[fadel_st]

I am trying to find any information that can help me to design this kind of gear. Can anyone tell me what to do or where to start? I need the equations that describe this gear.
I will attach a picture of what I am talking about.

[txcncman]

Well, for one thing, the gear cannot engage both racks at the same time as shown in your sketch.

Check out: [ame=http://www.youtube.com/watch?v=WYcqJ5HdxA4]These Gears Really Work? - YouTube[/ame]

Look for other gear videos there while you are at it.

[Al_The_Man]

The rack and pinion shown uses a 'mutilated' pinion with missing teeth, it is a known way of producing reciprocating motion of the rack by continuous rotary motion, the pinion drives the rack first by the top rack and then by the bottom to reverse rack direction.
Looks like a badly drawn example in the picture?
Al.

[txcncman]

As far as gear equations, that is pretty specialized. I doubt Machinery Handbook has anything on that specific application. But you can use the formulas there to extrapolate the information you need.

[handlewanker]

Hi fadel, thre's nothing "special" in the design of the gear/rack form you show in post #1, the pinion....epicycloid form, 14 1/2 deg pressure angle, just meshes with a standard rack, 29 deg included angle tooth form, and as Al says the pinion has half the teeth missing....as soon as the pinion gets to the end of the rack the last tooth on the pinion unmeshes at the moment the first tooth remeshes with the other side of the rack but the rack now moves in a different direction....it's a crafty arrangement, but in my opinion a gimmik.
Ian.

[Plan_B]

I'll put my "engineering cap" on for a sec here just for the fun of it...

It's just a particularized application of a rack/pinion. In my opinion it is a combined shock & vibration machine! The equations of motion for this are pretty straight forward - exept they are non-linear.

Here are the equations of motion:
where
v(t) is the speed linear speed of the rack,
w(t) is the pinion rotation speed (in radians)
RPM is the pinion rotation speed in RPM
r is the mean radius of the pinion (to roughly the center of the teeth)
theta is the angular position of the pinion.

V= +2(pi)rw for 0<=theta<=180; -2(pi)rw for 180<=theta<=360

This produces a square wave and that's why it's non-linear. this is exactly the same as for a normal rack and pinion except for the direction change. All of the equations for loading, torque are the same exept for the point where the direction changes. This will send shocks through your system and the forces could be great if w is any substantial speed.

Theoretically if the pinion was oblong and the two racks pring-loaded against it (really you would need a cam profile for them to follow), you could produce a back and forth motion with more rounded edges - like a sine wave.

This is an interesting contraption but there are more practical means to produce the motion that this would produce. Like a cam , or crankshaft and piston. Is there something that leads you to this rather than something more traditional?