A method for supporting a tire building assembly is disclosed. The method comprises the steps of supporting one end portion of a radially collapsible building drum (10) for assembling a green tire; moving the end portion in a first direction by an actuator acting in the first direction; and moving the end portion in a second direction by the actuator acting in the first direction. An assembly for moving an end portion of a tire building assembly comprises a support frame (211) for supporting the end portion; a longitudinal rail (213) slidingly mounted to the support frame (211); a transverse rail (215) slidingly mounted to the longitudinal rail (213); and an actuator for moving the longitudinal rail (213) in a first direction relative to the support frame (211), the actuator also moving the transverse rail (215) in a second direction relative to the support frame (211) and the longitudinal rail (213).