Spring (device)

Abstract: The spring constant of microfabricated cantilevers used in scanning force microscopy (SFM) can be determined by measuring their resonant frequencies before and after adding small end masses These masses adhere naturally and can be easily removed before using the cantilever for SFM, making the method nondestructive The observed variability in spring constant—almost an order of magnitude for a single type of cantilever—necessitates calibration of individual cantilevers in work where precise knowledge of forces is required Measurements also revealed that the spring constant scales with the cube of the unloaded resonant frequency, providing a simple way to estimate the spring constant for less precise work

Abstract: Trotting and hopping animals use muscles, tendons and ligaments to store and return elastic energy as they bounce along the ground. We examine how the musculoskeletal spring system operates at different speeds and in animals of different sizes. We model trotting and hopping as a simple spring-mass system which consists of a leg spring and a mass. We find that the stiffness of the leg spring (k(leg)) is nearly independent of speed in dogs, goats, horses and red kangaroos. As these animals trot or hop faster, the leg spring sweeps a greater angle during the stance phase, and the vertical excursion of the center of mass during the ground contact phase decreases. The combination of these changes to the spring system causes animals to bounce off the ground more quickly at higher speeds. Analysis of a wide size range of animals (0.1-140 kg) at equivalent speeds reveals that larger animals have stiffer leg springs (k(leg) [symbol: see text] M0.67, where M is body mass), but that the angle swept by the leg spring is nearly independent of body mass. As a result, the resonant period of vertical vibration of the spring-mass system is longer in larger animals. The length of time that the feet are in contact with the ground increases with body mass in nearly the same way as the resonant period of vertical vibration.

Abstract: Dynamic fluid grids are commonly used for the solution of flow problems with moving boundaries. They are often represented by a network of fictitious lineal springs that can become unreliable when the fluid mesh undergoes large displacements and/or deformations. In this paper, we propose to control the arbitrary motion of two-dimensional dynamic unstructured fluid grids with additional torsional springs. We show that such springs can be designed to prohibit the interpenetration of neighboring triangles, and therefore to provide the method of spring analogy with the robustness needed for enlarging its range of applications. We illustrate our new dynamic mesh motion algorithm with several examples that highlight its advantages in terms of robustness, quality, and performance.

Abstract: The frequency range over which a linear passive vibration isolator is effective, is often limited by the mount stiffness required to support a static load. This can be improved upon by employing nonlinear mounts incorporating negative stiffness elements configured in such a way that the dynamic stiffness is much less than the static stiffness. Such nonlinear mounts are used widely in practice, but rigorous analysis, and hence a clear understanding of their behaviour is not readily available in the literature. In this paper, a simple system comprising a vertical spring acting in parallel with two oblique springs is studied. It is shown that there is a unique relationship between the geometry and the stiffness of the springs that yields a system with zero dynamic stiffness at the static equilibrium position. The dynamic stiffness increases monotonically with displacement either side of the equilibrium position, and this is least severe when the oblique springs are inclined at an angle between approximately 48° and 57°. Finally, it is shown that the force–displacement characteristic of the system can be approximated by a cubic equation.

Abstract: For a V‐shaped atomic force microscopy cantilever beam, the spring constants in the three principal directions are given in terms of the beam geometry and material properties. For the lateral stiffness, a closed‐formed expression is presented. Also, the normal and the longitudinal stiffness are obtained from a few simple equations. The results are compared with a finite element study and found to be very accurate. All spring constants depend strongly on the cantilever thickness, which is difficult to measure. In addition, the lateral and longitudinal stiffness are sensitive to the location and the height of the attached pyramid.