Kinematisk och dynamisk modellering av den haptiska enheten TAU i sex frihetsgrader
The thesis presents an optimally designed kinematic structure for a new 6-DOF haptic devicebased on TAU configuration. The configuration of the TAU-2 proposed by Suleman Khan andKjell Andersson [1] was modified and its mobility was verified by using Grübler criterion tohave a 6 DOF. Analytical kinematic models for the inverse and forward kinematics weredeveloped 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 payload index, were defined based on the singular values of the Jacobian matrix. The Jacobianmatrix was scaled to homogenize the physical units. The Jacobian matrix dependent on theposition and orientation of the end-effector gives local isotropy and pay load index, so globaldesign indices were defined, which represent the performance of the mechanism in the wholeworkspace. A multi-objective function was defined based on the minimum of the global designindices in order to find a set of optimal design parameters. Genetic algorithm (GA) was used foroptimization due to the nonlinearity of the multi-objective function. The optimal designparameters were obtained by minimizing the payload index while maximizing the volume indexand isotropy indices.A close form dynamic model was developed using Lagrange mechanics to describe the dynamicbehavior of the configuration. A trigonometric helical trajectory was developed in Cartesianspace for each degree of freedom for the moving platform while moving along the trajectory