Our objective is to determine the minimum clamping force that keep the workpiece stable during the metal cutting process. In analyzing the stability of the workpiece, one usually proves that no instant center of motion can occur on the clamping plane. However, previous search algorithms for the instant center of motion either lack theoretical sufficiency or computational efficiency. This paper presents a new method derived from the correlation between cutting force and clamping moment. This method increases the search efficiency by pruning inadequate search directions. In addition, examples are provided to illustrate minimum clamping force analysis under different fixturing conditions.