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I have discussed this before but there is little room for pulleys of useful size if they are fixed one above the other. The main problem is the length of the arm does not allow room for two pulleys of any useful size without the radii going completely haywire. I tried shifting the arm pivot above the front changer clamp, to allow a much longer arm, but it looked much too "busy" even for my tastes. Placing the pulleys side by side on a T-shaped arm might introduce skewed forces unless the cable run was altered to suit.
The image at the top shows a rough drawing with a potential solution on the right. A shorter arm can be used without spoiling the radii of the horizontal entry and exit cable runs. The cable must not slip on its route around the pulleys so the arrangement shown on the right offers much better friction due to the much increased cable wrap. In the shallow system the cable wrap is nearer 270 degrees instead of less than 180 degrees in the arrangement on the left. Both systems demand an extra length of cable but should fall within normal, rear gear cable lengths.
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Pulley size seems optimum around 20mm in diameter with an arm length of 100mm. A T-piece bolted to the bottom of the swinging arm, to carry the two pulleys, would provide effortless change of radii and thereby, pull ratio. The T-piece need only to be rotated slightly to raise or lower both pulleys relative to each other and the swinging arm's pivot. The change in pull ratio may be easily calculated from the horizontal entry and exit heights of the pulleys before clamping the T-piece pivot/fixing bolt tight again.
In the image to the right the pulleys are shown rather far apart for clarity. In practice they should almost touch for maximum, ratio setting accuracy, increased cable friction and reduced cable pull error over the ratio arm's complete arc of swing.
R1:R2 must match the change in cable pull-ratio required. Note how R1 is measured to the top of the left pulley and R2 to the bottom. The downtube cable must join the top of the left pulley before being wrapped around the second pulley on the right. The cable finally exits rearward below the chainstay to reach the rear changer, cable stop.
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I like these blind grommets as pulleys because they are easily obtained, are made of long-lived, grippy material and require no machining. Once a suitable supporting washer is pressed into the center a normal hand drill will manage a central hole within any reasonable tolerance for concentricity. The pulleys [grommets] do not rotate but are an easy means to achieve the correct radii without causing damage to the gear cable. No cable clamping should be necessary.
Click on any image for an enlargement.
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