A new design of the Lobe pump is based on the meshing principle of elliptical gear pairs

The paper presents a new rotor design of an external coupling Lobe pump driven by pair of elliptical gears. The new rotor is a four-tooth elliptical gear with tooth profile is a improve cylocid curve. The improve cylocid curve is the locus of the fixed point on the generation circle, when the circle a pure rolling without slipping on the elliptical centrode of the rotor. The conditions of the rotor addendum and dedendum profiles are also considered. The limited supply angle addendum and dedendum rotor profiles are determined through an iterative algorithm when the generation circle makes a pure rolling without slipping on the ellipse base of the rotor. From there, we proceed to determine the pump design parameters according to the characteristic design parameters forming the rotor profile. The flow rate of the pump is determined by the area of the pockets on a cross-section perpendicular to the pump shaft. On that basis, a Matlab program is written from the mathematical model established by the paper to calculate the rotor design. In addition, the paper also investigates the effect of the coefficient l (semi-major axis divided semi-minor axis of the elliptical centrode ) on the average flow and axis distance. Survey results show that the design at l = 0.5 flow is 52.17% larger and the axis distance is reduced by 21.43% when compared to the traditional design at l = 1. This is the advantage of the new design proposed by this study.

Note on a ball rolling over a sphere: Integrable Chaplygin system with an invariant measure without Chaplygin hamiltonization

In this note we consider the nonholonomic problem of rolling without slipping and twisting of an ??-dimensional balanced ball over a fixed sphere. This is a ????(??)?Chaplygin system with an invariant measure that reduces to the cotangent bundle ??*?????1. For the rigid body inertia operator r I? = I? + ?I, I = diag(I1,...,In) with a symmetry I1 = I2 = ... =Ir ? Ir+1 = Ir+2 = ... = In, we prove that the reduced system is integrable, general trajectories are quasi-periodic, while for ?? ? 1, ?? ? 1 the Chaplygin reducing multiplier method does not apply.

Workspace of Multifingered Hands Using Monte Carlo Method

Multifingered hands have the capability of dexterous manipulation of grasped objects and thus significantly increase the capabilities of a robot equipped with multifingered hands. Inspired by a multijointed human finger and the hand, we propose a six degree-of-freedom (DOF) model of a three-fingered robotic hand as a parallel manipulator. Two kinds of contact, namely point contact with friction and rolling without slipping between the fingertips and the grasped object, are considered. The point contact with friction is modeled as a three DOF spherical joint, and for rolling without slipping, we use the resultant nonholonomic constraints between the grasped object and the fingers. With realistic limits on the joints in the fingers and dimensions of finger segments, we obtain the well-conditioned manipulation workspace of the parallel manipulator using a Monte Carlo-based method. Additionally, we present two new general results—it is shown that maximum position and orientation workspace is obtained when the cross-sectional area of the grasped object is approximately equal to the area of the palm of the hand and when rolling without slipping is ensured the size of the well-conditioned workspace is significantly larger (∼1.2–1.5 times). We also present representative experiments of manipulation by a human hand and show that the experimental results are in reasonable agreement with those obtained from simulations.

Rolling with and without Slipping during Orthocycloids Generation

The orthocycloid represents a plane curve generated by a point belonging to a circle which is rolling without slipping along a line. Our original idea (not approached in the specialty literature) is to consider the rolling with slipping of a wheel on a rail, instead of the rolling of the gear “gearwheel –rack” as in the case of the orthocycloid generation. In this case the length of the arc considered on the circle is no longer equal to the segment from the line supporting the rolling. The tracer point belonging to the wheel will generate other curves but orthocycloids. Various curves were obtained. Analyses were made considering the braking due to the friction between the rolling surfaces and respectively the case when the lubricant layer generates a “skating like” rolling. The yielded curves start from the classical form of the orthocycloid and afterward are distorted exhibiting an increased number of loops. Some curves are similar to elongated orthocycloids, obtained in different conditions. The curves resulted from rolling by slipping can be used in various domains.

Rolling with and without Slipping, during Epicycloids Generation

The starting point consists in the modality to generate epicycloids when two external circles are considered. The mobile circle is rolling on the fix circle without slipping, such as two arcs belonging to these circles are equal. The specialty literature presents an example with a simple planetary gear in which the “satellite porting” arm provides the rolling of the mobile circle on the fix circle. Our original idea, not approached in the specialty literature, considers the rolling with slipping of the mobile circle on the fix circle. Instead of the gears providing the rolling without slipping, two wheels with smooth surfaces are used now. The case when the two involved arc are no longer equal is analysed. Between them appear either frictions generating braking or “skating like” rolling when the lubricant layer is too thick. An analysis of the theoretical case when the slipping has a sense opposite to that of a normal rolling is also performer. A significant class of curves was obtained. Some are even epicycloids obtained with slipping, with other parameters.

Dynamics and Trajectory Tracking of a Spherical Rolling Robot on an Inclined Plane

In this paper, we derive the dynamics of a spherical rolling robot, called BYQ-III, rolling without slipping on an inclined plane through the constrained Lagrange method. We present a state space realization of this constrained system, and develop a control algorithm for stabilizing the robot to track a desired trajectory on the inclined plane based on input-output feedback linearization. The validity of the proposed control scheme is then verified through simulation study.