Machine Design
Gear Drive
Cycloidal teeth
A cycloid is the curve traced by a point on the circumference of a circle which rolls without slipping on a fixed straight line.
Cycloidal Teeth
A cycloid is the curve traced by a point on the circumference of a circle which rolls without slipping on a fixed straight line.When a circle rolls without slipping on the outside of a fixed circle, the curve traced by a point on the circumference of a circle is known as epicycloid.On the other hand, if a circle rolls without slipping on the inside of a fixed circle, then the curve traced by a point on the circumference of a circle is called hypocycloid
the fixed line or pitch line of a rack is shown.When the circle C rolls without slipping above the pitch line in the direction as indicated, then the point P on the circle traces the epicycloid PA. This represents the face of the cycloidal tooth profile.When the circle D rolls without slipping below the pitch line, then the point P on the circle D traces hypocycloid PB which represents the flank of the cycloidal tooth. The profile BPA is one side of the cycloidal rack tooth.Similarly, the two curves P' A' and P' B' forming the opposite side of the tooth profile are traced by the point P' when the circles C and D roll in the opposite directions. In the similar way, the cycloidal teeth of a gear may be constructed as shown.The circle C is rolled without slipping on the outside of the pitch circle and the point P on the circle C traces epicycloid PA, which represents the face of the cycloidal tooth.The circle D is rolled on the inside of pitch circle and the point P on the circle D traces hypocycloid PB, which represents the flank of the tooth profile.The profile BPA is one side of the cycloidal tooth. The opposite side of the tooth is traced as explained above.
Construction of two mating cycloidal teeth
A point on the circle D will trace the flank of the tooth T1 when circle D rolls without slipping on the inside of pitch circle of wheel 1 and face of tooth T2 when the circle D rolls without slipping on the outside of pitch circle of wheel 2.Similarly, a point on the circle C will trace the face of tooth T1 and flank of tooth T2.The rolling circles C and D may have unequal diameters, but if several wheels are to be interchangeable, they must have rolling circles of equal diameters.The common normal XX at the point of contact between two cycloidal teeth always passes through the pitch point, which is the fundamental condition for a constant velocity ratio.
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