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That is, the involutes of a curve are the roulettes of the curve generated by a straight line. The notions of the involute and evolute of a curve were introduced by Christiaan Huygens in his work titled Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae (1673), where he showed that the involute of a ...
Involute polar angle. Expressed as θ, the involute polar angle is the angle between a radius vector to a point, P, on an involute curve and a radial line to the intersection, A, of the curve with the base circle. [1]
In the case where the rolling curve is a line and the generator is a point on the line, the roulette is called an involute of the fixed curve. If the rolling curve is a circle and the fixed curve is a line then the roulette is a trochoid. If, in this case, the point lies on the circle then the roulette is a cycloid.
Helical involute gears are typically only used in limited situations where the spirals of the teeth are of the same handedness, the spirals of the two involutes are of different handedness, and the line of action is the external tangents to the base circles (analogous to a normal belt drive, whereas normal gears are analogous to a crossed-belt ...
of a line is an ideal point, of a nephroid is a nephroid (half as large, see diagram), of an astroid is an astroid (twice as large), of a cardioid is a cardioid (one third as large), of a circle is its center, of a deltoid is a deltoid (three times as large), of a cycloid is a congruent cycloid, of a logarithmic spiral is the same logarithmic ...
Line; Degree 2. Plane curves of degree 2 are known as conics or conic sections and include ... Involute; Isoptic including Orthoptic; Negative pedal curve. Fish curve;
A cycloid generated by a rolling circle. In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve.
When that happens, the curve traced out by the endpoints of the line segment is an involute that encloses the given curve without crossing it, with constant width equal to the length of the line segment. [9] If the starting curve is smooth (except at the cusps), the resulting curve of constant width will also be smooth.