The derivative of the Jacobian is required to calculate the acceleration as indicated in (16). We
have to derive Jacobians for t as an exterior derivative. Unfortunately Maple does not do this
job, but Mathematica does. Thus we convert the output of Maple to be
understandable as an input for Mathematica. Then Mathematica differentiates the Jacobian
and gets the output as a collection of sines and cosines. Mathematica can do a simple
conversion to C code but this would be not workable here because C compiler can accept
limited number of functions to be compiled in the same file. We have to convert the output of
Mathematica to be an understandable input for Maple and let Maple do the simplification.
Finally, a simplified C-code for the derivative of the Jacobian is found. This procedure is
used for each of the eight robot configurations. The derivative will be also
required to evaluate acceleration and inverse acceleration kinematics as shown in
(17) and (18). Appendix C shows the derivative for RRP:RRR manipulator.
The two examples mentioned above show how tough in general it is to find closed form solutions, but by playing around with different tools, it is possible. We keep doing this until we find final closed form solutions for all configurations of a 6 - DOF robot including a spherical wrist. This package is supported with a 3 - D & 2 - D graphical monitoring system in addition to supporting real time control and simulation.
Figure 7: Monitoring Menu for SIR-1 Robot
Figure 8: The interface window for the PID controller simulator
Figure 7 shows the monitoring
system for SIR-1 robot as an example. The monitoring will be supported with a controller and a
simulator. Figure 8 shows the interface window for a PID controller
simulator.