In this research, the concept of the kinematic roll center is reviewed from the viewpoint of three-dimensional spatial kinematics. The theory of screws, which is widely used in spatial kinematics and robotics, is used to prove the validity of the conventional planar methods for finding the roll center in an initial symmetric vehicle position. The kinematic roll axis, which is referred to as the roll twist axis in this paper, is defined as the instantaneous screw axis of the vehicle body in roll motion with respect to the ground, and a three-dimensional method to determine the roll twist axis of a full-vehicle model in an initial symmetric position is introduced. The proposed method is based on screw theory, which relates the kinematics of a full-vehicle model to the statics of the full-vehicle model using the concepts of screws, twists, wrenches, the rate of working, and the reciprocity of screws. The results of the proposed three-dimensional method are compared with those of the conventional planar methods, and it is found that the conventional methods are valid under the assumption that the vehicle is in a symmetric situation.