As what have been acknowledged, the current patent of driving head of rotary wrenching tools structured for fitting varieties of work pieces in different shapes such as U.S. Pat. No. 3,354,757, U.S. Pat No. 3,657,516 and U.S. Pat. No. 5,388,486 is having a sleeve on the driving head, twelve equally spaced convexities are angularly implemented inside the sleeve, with which varieties of work pieces in different shapes such as gear type or hexagonal type work pieces can be fit into the sleeve and rotated. In spite of the advantages of the three patents mentioned above, there are shortcomings for the three patents on the action of rotating as following: although there are twelve convexities inside the sleeve to accommodate varieties of bolt in different shapes, but the possibility for the sleeve to work on hexagonal bolts is very high because hexagonal bolts is the most prevalent bolts in the market; when the sleeve rotates the hexagon bolt, the two of the twelve convexities contact with the side of the six hexagon bolt, which will produce a gap in-between, then instability and damage are to be created.