The development of robotic hand that can imitate human movements has always been an important research topic. In this paper, a linkage-driven underactuated three-finger hand is proposed to imitate the flexion/extension (f/e) and abduction/adduction (a/a) motions of human hand. The robotic hand has three identical underactuated fingers, each of which contains an underactuated planar linkage, a spherical four-bar mechanism, and a set of bevel gears. The spherical four-bar mechanism is designed to provide 2-degree-of-freedom actuation, driving the f/e and a/a motions of the proximal joint simultaneously. Based on screw theory, the kinematic model of the spherical mechanism is established, and the maximum available workspace index (MAW) of the spherical mechanism is proposed to evaluate the workspace with the same adduction and abduction angle ranges. The effects of the parameters of the spherical mechanism on the MAW and the transmission efficiency are obtained, and the parameters of the spherical mechanism are optimized. The optimization results show that the MAW of the spherical mechanism can be increased by up to 3.5 times. Finally, experiments are carried out to show the proposed robotic hand can perform simultaneous adaptive grasping and in-hand manipulation.