Descriptions and Examples for the POV-Ray Raytracerby Friedrich A. Lohmüller     3D Animations with POV-Ray         Some basics and examples on animations.
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3D Animation Tutorial
Index of Content
0. Basic Knowledge
1. Basic Example
2. Example 2
3. Images to Animated Gif
4. From Images to Video
5. Basic Terms
6. Animation Commands
I. Cyclic Animations
1. Rotating Objects
1.2. Planets in Orbit
1.3. Clock Animation
2. Rotating Camera
2.1. Straight Moving Camera
3. Western Wheel
Problem
> 3.1. Rolling Wheels
4. Gears
4.1. Roller Chain
4.2. Bike Chain
5. Swinging Pendulum
5.2: Rock the Rocker
6. Spiral Pendulum
7. Coupling Rods
7.1. Connecting Rods
8. Psychedelic + Op-Art
9. Counters + Countdowns
10. Folding of a Cube
II. Non-linear Movements
1.0 Speed Up/Slow Down 1
1.1 Speed Up/Slow Down 2
2. Fall + Bounce
3. Acceleration by
physical Formulas
4. Speed Controll by
Spline Functions
III. Animation Paths
with Spline Curves
1. Spline Curves
2. Closed Splines
3. Animation Paths

The Rolling of the Wheels without slipping or spinning.

For correct rolling wheels we have
to know this basic on circles:

Circumference(C) = 2*pi*Radius(R) ;

or shorter:   C = 2*pi*R
The Greek sign for Pi ~ 3.14159...
in POV-Ray is simply "pi" (lower case!).

If a wheel rotates once around the axis,
then it will move foreward by the length
of it's circonference C.

If a wheel rotates by an angle Alpha,
the wheel will move forward by
S = C * Alpha/360 or
S = 2*pi*R*Alpha/360.

On the other hand:
If we want a wheel to move forward by S,
this wheel will rotate during this
movement by an angle of
Alpha = S*360/C or
Alpha = S*360/(2*pi*R).

Note: Here all angles were messured in degrees!
We should use capital letters for our variables
to avoid any collision with predefined POV-Ray variables!

Rolling wheel: rolled off circonference (orange) and angle of rotation (green)

Rolling Wheels with Different Radii

If we want to roll a vehicle with wheels with different radii R1 and R2
the wheels will rotatate with different speed.

While the first wheel with R1 is turning by an angle of Alpha1 degrees,
the second wheel with R2 has to be turned by an angle of Alpha2 = Alpha1*R1/R2 degrees.

Rolling wheels with different radii.
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© Friedrich A. Lohmüller, 2013
www.f-lohmueller.de