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The simplest case of rolling is that of a rigid body rolling without slipping along a flat surface with its axis parallel to the surface (or equivalently: perpendicular to the surface normal). The trajectory of any point is a trochoid ; in particular, the trajectory of any point in the object axis is a line, while the trajectory of any point in ...
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.
By breaking down the rolling wheel into several points, it can be more easily seen how all points of the wheel rotate around a single point at each instant. This point is the instant centre of rotation, shown in black. Consider the planar movement of a circular wheel rolling without slipping on a linear road; see sketch 3.
A prolate trochoid with b/a = 5/4 A curtate trochoid with b/a = 4/5. As a circle of radius a rolls without slipping along a line L, the center C moves parallel to L, and every other point P in the rotating plane rigidly attached to the circle traces the curve called the trochoid.
The red curve is an epicycloid traced as the small circle (radius r = 1) rolls around the outside of the large circle (radius R = 3).. In geometry, an epicycloid (also called hypercycloid) [1] is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle.
In geometry, a centered trochoid is the roulette formed by a circle rolling along another circle. That is, it is the path traced by a point attached to a circle as the circle rolls without slipping along a fixed circle. The term encompasses both epitrochoid and hypotrochoid. The center of this curve is defined to be the center of the fixed circle.
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The generator is the vertex of the rolling parabola and describes the roulette, shown in red. In this case the roulette is the cissoid of Diocles. [1] Roughly speaking, a roulette is the curve described by a point (called the generator or pole) attached to a given curve as that curve rolls without slipping, along a second given curve that is ...