# Does the amount of torque that can be transferred from wheel to rod change based on the distance of the connection to the rim of the wheel

Let's say I have a rod that I need rotating, like in a regular crank mechanism:

Now, the motor I use is too weak to generate the required amount of torque to move the mechanism. So I put a gear with 10 teeth on the motor, and replace the wheel with a 40-toothed gear. Now I have a mechanical advantage of 4, so the driven gear can deliver 4 times the amount of torque that the motor can.

Does the amount of torque that the driven gear can transfer differ when I connect the rod close to the hub of the gear, compared to when I connect it closer to the rim?

l Let's say the radius of your gear is R, and you connect the rod at distance x from the center, with the gear's torque 20Nm.

$$F_{rod}=\tau*\frac{R}{x}=20\frac{R}{x}$$

The smaller the x, the distance from the center the bigger F. But its displacement is smaller.

It works like a lever with a fulcrum at the center of the hub which you try to lift an object at a distance of x from the fulcrum. and you have an action force

$$F_{gear}=\frac{\tau}{R}$$

$$\frac{F_{rod}}{F_{gear}}=\frac{R}{x}$$

• So if F gets larger the smaller x gets, that would mean attaching the rod closer to the center would mean more force, at the cost of less “motion”, right? (In the picture shown, the piston would move a shorter distance but get pushed with greater force?
– Bas
Sep 16 '21 at 15:44
• @Bas, exactly. ultimately as you approach x-0 the force approaches infinity and the motion approaches 0. Sep 16 '21 at 17:06
• @Bas, why do you think they make the kik starter of big bikes so long (eg the old Royal Enfield). because they need a lot of force, but little motion. Sep 16 '21 at 17:47
• I had no idea they made kickstarters that long. But it makes sense. :) Thanks!
– Bas
Sep 16 '21 at 20:51

Torque = force * distance

If the distance from the centre line is 0 then torque is zero…

• Wait what? If it was that simple I could drive anything with a weak motor as long as the wheel attached to its axis is large enough.
– Bas
Sep 16 '21 at 15:39

If I understand correctly what you intend to do is

i.e. add the motor to the left.

if you use gears with 10 and 40 teeth, then the distance between the shafts is fixed (and it proportional to the module).

As you say this will offer to the wheel shaft 4 times the torque, but it will reduce the rotational velocity.

Additionally - IMHO- the placement of the rod closer to the wheel shaft will have the effect that the velocity and the stroke will reduce, but the force will be larger.

• Exactly what I meant, yeah. Thanks for the clarification.
– Bas
Sep 16 '21 at 20:52