Abstract: Based on the displacement manifold theory, the configuration synthesis of 3 T1 R parallel mechanism with fixed rotation axis and variable rotation axis was carried out. According to the general kinematics equation of spatial 4 R spherical mechanism, the characteristics of rotation axis of spherical 4 R mechanism with two fixed axes were analyzed. The characteristics of rotation axis of spherical 4 R mechanism with fixed axis rotation and variable axis rotation were analyzed. Through limit calculation, the two instantaneous continuous rotation axes of the connecting rod of the spherical 4 R mechanism with fixed rotation axis and variable rotation axis in the motion mode transformation configuration were analyzed. The results showed that the two instantaneous continuous rotation axes of this kind of mechanism did not coincide under the motion mode transformation configuration. According to the spherical mechanism with two motion modes of fixed rotation axis and variable rotation axis, the expression of connecting rod displacement manifold was established. The frame of the spherical mechanism was connected with three moving pairs, and a new 3 T1 R motion mode generator was obtained. Based on its displacement manifold, a 3 T1 R parallel mechanism with two motion modes was designed. Through the screw theory, the correctness of the degree of freedom and the selection of driving pair of the mechanism in the transformation of 3 T1 R motion mode with variable axis rotation and 3 T1 R motion mode with fixed axis rotation were verified. The results showed that the 3 T1 R parallel mechanism had two 3 T1 R motion modes: fixed rotation axis and variable rotation axis. Four drive pairs of four branch chains can realize the control of the mechanism under the above two modes. When the mechanism was in the transformation configuration of the two motion modes, an auxiliary drive pair needed to be added to realize the transformation of the two motion modes of the mechanism.