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A Simplified Approach for Involute Gear Tooth Flank Generation
Published in Stephen P. Radzevich, Theory of Gearing, 2018
Not only spur, but also helical and circular arc gear teeth in their lengthwise direction, can be designed in this way. The combination of either a straight motion with a rotation or of two rotations makes it possible to design gears with teeth shaped in the lengthwise direction as follows: cycloid, epicycloid, hypocycloid, trochoid, epitrochoid, hypotrochoid,* and involute of a circle. Parallel-axes gear pairs and intersected-axis gear pairs, as well as crossed-axis gear pairs, can be designed in this way.
Power Transmission and Gearing Systems
Published in Wei Tong, Mechanical Design and Manufacturing of Electric Motors, 2022
The profile of a cycloid tooth consists of two separate curves: an epicycloid curve above the pitch circle and a hypocycloid curve below the pitch circle, as shown in Figure 9.5. In a cycloid gearing system, the lines of action between two gears vary in position at different points of contact during the course of action. That is, the path of contact formed by joining the different points of contact at different positions of the intermeshing teeth is curvilinear.
Systems of First Order Linear Differential Equations
Published in Vladimir A. Dobrushkin, Applied Differential Equations with Boundary Value Problems, 2017
4. Consider a plane curve, called hypocycloid, generated by the trace of a fixed point on a small circle of radius r that rolls within a larger circle of radius R > r. Show that the coordinates of this curve are solutions of the initial value problem
Thermal stress analysis for a hypocycloid-type crack problem under remote thermal loading
Published in Journal of Thermal Stresses, 2021
In this paper, the following mapping function is used which maps the exterior region to the unit circle in -plane into the exterior region to the hypocycloid-type crack in z-plane (Figure 1).