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Jacobian construction

If the analytic expression is known for equation (1), then the evaluation of the Jacobian could be done by straightforward differentiation. For example, equation (6) for a structure with 6 DOF in 6D Cartesian space (3D for position, 3D for rotation) - (Figure 2b) can be expressed as:

\begin{displaymath}[ \dot x, \dot y, \dot z, \dot \theta_x, \dot \theta_y, \dot ...
...eta_3, \dot \theta_4, \dot \theta_5, \dot \theta_6 ] \eqno (8) \end{displaymath}

If the analytic expression is unknown for equation (1), numerical construction for the Jacobian is used. The Jacobian is obtained column by column from the transformation matrices $A_i$ [Chi96].

Lukas Barinka 2002-03-21