This paper presents a exact kinematics of the five degrees of freedom (DoF) surgical robot derived by the geometrical relation of the structure. In laparoscopic surgery, there are some advantages for patients because incision on abdominal wall is small. However, laparoscopic surgery is difficult for surgeons. Therefore, surgical robots with have been studied and developed to support surgeons. Conventional surgical robots have high position accuracy to realize delicate tasks. On the other hand, the transmission of force sensation is inadequate. Force sensation is important information for safer operation. Therefore, a five DoF haptic surgical robot is developed to transmit force sensation to the operator. The mechanism of five DoF surgical robot is suitable for implementing four-channel bilateral control which is one of the methods to transmit force sensation. Particularly, link mechanisms convert the motion of actuators into pitch motion and yaw motion of the end-effector. To control pitch motion and yaw motion precisely, the kinematics of the five DoF surgical robot is necessary. Besides, there is geometrical interference between pitch angle and yaw angle. In this paper, the exact kinematics for the pitch motion and yaw motion is derived. The validity of the kinematics is verified by step response. Then, the performance of four-channel bilateral control with the exact kinematics is verified by the experiments.