At present, the installation of steel arch during the construction of tunnel boring machine (TBM) is completed by manual operation, and the working environment is very harsh, thus leads to the problems of low support efficiency, high labor intensity and high construction risk. Therefore, the authors and their team had designed a steel arch rapid-looping installation mechanism to replace manual operation. As the core part of the looping installation mechanism that directly contacts with the steel arch, the grasping module demands sufficient transmission performance to meet the requirements of clamping operation. Based on the screw theory, the paper established a kinematics model of the grasping module, and deduced the virtual coefficient between the input screw and the output screw. Then, the transmission performance of the grasping module was obtained and its transmission index was proposed. On this basis, the size parameter optimization model of grasping module was established. According to the actual grasping requirements of the steel arch looping parts, the optimization results of each size parameter were obtained as follows: the initial included angle between the jaw and the connecting rod is α = 88°, the initial position of the guide rod is l_FJ= 170 mm, and the movement range of the guide rod is 0 ~ 63 mm. Using ADAMS software to analyze the posture change process of the grasping module from clamping to opening, it comes to the conclusion that, the distance between the ends of the jaws gradually increases from 50.0 mm to 234.6 mm, which meets the requirements of grasping space; the output torque increases first and then decreases. When the jaw is fully opened, the minimum torque is 21.23 N·m, which meets the output torque demand. Finally, the steel arch looping installation experiment shows that, the difference between the measured values and the calculated model is only 4.5 mm, which proves the correctness of the model; the whole looping installation time of the steel arch is 8.6 min. As compared with the traditional manual operation, the operation efficiency of the steel arch looping mechanism is improved by 20% ~ 70%.