A chuck for a laser cutting/engraving rotary fixture comprises a chuck plate having a chuck plate axis of rotation and at least two mount brackets spaced symmetrically radially with respect to one another about the chuck plate axis of rotation. Each mount bracket comprises an inclined contact surface and each mount bracket is rotatably attached to the chuck plate about the mount bracket axis of rotation. The inclined contact surface can be selectively rotated between a first position with the inclined contact surface inclined toward the mount plate axis of rotation and a second position with the inclined contact surface inclined away from the mount plate axis of rotation. An effectively concave contact surface is defined with each of the inclined contact surfaces in the first position. An effectively convex contact surface is defined with each of the mount brackets in the second position for engaging an inner diameter of a work piece.