An instrument comprises a handpiece, a boss member, a cylindraceous cam body, a linearly movable member, a cam follower, and a braking member. The cam body is rotatably supported in the handpiece and includes an exterior cam feature. The cam follower couples the linearly movable member with the cam feature of the cam body. The cam feature and the cam follower cooperatively drive the linearly movable member linearly in response to rotation of the cam body within the handpiece. The braking member extends about at least a portion of the exterior of the cam body and is positioned to progressively engage the boss member as the cam body rotates within the handpiece. The braking member and the boss member thus cooperate to provide gradual braking of the cam body. The instrument is operable to deploy a pressure equalization tube in the tympanic membrane of a patient.