for mounting on the beam of a mobile stand to hold a machine , a bracket assembly includes a bracket body supportable on the beam of the mobile stand , a front clamp mounted in the bracket body and clamped on the beam of the stand , a rear clamp pivoted to the bracket body , and a locking control device pivotally mounted in the bracket body for operation by the user to impart a biasing force to the rear clamp for enabling the rear claim firmly clamped on the beam of the stand so as to further hold down the machine on the beam between the front clamp and the rear clamp .