Source : Webster's Revised Unabridged Dictionary (1913)

Uncurl \Un*curl"\, v. t. [1st pref. un- + curl.]
   To loose from curls, or ringlets; to straighten out, as
   anything curled or curly.

         He sheaths his paw, uncurls his angry mane. --Dryden.

Uncurl \Un*curl"\, v. i.
   To become uncurled, or straight.

Source : WordNet®

uncurl
     v : move out of a curled position; "He uncurled himself"