**4.5.1 Optimization based on maximum workspace volume**

First we consider the volume of workspace as the objective function; namely,

*V\*=max(V)* 

*Subject to* 

$$1. \quad 1/\kappa(\mathbf{J}) \not\ge 0.01$$

$$0.01 < \frac{d}{\Delta q} < 0.15 \quad , \quad 0.01 < \frac{h}{\Delta q} < 0.15 \quad , \quad 0.35 < \frac{Q\_z}{\Delta q} < 0.55$$

The solution of this problem is given in Table 1. Moreover, the workspace for 0 and the conditioning index for 0 and *z*=0 are shown in Fig.5 and Fig.6, respectively. While the workspace size is acceptable, the manipulator suffers from a poor dexterity throughout its workspace.


Table 1. Optimization result for H4

As it is observed the GA reaches a convergence after 30 iterations as depicted in Fig. 7.
