A model to predict the oscillation frequency for drops pinned on a vertical planar surface

Accurate prediction of the natural frequency for the lateral oscillation of a liquid drop pinned on a vertical planar surface is important to many drop applications. The natural oscillation frequency, normalized by the capillary frequency, is mainly a function of the equilibrium contact angle and the Bond number ( $Bo$ ), when the contact lines remain pinned. Parametric numerical and experimental studies have been performed to establish a comprehensive understanding of the oscillation dynamics. An inviscid model has been developed to predict the oscillation frequency for wide ranges of $Bo$ and the contact angle. The model reveals the scaling relation between the normalized frequency and $Bo$ , which is validated by the numerical simulation results. For a given equilibrium contact angle, the lateral oscillation frequency decreases with $Bo$ , implying that resonance frequencies will be magnified if the drop oscillations occur in a reduced gravity environment.

Lateral Oscillation and Body Compliance Help Snakes and Snake Robots Stably Traverse Large, Smooth Obstacles

Snakes can move through almost any terrain. Similarly, snake robots hold the promise as a versatile platform to traverse complex environments such as earthquake rubble. Unlike snake locomotion on flat surfaces which is inherently stable, when snakes traverse complex terrain by deforming their body out of plane, it becomes challenging to maintain stability. Here, we review our recent progress in understanding how snakes and snake robots traverse large, smooth obstacles such as boulders and felled trees that lack “anchor points” for gripping or bracing. First, we discovered that the generalist variable kingsnake combines lateral oscillation and cantilevering. Regardless of step height and surface friction, the overall gait is preserved. Next, to quantify static stability of the snake, we developed a method to interpolate continuous body in three dimensions (3D) (both position and orientation) between discrete tracked markers. By analyzing the base of support using the interpolated continuous body 3-D kinematics, we discovered that the snake maintained perfect stability during traversal, even on the most challenging low friction, high step. Finally, we applied this gait to a snake robot and systematically tested its performance traversing large steps with variable heights to further understand stability principles. The robot rapidly and stably traversed steps nearly as high as a third of its body length. As step height increased, the robot rolled more frequently to the extent of flipping over, reducing traversal probability. The absence of such failure in the snake with a compliant body inspired us to add body compliance to the robot. With better surface contact, the compliant body robot suffered less roll instability and traversed high steps at higher probability, without sacrificing traversal speed. Our robot traversed large step-like obstacles more rapidly than most previous snake robots, approaching that of the animal. The combination of lateral oscillation and body compliance to form a large, reliable base of support may be useful for snakes and snake robots to traverse diverse 3-D environments with large, smooth obstacles.

The study on crossover layouts of multi-layer winding grooves in deep mine hoists based on transverse vibration characteristics of catenary rope

In a deep mine winding hoist system, the lateral oscillation of the catenary rope is an important evaluation index of orderly rope arrangement and engineering safety. Different boundary excitations will appear when the wire rope winds on symmetrical or asymmetrical grooves, which results in the different dynamic responses of the hoisting system. In this article, the vibration equations of a deep mine hoisting system are established by using the Hamilton principle, and excitation functions of different crossover zone layouts are deduced. The operation curves are introduced to conduct the experiment based on a certain experimental platform. The lateral oscillation of the catenary rope is recorded by high-speed cameras, and an effective image processing method is proposed to obtain the vibration response of a certain point in the catenary rope. The numerical simulations are compared with the experimental results to prove the vibration models derived in this article are valid. The models could provide reliable basis for the grooves type selection in deep mine hoisting.