In order to avoid the introduction of aberrations which make the image quality degrade, both alignment and shift of the optical components are strictly guaranteed in the optical system. The kinematic interface has a wonderful performance in repeatability and low level of contact stress. So it is widely used in optical system. The thirty meter telescope (TMT) is an Ritchey-Chirtien (R-C) optical system. The tertiary mirror is employed to bend the light to the instruments. According to the requirement of the accuracy assembly this mirror is frequently removed to clean and recoat. So a kinematic interface is designed to meet the requirement. The study on the kinematic principle in positioning the rigid body is introduced. Then a preliminary design is constructed according with the mechanical principles. Thus the Hertz contact theory and IBM wear theory are employed to check the contact stress and the wear situation. At last, a positioning accuracy simulation is carried out by the Monte-Carlo method. In addition, a simulation is carried out to analyze the support performance in Ansys software. And some parameters is optimized. The results show that both the contact stress and the wear situation can meet the requirements. In addition, the repeatability in three directions and the support performance are achieved.