In this paper the workspace optimization of translational 3-UPU parallel platforms with prismatic and universal joint constraints is performed. The workspace is parameterized using two design parameters, which are the prismatic joint stroke and the difference between the distances of the center to one of the corners of the triangular plate of the base and of the moving platform. For a large range of values for these design parameters the workspace of the corresponding 3-UPU platforms is calculated. This workspace is called the constrained workspace. For each design of the constrained workspace, three performance indices are calculated: 1) the workspace volume; 2) the average of the inverse of the condition number; and 3) a global condition index which is a combination of the other two performance indices. Plots of each performance index as a function of the two design parameters are generated and optimal values for these design parameters are determined. Finally, for the optimal design, it is shown that by introducing limits to the angles of the universal joints axis, the isotropy of the parallel platform is improved.