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My daughter has trouble with the twist shifters on her bike, can you get trigger shifters for a 6 speed? Cheap like.
Triggers here
http://www.ukbikestore.co.uk/product/97/sltx506pa/shimano-sl-tx50-sis-thumb-shifter-plus---6-and-3-speed-pair.html
Or use a 7 speed but index from 6 so there will be a click to 7th but no change.
jonk +1
Be careful with a 7-sp shifter and a 6-sp freewheel or vice-versa.
Spacing is not the same and it will be difficult/impossible to get a good shift across the whole block.
I had this issue with a 6-sp indexed downtube shifter with a 7-sp wheel. It would not index, so I switched back to a 6-sp block.
Friction shift is never a problem, but your daughter may not be capable.
Check it out on Sheldon Brown.
PaulD
having been in the same boat, i'd suggest a good clean and lube on the twisters first, and a nice new cable. If you girl is small she might have trouble with triggers plus they are not as straight forward in function as a twister.
I am sure I have a new 6 speed shifter in the shop. Cheap but ugly though.