This paper presents a novel approach to an online trajectory planning of robot arms for the interception of a fast-maneuvering object under torque and velocity constraints. A body axis is newly introduced as a trajectory-planning coordinate in order to meet the position and the velocity matching conditions for a smooth grasp of the fast-maneuvering object. Using the position of the object and the end-effector in the inertia axis, the acceleration commands are generated in the X-, Y-, and Z-directions of the body axis and the acceleration commands are modified considering the torque and the velocity constraints. The trajectory planning in the X-direction becomes the speed planning to achieve the maximum speed, whereas the trajectory planning in the Y- and Z-directions becomes the direction planning where a missile-guidance algorithm is employed to intercept the maneuvering object. Finally, the acceleration commands in the body axis are transformed into the angle commands of the end-effector in the joint axis, which is used as the actual trajectory commands in robot arms.