Vibrot, a simple device for the conversion of vibration into rotation mediated by friction: preliminary evaluation

Abstract

While "vibrational noise" induced by rotating components of machinery is a common problem constantly faced by engineers, the controlled conversion of translational into rotational motion or vice-versa is a desirable goal in many scenarios ranging from internal combustion engines to ultrasonic motors. In this work, we describe the underlying physics after isolating a single degree of freedom, focusing on devices that convert a vibration along the vertical axis into a rotation around this axis. A typical Vibrot (as we label these devices) consists of a rigid body with three or more cantilevered elastic legs attached to its bottom at an angle. We show that these legs are capable of transforming vibration into rotation by a "ratchet effect", which is caused by the anisotropic stick-slip-flight motion of the leg tips against the ground. Drawing an analogy with the Froude number used to classify the locomotion dynamics of legged animals, we discuss the walking regime of these robots. We are able to control the rotation frequency of the Vibrot by manipulating the shaking amplitude, frequency or waveform. Furthermore, we have been able to excite Vibrots with acoustic waves, which allows speculating about the possibility of reducing the size of the devices so they can perform tasks into the human body, excited by ultrasound waves from the outside.

Figure 1. A typical Vibrot.

(a) Photograph and labels of the relevant dimensions. (b) Sketch of the bottom view.

Figure 2. Basic characterization of the Vibrot motion.

(a) Dependence of the rotation frequency on the vibrating plate's adimensional acceleration, for a fixed frequency excitation. (b) Dependence of the rotation frequency on the vibration frequency, at a fixed adimensional acceleration. (c) Rotation frequency as a function of the Vibrot mass for constant vibration frequency and adimensional acceleration of the platform. (d) Threshold adimensional acceleration as a function of the Vibrot mass, at a fixed vibration frequency. (In this plot, the point corresponding to the biggest mass is associated to a high deformation of the legs).

Figure 3. Qualitative stride mechanism.

Sketch of the motion of one Vibrot leg near the vibrating platform. The solid line represents the trajectory of the vibrating plate (grey) during one cycle (Video S3).

Figure 4. Dependence of the stride length on the flying time.

(a) Stride length dependence on the frequency ratio, . The slope of the solid line is . (b) Frequency of rotation as a function of the flying time, (as a fraction of the period ). The doted line is just a guide to the eye. In the inset, the flying time (as a fraction of the period ) is shown versus the acceleration for an inelastic bouncing object. See text for details.