Kinematisk och dynamisk modellering av den haptiska enheten TAU i sex frihetsgrader

Sammanfattning: The thesis presents an optimally designed kinematic structure for a new 6-DOF haptic device based on TAU configuration. The configuration of the TAU-2 proposed by Suleman Khan and Kjell Andersson [1] was modified and its mobility was verified by using Grübler criterion to have a 6 DOF. Analytical kinematic models for the inverse and forward kinematics were developed for the haptic TAU configuration to determine a set of optimal design parameters. Kinematic performance indices such as volume of the workspace, kinematic isotropy and pay load index, were defined based on the singular values of the Jacobian matrix. The Jacobian matrix was scaled to homogenize the physical units. The Jacobian matrix dependent on the position and orientation of the end-effector gives local isotropy and pay load index, so global design indices were defined, which represent the performance of the mechanism in the whole workspace. A multi-objective function was defined based on the minimum of the global design indices in order to find a set of optimal design parameters. Genetic algorithm (GA) was used for optimization due to the nonlinearity of the multi-objective function. The optimal design parameters were obtained by minimizing the payload index while maximizing the volume index and isotropy indices. A close form dynamic model was developed using Lagrange mechanics to describe the dynamic behavior of the configuration. A trigonometric helical trajectory was developed in Cartesian space for each degree of freedom for the moving platform while moving along the trajectory