Abstract: Research on kinematics of robot with passive wrists in minimally invasive surgery not only makes surgeons get Cartesian control mode in open surgery, but also lays the foundation for further research on control algorithm and trajectory planning. Taking the laparoscopic robot developed by Harbin Institute of Technology as an example, kinematics of robot is researched under minimally invasive environment. The position of incision point is influenced by diaphragm thickness and breath of patient, so a method of calculating incision position is given, position kinematics is presented by geometry and vector algebra method, velocity kinematics is solved through constraint conditions under minimally invasive environment. In order to verify the validity of algorithms, a series of experiments including inserting motion and rotation motion are performed, and the results show the validity of kinematics algorithms.

Key words: Kinematics, Laparoscopic robot, Minimally invasive technique, Velocity Jacobian matrix