Series elastic devices are widely used in driving joints of exoskeleton robots, because they are conducive to the soft start of motors under heavy loads. Aiming at the problems of the transmission torque fluctuation caused by the change of the rotation stiffness of the rotating series elastic device, and the transmission shock during the transition between the elastic transmission and the rigid transmission, an involute tooth surface elastic device was proposed. Firstly, the characteristic that the involute tooth profile transmission would not change due to the deviation of the axis center can make a smooth transition when the elastic-rigid transmission was converted. Secondly, the transmission dynamics model of the involute tooth surface elastic device was established, and the elastic-rigid transmission process of the device was mechanically analyzed. By optimizing the installation inclination angle parameters of the elastic device, the minimum change rate of the rotational stiffness of the transmission part was 0.11757, and torque fluctuation in the elastic transmission process was effectively controlled. Then, under the optimal installation inclination angle (π/4±1.33785rad) model, the dynamic simulation of the transmission process and the mesh process finite element simulation were carried out to analyze the effect of the axis assembly deviation on the sliding rate of the involute tooth mesh and the contact surface joint impact. Finally, the device was verified by the lower limb exoskeleton drive joint engineering verification and the transmission static characteristics test. The results showed that the axis deviation would cause the torque to increase sharply when the contact surface was engaged. Compared with the flat rectangular elastic device, the torque excitation value was reduced by 43.55% on average when the axis deviation was within 0.05mm (the maximum involute tooth surface meshing sliding ratio was 0.0065).