Swing Gear Animation August 2000

Ok, If you've seen my first animation "temple of the gear" you may have noticed that the gears were actually nothing more than tri-angular teeth. The real shape of a gear is call an involute curve and is shown in the drawing to the right

This is a Close-Up of the gear tooth shape.
Yes, it is a pain to drawn.
No, you cant really avoid drawing it correctly.
No, I'm not going to describe how to draw it here.

This is a close up picture and shows why this complicated shape is needed.
This is the AVI for the above.

I choose the 12 tooth gear to be my 'Base' Gear. You can pick any size you want just be constant. What this means is that it takes a gear with 12 teeth 1 unit of time to make 1 complete revolution (i.e 1=12/12). Likewise it takes a gear with 24 teeth 2 units of time (i.e. 2=24/12) and a gear with 18 teeth 1.5 (i.e. 1.5=18/12). Etc, Etc.
This is the AVI for the above.

Ok, now the hard part.
To rotate a gear right and then left requires some heroic measures. You must know the ending rotation of the gear from when you rotated right so that you can rotate it to the left starting from that point. The only easy way I could see to do this was to make a string of variables for the x,y,z positions and rotation at the end rotation points for every moving item in the file
Gear rotates right 5 degrees per frame for 7 frames then left for 4 frames
Make a variable called rotation7 (the rotation of the gear at frame 7)
Then script 1-7 Rotation= -1 * (5*frame)
and script 8-12 Rotation = rotation7 + (4 * (frame-7))

Note the (-1) is for a clockwise rotation
Note the (frame-7) will equal 1 at frame 8, 2 at frame 9, etc,etc

I was going to try and totally explain this, but it got to be way to much. Note that the Red piston length does NOT change length. In short the problem is that the rotation of the piston is at a constant rate, which means the distance that the gear moves is NOT constant. Just think Trig, Sin, c^2=a^2 + b^2 , and the fact that if a circle rolls along the ground and makes 1 complete rotation it has gone a distance equal to it's circumference... And then a miracle happens...And you get the formula

Quick , Low-Resolution Version
This is the Basic Animation with a single moving camera. Smaller resolution, no anti-alias, and no sound.

Full Version with Sound

Full Length, Multiple Camera Angles, with Sound!

The same animation was filmed with about 6 different cameras, some moving some not. Then Adobe Premier was used to make the transitions from one angle to the next. The Program 'Acid Music' was used to create the music (by me of course) and Premier was once again used to put it all together.