This paper presents the design of an underactuated robotic arm for capturing moving targets with an impact-absorbing capability. The arm consists of three joints (a base joint (BJ), a medial joint (MJ), and a distal joint (DJ)) that are driven by two actuators. A one-input dual-output planetary gear (PG) system, in which neither the ring gear nor the planetary carrier is fixed, is employed to distribute the driving torque between the MJ and DJ. As is well known, an underactuated arm may exhibit unstable grasping performance such that the arm loses contact with the target in certain grasping postures. Therefore, a method is presented for analyzing the equilibrium contact force and the relative movement trend between the target and the arm to determine the work space in which stable grasping is possible. The structural configuration parameters, such as the length ratios among the three beams and the reduction ratio of the PG system, were optimized to maximize the grasp stability work space. Subsequently, a prototype was designed and fabricated based on these optimized parameters. Experiments indicate that this arm design can effectively reduce the peak torque on the joints when grasping a moving target.