How do I calculate the speed or a crane the moves by a rack using a pinion?

The crane has a rack that uses a pinion that measures 9 1/2" O.D. and has 36 Teeth. The servos are rated for 15 Hp. and 0 - 25 rpm.

Answer 1

[dpb]

One revolution is 9.5*pi linear inches, roughly. Exactly will depend on the actual contact radius of the gear with the track. You'll have to have an input rpm from the device.

[Joy Walker]

does the horse power from the motor with a rated velocity that can go up to 25 rpm figure into the crane's speed?

[dpb]

Not really, only how fast the drive is turning at the moment in the final say-so. Of course, the motor has to have sufficient torque to be able to overcome inertia and friction to get it going, but you can't really say anything about velocity from that except by a fullblown model of the whole system which would be a major undertaking other than there's an upper and lower limit established by those limits. Of course you need to know the gearing from the motor shaft speed to the final drive to relate motor speed to the drive gear rpm unless it is direct connection. Let's see,

[9.5*pi"/rev]*25 rpm/[12 in/ft] = 62.2 ft/min ~ 1 ft/sec

That's not unreasonable so sounds as though it might be direct drive...