How to makes the Pattern with the Laser pointer

I am surprised by the illuminated Batman....

Even so, it is mysterious a shine. The light of the stars we are looking up at night, what we can perceive as long as the light of the old star has finally reached the earth. Oops, sorry, that topic is too big. This time it is a story of " laser pointer ".

Did you not play well with your laser pointer when you were a child? I remember being hooked very much because it can illuminate the light like the laser beam of the SF movie. If you quickly move the tip of the laser pointer, the eyes perceive the afterimage and it looks like a pattern and it's interesting.

The same principle is basically the same as a full-fledged laser projector. But even a handmade device that assembled such cheesy plastic parts can make a nice light show using a laser pointer! When the gear is turned, the afterimage of the light of the laser pointer shapes the pattern.

The plastic parts of this device are formed by 3D printers, and the required type is already available for download from Thingiverse. Among them, parts called " cam " (a mechanism for changing the rotation of the shaft to reciprocating motion such as up and down, front and rear, etc.) are important. The edges of this cam are irregular in accordance with each pattern, and the shift of movement caused by this unevenness changes the direction of the light of the laser pointer.

See the video Laser Show;

Of course, just by illuminating it will not be a pattern, so we need to rotate this gear at more than 5 revolutions per second. You can change the pattern by replacing the cam, such as Batman, Clover, Star pattern, etc. Try watching the previous video while thinking. And pay attention to commentary on the design of the device which starts from around 2 minutes and 40 seconds.

Mathematical Formula

"Well, yes, I heard that the unevenness of cam is shifting the laser pointer," I realized that I knew the first half and I was disappointed, as I noticed, I was shifting to a difficult expression.

Oh, but yertle vert, the distributor of this video, is casually and explicitly explained to me, probably I just can not understand.... I'm sorry.

By the way, you can make your own favorite patterns! Of course, it is a 3D printer, and then... I need knowledge of a well- rounded math!