In this paper, an alternate passive leg structure is proposed for the Tricept machine tool to form a modified Tricept machine tool. The global stiffness of the modified Tricept machine tool is derived and compared with that of the Tricept machine tool. First, the configurations of the Tricept machine tool and the modified Tricept machine tool are introduced, respectively. Then, the global velocity equations are derived and the stiffness models of the two configurations are presented and analyzed. Finally, the advantages and disadvantages of the two types of passive leg structure are analyzed and discussed and stiffness simulations are conducted.