An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of t...

We present a micrograting-based force sensor integrated with a surface micromachined silicon-nitride probe for penetration and injection into Drosophila embryos. The probe is supported by springs of a known spring constant, and the penetration force is determined from displacement measurements using a high-resolution, miniaturized optical encoder that is designed to only be sensitive to axial d...

We consider the wide class of systems modeled by an integrable approximation to the 3 degrees of freedom elastic pendulum with 1:1:2 resonance, or the swing-spring. This approximation has monodromy which prohibits the existence of global action-angle variables and complicates the dynamics. We study the quantum swing-spring formed by bending and symmetric stretching vibrations of the CO2 molecul...

The spring rates of a coiled helical spring under an axial force and an axially directed torque are derived by a consistent application of Castigliano’s second theorem, and it is shown that the coupling between the two loads may not always be neglected. The spring rate of an extensional spring is derived for the first time through the use of the displacement based principle of minimum total pot...

We consider a model, given by two interacting electrons in an external harmonic potential, that can be solved analytically for a discrete and infinite set of values of the spring constant. The knowledge of the exact electronic density allows us to construct the exact exchangtiorrelation potential and exchange-correlation energy by inverting the Kohn-Sham equation. The exact exchange-correlation...

Within the context of impedance controlled exoskeletons, common actuators have important drawbacks. Either the actuators are heavy, have a complex structure or are poor torque sources, due to gearing or heavy nonlinearity. Considering our application, an impedance controlled gait rehabilitation robot for treadmill-training, we designed an actuation system that might avoid these drawbacks. It co...

The simple harmonic vibration, damping vibration and forced vibration of an oscillator attached to the massless spring are always discussed in general mechanics courses. In this article, we focus on the heavy-spring conditions. We first investigate the general situation where both viscous resistance and applied force are considered under the perspective of the renormalization group theory. Then...

the joints between segmental rings can withstand a certain amount of bending moment as well as axial and shear forces. generally, in the structural analysis of tunnel segmental lining, the joints can be modeled as elastic hinges or rotational springs, and their rigidity should be demonstrated in terms of the rigidity of the joints or their rotational stiffness. therefore, the bending moment act...