The co-rotating and reverse screw direction configurations between inner and outer screw pairs in the double-screw-pair transmission are analyzed and compared, its kinematics and dynamics are modeled, and different ways of axis force compensation are chosen according to their different configurations and their screw leads. It is shown that the ratio between the output swing angle and the piston movement is larger in the reverse screw direction configuration between inner and outer screw pairs, while the output torque is larger in the co-rotating screw direction configuration. Through output axis force compensation in the double-screw-pair swing rotary actuator, the linearity relationship between input pressure and output torque can be guaranteed, and transmission efficiency is improved. By using the reverse screw direction configuration between inner and outer screw pairs of the double-screw-pair rotary actuator driving model, the models of two kinds of underwater hydraulic manipulator elbows are established, one with axis force compensation and the other without axis force compensation. The kinematics and dynamics relations in the reverse screw direction configuration between inner and outer screw pairs are verified through the driving experiments of two kinds of manipulator elbows, and the comparison of the output torques shows that the one with axis force compensation has better transmission characters than the other one.