Kinematic and Jacobian analysis of a parallel-structured haptic interface for laparoscopy simulation

This paper reports a kinematic and Jacobian analysis of a haptic interface to simulate laparoscopic surgery. The haptic interface consists of a cylindrically-shaped moving platform and a dummy tool link. The moving platform, which determines the direction of the dummy tool, is fixed at the center and has 2 degree-of-freedom of pitch and yaw. The dummy tool has 3 degree-of-freedom which are translational and rotational movements and end effect operation. Direct kinematics of the haptic interface cannot be computed by using Denavit-Hartenberg model because two parallel links are connected with the moving platform. The developed method to solve the kinematics is deciding the direction vector of the dummy tool link. Six vectors are given to links and the relationship of the vectors is used to decide the direction of the dummy tool link. Finally a closed-form kinematics of the haptic interface is obtained by using the information of the vectors. Derivative of the closed-form kinematics can be utilized as Jacobian. Every components of Jacobian matrix also can be obtained as a closed-form expression. A virtual model of the haptic interface is used to verify the analytic result.