Parameter determination and optimization play an important role for parallel kinematic machines since the machines properties depend significantly on an appropriate choice of the geometry. In this paper, the design of parallel machines is formulated in terms of a global constrained optimization problem, where the constraints are deduced from imperative process requirements e.g. size of the workspace and upper bounds on the kinematic dexterity. Furthermore, the total costs of the machine are proposed as objective function. It is shown, how this problem may be solved, applying interval analysis, and an implementation for parallel computation is introduced. Results for the parallel kinematic machine Linapod are presented.