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| Verwijderingen worden op deze manier gemarkeerd. | Toevoegingen worden op deze manier gemarkeerd. |
| Regel 10: | Regel 10: |
| So if | {{{Involute: a quick and dirty example}}} In plain language. A cord is coiled around a cylinder. At the end of the cord is a pencil. The cord is unrolled while the cord is held taut. The pencil draws a curve. This curve is called an involute. {{attachment:involute_basic_0-4pi.svg}} {{{Involute curve with x- and y-axis, without base circle.}}} = Practical use = |
| Regel 14: | Regel 22: |
| It is the gear application that makes a polar calculation based on radii more useful than a Cartesian calculation based on (x,y) - we are only interested in the first small part that starts from the base circle. | It is the gear application that makes a polar calculation based on radii more useful than a Cartesian calculation based on (x,y) - we are only interested in the first small part that starts from the base circle. On the other hand, a polar approach has its limits, see below. = Mathematics = |
Involute - or evolvent - curves are used as the shape of teeth of gears. For an introduction to more advanced math, see https://en.wikipedia.org/wiki/Involute.
What is an involute curve?
The quick and dirty example in the picture says more than words.
Involute: a quick and dirty example
In plain language. A cord is coiled around a cylinder. At the end of the cord is a pencil. The cord is unrolled while the cord is held taut. The pencil draws a curve. This curve is called an involute.
Involute curve with x- and y-axis, without base circle.
Practical use
The main reason for using gears with involute shapes is that there is no friction between teeth - against common believe. The teeth roll on each other when rotating.
It is the gear application that makes a polar calculation based on radii more useful than a Cartesian calculation based on (x,y) - we are only interested in the first small part that starts from the base circle. On the other hand, a polar approach has its limits, see below.