# Euclid's Muse

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# Search Results for “involute”

##### Circle Involute Gear Pair
The circle involute is the curve described by the end of a taught string as it is wrapped around a circle. A pair of circle involutes mesh to replicate the motion of a belt wrapped round the two circles.  Hence the involute is a shape used for the surface of gear teeth.

Tags: involute, gear

##### Circle Involute
Find the area of grass accessible to a goat who is tethered to a circular silo.

Tags: Involute, Circle, Goat

##### Cardioid Involute
An endearing feature of the cardioid curve is that its involute is a dilation of itself (by a factor of -3).  The involute is the curve traced by wrapping and unwrapping a piece of string.  The evolute is the inverse of the involute, and is the locus of the centers of curvature of the curve.  The circle of curvature (otherwise known as osculating circle) is the circle which most closely matches the curve at a given point.

Tags: clock

##### Circle Involute
In this clock each hand is a piece of string attached to the edge of a circle. The string is pulled tight at the twelve o?clock position and as the hand moves, it wraps around the circle, and thus gets shorter.?The curve is called the circle involute. It is used for designing gear teeth.  As the strings are stretched tight, they are perpendicular to the involute curve and tangential to the circle.

Tags: clock

##### gear related to belt
We imagine two wheels connected by a belt which is wrapped in a figure 8, so that the wheels rotate in opposite directions. We show half the belt.  Drag the red point to see it move. Now imagine we cut the belt at the blue point.  You can drag the two blue points to see the involute curves. Press Show to turn the curves on permanently. Now drag the red point again, to observe how involute gears mimic a belt drive.

Tags: gear, circle, involute, mechanical-engineering

##### Gear pair
A crossed over belt makes wheels rotate in opposite directions.  This mimics the action of a gear pair. Drag the red point to see how the involute curves mimic the motion generated by the belt.

Tags: involute, gear, mechanical-engineering

##### The Goat and the Silo
A solution to the goat and silo puzzle with a rope longer than pi * R

Tags: Goat-and-silo-problem, involute-of-a-circle