Animation and Variation of a cycloid or rather a trochoid by sliders
Epitrochoid (or rather - if with cusps - a Epicycloid) a moving (yellow) wheel scrolls around a fixed (grey) wheel
Hypotrochoid (or rather - if with cusps - a Hypocycloid)
Peritrochoid (or rather - if with cusps - a Pericycloid)
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Google Chrome 14 and higher
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iOS Safari 3.2 and higher
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Android Browser 2.2 and higher
Double generation of trochoids
Every trochoide can be generated by exact one alternative couple of wheels:
with the ratio
and the distance
is identical to the
with the ratio
and the distance
Explanations of the human interface of this page
Select between the simulation of
a epitrochoid (a moving wheel scrolls around a fixed wheel)
a hypotrochoid [a moving wheel scrolls inside a fixed wheel (ring gear)] and
a peritrochoid [a moving wheel (ring gear) scrolls around a fixed wheel]
using the radio button above the graphic
The moving yellow wheel can be stopped using the button 'Stop' in the first row of the table left of the graphic
The animation can be controlled by the sliderφ (Phi), if the automatic rotation is stoped.
All other slider can be used although the moving wheel is running.
The animation can be started again with the 'Start' button. Pushing the button 'Start' more than one times accelerates the rotation.
The diameter of the fixed grey wheel can be modified using the slider rR.
A modification of the slider rR modifies the number of rows in the table with the background in light blue
The diameter of the yellow moving wheel can be modified using the slider rG.
If rG = 1 then 1 Period = 1 Rotation (please notice the equation at the right side of the slider φ (Phi))
If rG > 1, then the moving wheel has to rotate more than on time during each period.
The trochoid changes the color for each rotation of the moving wheel.
The diameter of the moving yellow wheel rG cannot be set to any value,
because the ratio rR : rG have to be a fraction reduced to lowest term.
The shape of trochoid can be modified using the slider a.
The characteristic of the resulting trochoid is highlighted in yellow in the table below the slider a
The radio button of the table can be used to select and highlight another column in yellow.
The graphic will be modified to show a trochoid with the required characteristic
Dependend on the selected row the minimal and maximal value of the slider varies
If no entry exists in the column anomaly, then the trochoid does not change the characteristic by moving the slider.
Exeption: The first row with the entries "any" allows the slider to change between any characteristic
Exists an entry exists in the column anomaly then a trochoid is displayed with the characteristic of the anomaly.
By moving the slider the trochoid will be modified closed to the anomaly and the characteristic varies.
The variaton of the minimal and maximal value of the slider allows to investigate, how the anomaly is based on the characteristics of the trochoids in the neighborhood.
The starting angle of the moving yellow wheel can be modified using the slider γ0 (Gamma0)
Instead of the slider the value can be influenced by the buttons '<' or rather '>' left and right of the slider.