1

I am not a mathematician so please bare this in mind. I am designing a computer steering wheel, using real car parts (fitting the steering wheel from a hatchback via gears to a potentiometer which is wired to a game controller). The steering column needs to turn 900 degrees. However the degrees of turn that my potentiometer has is 270 degrees (135 degrees +/- from centre).

If the gear attached to the steering column has a diameter of (x) and the gear has a diameter of (y). What is the value of X and what is the value of Y.

Ideally although I do want the answer, more importantly I would like the formula about how to calculate two gear sizes given the degrees that both can/should turn.

Also does the physical distance between two gears effect the turn ratio? To my knowledge it shouldn't, but I thought I would check.

Thanks in advance.

gcoulby
  • 113
  • Consider for the next time to attach an image What is the difference of the rotation of the potentiometer and the centre? – PenasRaul Sep 10 '14 at 11:16
  • OK I will consider this for next time. This is my first post in the maths section so I apologise for that. – gcoulby Sep 10 '14 at 11:22

1 Answers1

0

So, a full turn in the steering column walks a distance of $\pi x$, then 900 degrees = 2.5 turns, so the steering column walks $2.5 \pi x$ while rotating 900 degrees. A full turn of the gear walks $\pi y$, so as 270 degrees = 0.75 turns, the gear will walk $0.75 \pi y $. Now as they are attached the walking of both gears are the same, so you have the equation $$2.5 \pi x=0.75\pi y \Leftrightarrow x = \frac{3}{10} y$$

Of course the diameter and the distance are related, as de distance between the centers is z, you should have $$ 2z = x + y$$

So, solving this equation on $z$ you should get

$$2 z = y \frac{13}{10} \Leftrightarrow y = \frac{20}{13} z$$ $$x = \frac{3}{10} y = \frac{6}{13} z$$

In general, if two gears A, B with diameter $x, y$ and centre distance $z$ have to turn $\alpha$ degrees for A, and $\beta$ degrees for B. The fundamental equations are

$$\alpha x = \beta y$$ $$x + y = 2z$$

And the solution is

$$y= z \frac{2}{1 + \frac{\beta}{\alpha}}$$ $$x = z \frac{2}{1 + \frac{\alpha}{\beta}}$$

PenasRaul
  • 1,194
  • 6
  • 10
  • Thank you for this answer. I don't fully understand it, but I will sit with it and figure it out. Thanks for you help.... and quick response. – gcoulby Sep 10 '14 at 11:25
  • What have you not understand? – PenasRaul Sep 10 '14 at 11:26
  • first what is this ⇔ – gcoulby Sep 10 '14 at 11:29
  • Is just a way of saying "manipulating the equation using the normal operations (multiplicating / dividing / suming the same thing in both sides ) we get" – PenasRaul Sep 10 '14 at 11:31
  • So with this equation -> 2.5πx=0.75πy⇔x=3/10y

    You mean the value of (2.5πx=0.75πy) is the same as the value of (x=3/10y). I apologise for my lack of understanding

     – gcoulby Sep 10 '14 at 11:42
  • No, I say that the equation $2.5πx=0.75πy$ can be translated to $x=3/10y$. So, if the first one holds, then the second one holds. – PenasRaul Sep 10 '14 at 12:18