Also twilley. [Altered f. willy, WILLOW.] A willowing machine: = DEVIL sb. 8 a; also called twilly-devil. Hence Twilly v. trans. to willow.
1858. Simmonds, Dict. Trade, Twilly, a common name for the willying machine.
1859. Tomlinson, Illustr. Usef. Arts, 19/1. Supposing the wool to be dyed, it is passed through the willy, or twillyresembling the willow of the cotton manufacture. Ibid. (1860), Usef. Arts, Ser. I. 37. The willy, or shakewilly, as it is called in Yorkshire, and twilly in Gloucestershire.
1869. Eng. Mech., 19 Nov., 240/2. The best machine for pulling flocks is called a twilly.
1894. C. Vickerman, Woollen Spinning, viii. 117. This is the first operation after the wool is dyed, and is known by a variety of names, as teasing, willeying, willowing, and twilleying.