conformator

from The Century Dictionary.

• noun An apparatus consisting of a number of bent levers arranged in a circle and controlled by springs, fitted on the head to ascertain its shape in order to make a pattern for a hat.

from the GNU version of the Collaborative International Dictionary of English.

• noun An apparatus for taking the conformation of anything, as of the head for fitting a hat, or, in craniometry, finding the largest horizontal area of the head.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun An apparatus used to take the conformation of part of the body in order to produce something that will fit it (especially of the head, for a hat)