A curtate epicycloid is a fascinating type of curve generated by a point fixed at a distance less than the radius of a small circle as it rolls without slipping along the outside of a larger fixed circle. Unlike the standard epicycloid—where the tracing point lies exactly on the circumference—the curtate version creates loops that do not reach out as far, forming rounded, petal-like lobes that remain closer to the larger circle. This curve appears in various applications, including gear design a
A curtate epicycloid is a fascinating type of curve generated by a poin…
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A curtate epicycloid is a type of curve formed by a point that lies inside (but not at the center of) a circle as it rolls without slipping around the outside of another fixed circle.📐 Geometric DescriptionImagine:* A fixed circle of radius RR* A rolling circle of radius rr rolling around the outside of the fixed circle* A point P located inside the rolling circle at a distance d rd>r, it becomes a prolate epicycloid (longer, with loops)📚 Applications* Used in gear tooth design and camshaft pr
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