be determined dynamically (for oscillations below 5 Hz). Moreover, the damping constants could be inferred depending on whether sandblasting treatment was performed. Finally, the effects of the oscillation, surface condition, and volume of liquid metal droplets on the spring constant were analyzed. [ABSTRACT FROM AUTHOR]

A simple thought experiment is carried out through which it is shown that the accepted Lorentz transformation for force results in irrational anomalies in the transverse direction. A spring, in its equilibrium state, is set in motion and considered to pass under a contracted spring located in the lab frame of reference. Applying the traditional Lorentz transformation, it is demonstrated that the final lengths of the springs, as they meet each other, are measured differently from the viewpoint of two inertial observers. [ABSTRACT FROM AUTHOR]

Micro electromechanical system switches (MEMS) have procured remarkable attention in recent years due to their perceptible accomplishment in RF and microwave areas. The major challenge in RF-MEMS is to minimize the actuation voltage deprived of restoring force losses. The proposed design presents the analysis of a low actuation voltage shunt capacitive RF-MEMS switch. The proposed switch comprises low actuation voltage, low insertion loss and very high isolation. A horizontal structure of bridge membrane is exhibited in this design and its vertical movement is presided by the electrostatics MEMS actuation technique, which actually provides the ON and OFF conditions of the switch. The actuation pad is fed by coplanar wave guide (CPW) transmission line. The switch performance is successfully evaluated for a large frequency range from 1 GHz to 40GHz. The actuation voltage of the proposed design has been observed to be 3.0 Volts for a vertical displacement of 1.5 μm. Moreover, the fixed-fixed flexures beam structure offers the isolation of -43 dB and insertion loss of -0.12 dB at 28 GHz. [ABSTRACT FROM AUTHOR]

Recently, wave-powered electrical generators, using double-cones moving on circular rails, have been proposed. Rotational motion of the generator’s hull, induced by waves, is changed into the rotational and translational movement of either a rigid magnetized double-cone, rolling on divergent-convergent circular rails, or a double-cone geared motor-generator, rolling on concentric circular rails. However, if such generator is not directly floating on the water waves of random direction, period and height, but it is placed inside of the hull of a ship, the movement of the double-cone is one-directional and dictated by the rolling period and amplitude of the ship’s hull. In such case, divergent-convergent straight rails resembling an O letter might be more efficient than the circular rails. In this work, the optimal design conditions of such a mechanism are examined. Concretely, the O-rails are fixed on the hull of a ship, which is excited to roll along its longitudinal axis, by using a pendulum. Movies of the double-cone moving on the O-rails were shot, and the total travelling time was determined through the slow motion processing of the movies, for various values of the inclination angle of the hull, and energies introduced into the system by the pendulum. Optimal geometry of the O-rails was decided in order to maximize the kinetic energy of translation of the double-cone. Apparent spring constants and damping ratio for the oscillatory movement of the double-cone were experimentally found and validated by a theoretical model. Experimentally observed optimal length of the pendulum arm, to maximize the total traveling time of the double-cone, was justified by a two degree of freedom vibration model of the test rig.

Spring associations are often explored in Physics teaching through a theoretical model that defines the equivalent elastic constant of a set of springs in parallel as the sum of the spring constants of each of the associated springs. Like any scientific model, this representation is constructed by assuming a series of idealizations that delimit its validity domain. In the mentioned model, it is assumed that, when a force is applied, the associated springs extend equally, that is, they present a same deformation. For the case where two springs are used to sustain an object vertically, we will hardly have this condition respected In this paper, we present a discussion about the association of two springs in parallel from the perspective of the Bunge modeling process. We propose an expansion of the traditionally explored theoretical model considering the association of two parallel springs that do not deform equally. We also present an empirical comparison of the traditional model and the proposed expanded model. We understand that the discussion built has the potential to, besides providing the mobilization of basic physics knowledge, foster discussions about the representational role of scientific knowledge, enabling situations that demand reflection on the nature of Science. [ABSTRACT FROM AUTHOR]

