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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 ...

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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 : $$a= \frac{d_1+d_2}{2}$$ $$a= \frac{i\cdot d_2+d_2}{2}$$ $$d_2= \frac{2a}{i+ 1}$$ So assuming: $d_1$ ...

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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 ...

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