For smoothing the motion of a robot hand, a simple method for trajectory interpolation of the robot hand has been developed, in which successive straight line trajectories are connected continuously by parabolas. Only a linear interpolation function of computation is required for this method and it makes the computation time so short that the trajectory interpolation can be performed real time while the robot is in motion. Determination of a closed loop spatial mechanism with single mobility which is equivalent to the robot arm with a specified hand location is also described in the paper for the purpose of analyzing joint displacements of the robot arm.