Cantilever devices have found applications in numerous scientific fields and instruments, including the atomic force microscope (AFM), and as sensors to detect a wide range of chemical and biological species. The mechanical properties, in particular, the spring constant of these devices is crucial when quantifying adhesive forces, material properties of surfaces, and in determining deposited mass for sensing applications. A key component in the spring constant of a cantilever is the plan-view shape. In recent years, the trapezoidal plan-view shape has become available since it offers certain advantages to fast-scanning AFM and can improve sensor performance in fluid environments. Euler beam equations relating cantilever stiffness to the cantilever dimensions and Young's modulus have been proven useful and are used extensively to model cantilever mechanical behaviour and calibrate the spring constant. In this work, we derive a simple correction factor to the Euler beam equation for a beam-shaped cantilever that is applicable to any cantilever with a trapezoidal plan-view shape. This correction factor is based upon previous analytical work and simplifies the application of the previous researchers formula. A correction factor to the spring constant of an AFM cantilever is also required to calculate the torque produced by the tip when it contacts the sample surface, which is also dependent on the plan-view shape. In this work, we also derive a simple expression for the torque for triangular plan-view shaped cantilevers and show that for the current generation of trapezoidal plan-view shaped AFM cantilevers, this will be a good approximation. We shall apply both these correction factors to determine Young's modulus for a range of trapezoidal-shaped AFM cantilevers, which are specially designed for fast-scanning. These types of AFM probes are much smaller in size when compared to standard AFM probes. In the process of analysing the mechanical properties of these cantilevers, important insights are also gained into their spring constant calibration and dimensional factors that contribute to the variability in their spring constant. [ABSTRACT FROM AUTHOR]

The nanonewton force facility of Physikalisch-Technische Bundesanstalt (PTB), Germany, has been significantly improved. We demonstrate the possibility of using the facility as a calibration device that can accurately determine spring constants of soft cantilevers ($k < 0.1\,\,\text {N}\cdot \text {m}^{-1}$) with traceability to the SI units. This paper is described the possibility of increasing the range of the measured forces to 1 mN. We demonstrate the possibility of using PTB’s nanonewton force facility to accurately determine and compensate for the contact potential difference. To measure the contact potential difference and at the same time the distance between a force sensor and a measured object, a new three-voltage method was developed. For a so-called “plan–plan geometry,” the results of measuring the contact potential difference and the distance in vacuum are presented. A new method of adjusting the parallelism of the plates is also presented. The method used to measure the negative light pressure (light-induced force), which had previously been only theoretically predicted, and the first results of the measurement are presented as well. [ABSTRACT FROM AUTHOR]

In this paper, the influence of heat treatment on PH17-7 stainless steel spring was evaluated. Precipitation hardening phenomenon of PH 17-7 steel was evaluated in three stages. First, the spring constant changes with time and temperature was evaluated. Second, the spring constant changes with respect to its original length at constant temperature and time with blocking (spring length after compression, 18 and 21 mm) were investigated. And finally, the spring heat treatment at 480 °C for 80 min and then holding at 230 °C in oil bath for 60 min without blocking were investigated. The results showed that the use of 18 mm block have large spring constant than 21 mm block. The optimal conditions (480°C for 80 min) for this spring to reaching maximum spring constant were determined.

Micro- and nanocantilevers are employed in atomic force microscopy (AFM) and in micro- and nanoelectromechanical systems (MEMS and NEMS) as sensing elements. They enable nanomechanical measurements, are essential for the characterization of nanomaterials, and form an integral part of many nanoscale devices. Despite the fact that numerous methods described in the literature can be applied to determine the static flexural spring constant of micro- and nanocantilever sensors, experimental techniques that do not require contact between the sensor and a surface at some point during the calibration process are still the exception rather than the rule. We describe a noncontact method using a microfluidic force tool that produces accurate forces and demonstrate that this, in combination with a thermal noise spectrum, can provide the static flexural spring constant for cantilever sensors of different geometric shapes over a wide range of spring constant values (≈0.8–160 N/m).

