This paper presents the dimensional synthesis of a 4 dofs (3T-1R) actuatedly redundant parallel manipulator (called ARROW V1) based on dual criteria related to rapidity and precision. The dynamical (rapidity) criterion is the worst isotropic linear acceleration starting from rest, and the precision related criterion is the worst translational resolution amplification factor. This latter amplification factor happens to be equal to the theoretical translational repeatability and accuracy amplification factors as well. Also, other kinetostatic and dynamic performances have been evaluated for the synthesized set of geometric parameters as to validate global performances. The results are quite interesting showing a highly performant parallel kinematic machine (PKM).