An upright chuck assembly includes a base having two elongate notches respectively defined in two sides thereof. A rotary device is connected to the base and includes a horizontal gear set and a vertical gear set which are engaged with the horizontal gear set in the body of the rotary device. An insertion extends from the horizontal gear set and is inserted into one of the adjustable members. The vertical gear set has a connection portion on the top thereof, and a T-wrench is mounted to the connection portion. The rotary device is cooperated with a vertical machine center.