A Cove is a simple elegant shape that we can turn on the lathe. They can range from small deep profiles to large sweeping coves.
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A Cove should be turned using a spindle
gouge.
To turn a cove we employ a simple rolling action with the gouge starting on its side at 90 degrees before being rotated down into the cove finally ending on its flat:

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Below is a simple video on turning coves: