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Raleigh Competition backwards-pedal fixed-gear road bicycle (England; c.1968)
Years ago I'd read about reverse pedaling and it's relative benefit.
This year I've tried to convert this bike. While it's not yet reliable, it's been lots of fun.
In this set up, the rear hub has both fixed cog and freewheel.
The chain runs backwards from top of chainwheel to freewheel,
then it runs forward around a tension wheel fit to the chain stay.
It loops back around turning the fixed cog forward.
The chain then runs forward to the bottom of the chainwheel.
Beside adapting to fixed-gear backward pedaling, the weird thing is it cannot be pedaled forward.
That is, it locks up when resistance is applied to the backward motion by pedaling forward.
Below is the article "Backward Verses Forward Pedaling"
by Ramondo Spinnetti, from Human Power, Fall 1987.