In this paper the kinematic design of a 6-dof parallel robotic manipulator is analysed. Firstly, the condition number of the inverse kinematic jacobian is considered as the objective function, measuring the manipulator's dexterity and a genetic algorithm is used to solve the optimization problem. In a second approach, a neural network model of the analytical objective function is developed and subsequently used as the objective function in the genetic algorithm optimization search process. It is shown that the neuro-genetic algorithm can find close to optimal solutions for maximum dexterity, significantly reducing the computational burden. The sensitivity of the condition number in the robot's workspace is analysed and used to guide the designer in choosing the best structural configuration. Finally, a global optimization problem is also addressed.