Three translational (3T) degree-of-freedom (DOF) parallel mechanism is widely used in the industrial field because of its compact structure and excellent dynamic performance. Combined with the 3T parallel mechanism studied at this stage, a novel 3T parallel mechanism is proposed. Firstly, the DOF of the mechanism is analyzed by using the screw theory. Secondly, the position, velocity, and singularity of the mechanism are analyzed, and the workspace of the mechanism is analyzed through the positive position solution. Then, the trajectory planning in joint space and coordinate space is completed, and a common mathematical model of grasping trajectory is established. Thirdly, the kinematics simulation analysis of the mechanism is carried out. Finally, the prototype platform was built and the grasping experiment was carried out, which verified the rationality of the mechanism design and the correctness of the theoretical analysis.