The Collaborative International Dictionary of English v.0.48:

Sinch \Sinch\, n. [See Cinch.]
   A saddle girth made of leather, canvas, woven horsehair, or
   woven grass. [Western U.S.]
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Sinch \Sinch\, v. t.
   To gird with a sinch; to tighten the sinch or girth of (a
   saddle); as, to sinch up a sadle. [Western U.S.]
   [1913 Webster]