The History of Punishment: The 1600s

I wonder: in the 1600s, if you were placed in a device (frequently depicted in movies and therein called a 'stock'), that locked your arms and head in place holding you captive for active public abuse and shaming; would that have been called getting 'stocked'?

If so, would a repeat offender be 're-stocked', and was there a re-stocking fee?