In this paper, a polyimide (PI)/Si/SiO2-based piezoresistive microcantilever biosensor was developed to achieve a trace level detection for aflatoxin B1. To take advantage of both the high piezoresistance coefficient of single-crystal silicon and the small spring constant of PI, the flexible piezoresistive microcantilever was designed using the buried oxide (BOX) layer of a silicon-on-insulator (SOI) wafer as a bottom passivation layer, the topmost single-crystal silicon layer as a piezoresistor layer, and a thin PI film as a top passivation layer. To obtain higher sensitivity and output voltage stability, four identical piezoresistors, two of which were located in the substrate and two integrated in the microcantilevers, were composed of a quarter-bridge configuration wheatstone bridge. The fabricated PI/Si/SiO2 microcantilever showed good mechanical properties with a spring constant of 21.31 nN/μm and a deflection sensitivity of 3.54 × 10−7 nm−1. The microcantilever biosensor also showed a stable voltage output in the Phosphate Buffered Saline (PBS) buffer with a fluctuation less than 1 μV @ 3 V. By functionalizing anti-aflatoxin B1 on the sensing piezoresistive microcantilever with a biotin avidin system (BAS), a linear aflatoxin B1 detection concentration resulting from 1 ng/mL to 100 ng/mL was obtained, and the toxic molecule detection also showed good specificity. The experimental results indicate that the PI/Si/SiO2 flexible piezoresistive microcantilever biosensor has excellent abilities in trace-level and specific detections of aflatoxin B1 and other biomolecules.

This study aims to establish a test method to obtain the dynamic characteristics of hydraulic-pneumatic semi-active suspensions used in tractor cabins. Because dynamic characteristics are utilized in simulation models for developing suspension control logic and must be secured to improve control performance, an accurate test method must be established. The dynamic characteristics of the suspension, i.e., the spring constant and damping coefficient, were obtained by changing the current and velocity conditions. An exciter was used as a test device to control the displacement and velocity of the hydraulic cylinder. In order to derive the spring constant of the suspension, a low-speed reciprocating motion test was performed to obtain the force-displacement diagram and to derive the damping coefficient; 48 tests were performed under 6 velocity conditions and 8 current conditions to obtain a force-velocity diagram for each result. The spring constant of the suspension was confirmed using the slope of the trend line in the force-displacement diagram obtained through the low-speed reciprocating motion test of the suspension. In addition, the damping coefficient was calculated using the force-velocity diagram obtained through the reciprocating motion test of the suspension under various current and velocity conditions.

This paper introduces a piezoresistive microcantilever with a low spring constant. The microcantilever was fabricated with titanium (Ti) as the piezoresistor, a low spring constant polyimide (PI) layer, and a thin silicon oxide (SiO2) layer as the top and bottom passive layers, respectively. Excellent mechanical performances with the spring constant of 0.02128 N/m and the deflection sensitivity (∆V/V)/∆z of 1.03 × 10−7 nm−1 were obtained. The output voltage fluctuation of a Wheatstone bridge, which consists of four piezoresistive microcantilevers, is less than 3 μV@3 V in a phosphate buffered saline (PBS) environment. A microcantilever aptasensor was then developed through functionalizing the microcantilevers with a ricin aptamer probe, and detections on ricin with concentrations of 10, 20, 50 and 100 ng/mL were successfully realized. A good specificity was also confirmed by using bovine serum albumin (BSA) as a blank control. The experiment results show that the Ti and PI-based microcantilever has great prospects for ultrasensitive biochemical molecule detections with high reliability and specificity.

Structural biology techniques have greatly contributed to unveiling the interplay between molecular structure, physico-chemical properties, and biological function of viruses. In recent years, classic structural approaches are being complemented by single-molecule techniques such as atomic force microscopy and optical tweezers to study physical features of viral particles that are not accessible to classic structural techniques. Among these features are mechanical properties such as stiffness, intrinsic elasticity, tensile strength, and material fatigue. The field of virus mechanics is contributing to materials science by investigating some physical parameters of "soft" biological matter and biological nano-objects. Virus mechanics studies are also starting to unveil the biological implications of some physical properties of viruses and their contribution to virus function. Virus particles are subjected to internal and external forces and they may have adapted to withstand, and even use those forces. This chapter focuses on the mechanical properties of virus particles, their structural determinants, their use to study virus function, and some possible biological implications, of which several examples are provided., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

This paper proposes a very high sensitivity pressure sensor with a novel technique for temperature compensation. The proposed technique employs a geometrical method for self-compensation of Young’s modulus reduction due to temperature increase, where a stronger spring with much larger length and width is anchored. According to the connection of the suspension spring to the larger spring, in higher temperatures, the large spring experiences more length increase, which in turn increases the stiffness of the suspension spring and, consequently, could compensates the Young’s modulus reduction. Simulation results verify that the temperature variation related error in the compensated sensor is less than 0.66% of full-scale under 260 ℃ of temperature range, which shows considerable improvement in comparison with literature. The total consumed area is about 0.033 mm2 with the sensitivity of 290 × 10−6 K−1. [ABSTRACT FROM AUTHOR]