The Jacobian and Inverse Jacobian are fundamental objects for calculating the velocity and inverse
velocity as shown in (15) and (16). We have used Maple as a math engine to find the
Jacobian. They start by defining the variable 
and 
. After
that the program starts to calculate 
's and then find the final transformation matrix
To calculate the Jacobian, 
's and 
's should be involved. Maple computes
them and store them as variables. By then all parameters required to evaluate the Jacobian are
ready. When one looks at the elements of the Jacobian one can see
amazing number of trigonomotric functions. When trying to pass the Jacobian to C compiler, the
compiler gets stuck, it can not cope with this number of sines and cosines. We let Maple
simplify the code. After that, maple has to calculate the inverse Jacobian. To pass the result
of the inverse Jacobian, it should be converted to an understandable and simplified C code.
This job has to be done for each one of the eight robot configurations listed in table 1.
Appendix B shows how to use Maple to calculate the Jacobian matrix for RRP:RRR