On coopers planes the mouth is often nearer the centre of the length. As marcros says a barrel stave is drawn along the sole. The mating surface of the stave needs to be flat, think the wedges in an orange. This is easier to do 'upside down', the altenative would be to attempt to clamp the curved stave in a manner which would allow 'right way up' planing. The same, or similar methods, have been used to flatten the plane surface of the staves edges in Lute backs. Apparantly some journeymen coopers had a plane with an interlocking joint in the middle of the length to allow ease of carrying around.
The folk museum at Shibden Hall, in Halifax, had a fine example last time I was there.
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