Spur Gear

you need to give more information, like the weight would help, so one can begin to calculate the torque.

Also, you will be depending upon the charity of people to figure it out for you. As well as designing it.

good luck.

You should find something here that will help....

http://www.lowtechmagazine.com/2011/05/pedal-powered-farms-and-factories.html

I would suggest some sort of regulator to compromise any jerky motion....

http://www.wikihow.com/Determine-Gear-Ratio

GA.

Safer to.

Figure 8 from vertical to horizontal, tireless stationary bike wheel for pulley, bob's you uncle!

If you used a size 48 chainwheel fixed to the underside of the stage, and also used one on the bicycle, the stage would match the speed you pedaled. If you used a size 24 on the stage, it would go twice as fast.

I think you will find that the gear on the stage will be the larger

Normal bicycle ratio is about 3, i.e. one turn of the pedals turns the wheel three rotations. What speed do you want to pedal?

If the stage is being used as a centrifuge....

http://www.anaheimautomation.com/marketing/stepper/stepper-motors.php?gclid=CKSr3czpyMICFcpDMgodenwA8w

Take an ordinary 10-speed bike, replace the rear tire with one much smaller in diameter, say a wheelbarrow wheel (Will let you engineer this). Mount the bike in a stationary position with the rear tire at the outer top edge of your stage. Throw 'er down in granny gear and away you go! Glue down rubber sheet to the stage where the tire contacts for extra traction. Gears, chains, sprockets on the stage is overkill. Keep it simple.

Looks like you got some good advice on how to get this thing going, your next, and bigger, challenge is to keep it moving. Since this is a human-powered endeavor, your biggest enemy is friction.

You now have to figure out how you're going to support whatever (unbalanced) weight will be on the platform, while keeping it rotating around some sort of centering/restraining mechanism. Small wheels, thrust bearing bearings, ball bearings, supports, bearing surfaces, etc. are items that I will leave to the more mechanically sophisticated in the group.

Just remember, it is easier to engineer friction out now than to try and overcome it when you're pedaling. You want to engineer smart now so as to pedal easier later.

The stage is 8' in diameter. I'm thinking the max speed would be something like 3 - 4 rpm.

25 feet of gear will be pricey.

Tornado has the right idea. You don't need gears, just a belt and something to press the belt onto the drive wheel.

I see a groove around the stage that the belt rides in, and another one in the drive wheel with something to provide friction. Ratios shouldn't be too hard to work out, after you decide how long you can pedal the bike without having a heart attack.

You'll need some gizmo to convert the rotation of the wheel vertically oriented to horizontal to drive the stage. Right angle gear drive comes to mind.

If you are really hooked with the idea of using a spur gear I would find a pinion you can purchase that fits your design then use solid works to create a spur gear for the large girth gear.

Then blow a huge hole in it in solid works so you would have your 8' OD or whatever it ends up being and then your ID of the large gear can now be 7'-6" so you have a ring with teeth on it.

Now make a hole pattern in it.

Now segment it in a angular increments so you have ring gear segments that can be laser burned out of bar stock at the required thickness depending on inertia and torque required.

Now you can put these gear segments between two pieces of steel with a matching hole pattern so you have a removable gear that can be replaced when it wears out since your pinion will be hardened and your laser burned gear is not.

Just remember that DPs and PAs must match for meshing. If you do not know what those are you will need to know.

You should also consider stopping this thing once it gets going in a circle, perchance you could rig up one of your bicycle handlebar brakes to help stop the momentum.

Larger DP is smoother running, lower DP is for more torque required.

14.5° & 20° are very popular PAs and are usually stocked in small diameters.

Good Luck.