Linkage of two shafts that need to rotate different angles

If you were to set up a gear mechanism, it would be two gears with circumference and radius ratio of 95/83, with the smaller gear at 95 switch.

Therefore the same ratio links would rotate the switches with the same angles.

Of course, only the start and stop position of the rotation is going to be correct. The other positions will be off by various differences, because we are using straight links as opposed to circular gears.

If you wanted to use circular gears

you can use the following procedure.

Assuming $i$ is the gear ratio, you'd need $$i = frac{d_1}{d_2} = frac{n_2}{n_1} = frac{theta_2}{theta_1}$$

The distance between the two centers $a= 225 mm$ will be equal to :

$$a= frac{d_1+d_2}{2} $$ $$a= frac{icdot d_2+d_2}{2} $$ $$d_2= frac{2a}{i+ 1} $$

So assuming:

• $d_1$ is the left most knob (i.e. 95 deg rotation)
• $d_2$ is the right most knob (i.e. 83 deg rotation)

Then $$i = frac{theta_2}{theta_1}= frac{83}{95} = 0.8737$$

And:

$$d_2 = frac{2a}{i+ 1} = 240.16$$

and $$d_1 = 209.83 [mm]$$

Just to verify $frac{d_1+d_2}{2}=frac{450}{2}=225$.

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Note that the above dimension refer to the pitch circle of the gear tooth.

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You can probably get away with 21 and 24 teeth (then for a 95 deg on the right know you'd instead of 83 degree you'd get 83.125[deg], which I expect is acceptable.

Figure 1. A CAD calculation for a direct linkage.

• You want the left wheel to turn 95° from 1 to 2.
• You want it to rotate the right wheel 83° from 3 to 4.
• The direct distance from 1 to 2 is 44.2 mm on a 30 mm radius.
• Construct a 44.2 mm line centred on the right linkage and project down onto the 83° symmetrical angle.
• The linkage pivot radius measures 33.4 mm.
• Scale up or down as required.

We've ignored any error due to the slight angle of the linkage.