**5. Conclusions**

414 Serial and Parallel Robot Manipulators – Kinematics, Dynamics, Control and Optimization

For the problem at hand one needs a good fitness function, because the optimization based on maximal workspace volume, decreases the performance indices and the optimization based on GDI decreases the workspace volume. Therefore, one can optimize the manipulator based on performance index that described in subsection 5.3. The optimization

Moreover, for different values of *wd*, the problem is solved and the GDI, SURI and the mixed performance index are calculated and plotted in Fig. 8. As the result, any value of *wd* greater than 0.74 leads to a limited workspace and for any values smaller than that has no substantial effects on GDI and the workspace. Therefore, it clearly shows that by introducing this measure, the performance of the manipulator can be improved at a minor

Fig. 7. Convergence of GA

cost its workspace volume.

**4.5.3 Optimization based on the mixed performance index** 

Fig. 8. GDI and SURI and Performance Index versus weight parameter

results for *wd*=0.25, 0.5, 0.75 are given in Table 3.

First, the forward and inverse kinematics of H4 parallel manipulator has been studied here, in which the former problem has leaded to a univariate polynomial of degree eight. Then, the optimal design of the manipulator has been addressed. Using genetic algorithm the manipulator has been optimized based on a mixed performance index that is a weighted sum of global conditioning index and its workspace volume. It has been shown that by introducing this measure, the parallel manipulator has been improved at minor cost of its workspace volume.
