Locomotion of a Cylindrical Rolling Robot with a Shape Changing Outer Surface

A cylindrical rolling robot is developed that generates roll torque by changing the shape of its flexible, elliptical outer surface whenever one of four elliptical axes rotates past an inclination called trigger angle. The robot is equipped with a sensing/control system by which it measures angular position and angular velocity, and computes error with respect to a desired step angular velocity profile. When shape change is triggered, the newly assumed shape of the outer surface is determined according to the computed error. A series of trial rolls is conducted using various trigger angles, and energy consumed by the actuation motor per unit roll distance is measured. Results show that, for each of three desired velocity profiles investigated, there exists a range of trigger angles that results in relatively low energy consumption per unit roll distance, and when the robot operates within this optimal trigger angle range, it undergoes minimal actuation burdening and inadvertent braking, both of which are inherent to the mechanics of rolling robots that use shape change to generate roll torque. A mathematical model of motion is developed and applied in a simulation program that can be used to predict and further understand behavior of the robot.

Velocity Control of a Cylindrical Rolling Robot by Surface-Morphing

A mathematical model is developed for a rolling robot with a cylindrically-shaped, elliptical outer surface that has the ability to alter its shape as it rolls, resulting in a torque imbalance that accelerates or decelerates the robot. A control scheme is implemented, whereby angular position and angular velocity are used as feedback to trigger and define morphing actuation. The goal of the control is to direct the robot to follow a given angular velocity profile. Equations of motion for the rolling robot are formulated and solved numerically. Results show that by automatically morphing its shape in a periodic fashion, the rolling robot is able to start from rest, achieve constant average velocity and slow itself in order to follow a desired velocity profile with significant accuracy.

A unified criterion for the centrifugal instabilities of vortices and swirling jets

Swirling jets and vortices can both be unstable to the centrifugal instability but with a different wavenumber selection: the most unstable perturbations for swirling jets in inviscid fluids have an infinite azimuthal wavenumber, whereas, for vortices, they are axisymmetric but with an infinite axial wavenumber. Accordingly, sufficient condition for instability in inviscid fluids have been derived asymptotically in the limits of large azimuthal wavenumber $m$ for swirling jets (Leibovich and Stewartson, J. Fluid Mech., vol. 126, 1983, pp. 335–356) and large dimensionless axial wavenumber $k$ for vortices (Billant and Gallaire, J. Fluid Mech., vol. 542, 2005, pp. 365–379). In this paper, we derive a unified criterion valid whatever the magnitude of the axial flow by performing an asymptotic analysis for large total wavenumber $ \sqrt{{k}^{2} + {m}^{2} } $. The new criterion recovers the criterion of Billant and Gallaire when the axial flow is small and the Leibovich and Stewartson criterion when the axial flow is finite and its profile sufficiently different from the angular velocity profile. When the latter condition is not satisfied, it is shown that the accuracy of the Leibovich and Stewartson asymptotics is strongly reduced. The unified criterion is validated by comparisons with numerical stability analyses of various classes of swirling jet profiles. In the case of the Batchelor vortex, it provides accurate predictions over a wider range of axial wavenumbers than the Leibovich–Stewartson criterion. The criterion shows also that a whole range of azimuthal wavenumbers are destabilized as soon as a small axial velocity component is present in a centrifugally unstable vortex.

Tracking Control of a Software Cam Machining System

This paper presents a software cam manufacturing system. It includes a position tracking control system, a programmable cam profile, and a programmable variable angular velocity profile. The position tracking system consists of a rotary direct drive (DD) servo motor and a linear servo-motor. The rotary DD servo-motor is controlled to track the variable angular velocity profile, while the linear servo-motor is controlled to synchronously track the desired cam profile. Such a tracking control system is proposed to achieve a constant removal rate for fine machining (i.e., the relative tangential velocity at the contact point should be constant). A numerical method for off-line derivation of the variable angular velocity profile with respect to the desired cam profile is developed to achieve constant relative tangential velocity at the contact point. An experimental tracking control system with two servo controllers is developed to study the feasibility of this approach.

Comparison of Stellar Oscillations and Activity Data to Infer Internal Rotation

Recently it has beeen suggested that the latitude distribution of the main surface features of solar activity is intimately related to the angular velocity profile inside the Sun through the working of a MHD dynamo in the boundary layer between the convective and the radiative zones (Belvedere et al. 1991).Although the present observational capabilities are not very encouraging, here we want to point out, in the framework of the analogy to the Sun (solar-stellar connection), that space observations of surface distribution and latitudinal migration of active regions on stellar surfaces, which could be carried out in this decade with more sophisticated techniques, may conversely allow us to infer the rotation profile, and consequently the angular momentum distribution, in stellar interiors. This methodology may in principle be considered alternate or complementary to the classical one based on observation of acoustic oscillations.