The main goal of this paper is the design of 4PUS+1PS parallel manipulator, using an optimization problem that takes into accounts the characteristics of the workspace and dexterity. The optimization problem is formulated considering constraints on actuated and passive joint limits. A comparison between quantum particle swarm Optimization (QPSO) and PSO is developed. Two numerical examples are presented, which reveal the advantages of QPSO to PSO. Moreover, it is shown that by introducing the dexterity index as a quality measure throughout the workspace, the parallel manipulator is improved at the cost of a minor reduction in its workspace.