They can, and i even owned one like this for some time.
The problem is that you have to produce two mirrored sets of ratchet mechanisms, which is not economical.
When my bike was in the shop for maintenance, they replaced both of them with the same spare part, since a mirrored version was to hard to get.
The thumb moves the chain to a larger gear and the index finger to a smaller gear. That has the opposite effect on the pedal versus the wheel sprocket.
The question of why that setup. One reason is to move the change to a large sprocket you push the chain against the larger sprocket to force it to jump up. The motion extends the chain and is again the chain tension system. The required force to move to a smaller gear is just to pull the chain off a gear into the air so the tension mechanism pulls it tighter and to the smaller gear.
There is inherently less force required to move to a smaller than a larger gear so the springs in the gear shift system are set up to move the chain to the smaller gear.
Your thumb can apply move force the your index finger so it is used to pull against the spring and apply enough force to move the change to a larger gear. Your index finger just loosens the locking mechanism and lets it jump to another-looking position.
With good gears where not a lot of force is required, you can have a setup where the index finger increases the tension of the wire. They are just not as common.
Smaller to larger gear requires pressure. Larger to smaller releases pressure. With the chain rings (front) bigger to smaller is a lower gear…easier pedaling…more pedaling for same rear wheel rotation. With the sprocket (the rear wheels), larger to smaller is a higher gear…harder pedaling…less pedaling for more rear wheel rotation
Former mechanic here. There are two pieces to this:
1. Why do we push instead of pull: we push the lever to go to a larger sprocket because the chain needs that force to leap to a larger sprocket. Going to a smaller sprocket doesn’t require a much force because gravity takes over. All you have to do to go to a smaller sprocket is move the chain and it will naturally go down but it needs more push to go up and our thumbs are better at pushing.
2. Why does this have the opposite effect for front/back left/right: in the front (left) the bigger gear pulls more chain per pedal revolution. The back (right) the bigger gear takes more chain to complete a revolution of the wheel. If the front is pulling more chain links and the back takes less links to rotate the wheel, you go fast. If the font is pulling less chain and the rear takes more links to rotate the wheel, you goo slow.
Your pedaling is translated to the rearwheel from the chainrings to the rear cogs via the chain.
Think of it like this. Suppose you have 36 teeth (t) in the front (this is the left hand), and 36t in the back (Right hand). For 1 pedal rotation in the front, the rear wheel spins once. If the rear cog is on 12t, for 1 rotation in front, the rear wheel spins 3x, which makes you go faster, but also requires considerably more effort. Now if you switch the front cogs to say, 48t, with 12t on the back, you’ll be rotating that rear wheel 4 times, instead of 3 previously
The thumb shifts to a larger size of ring for both the left and right-hand controls, but the effect that they have is the opposite due to the above reasons.
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