In the present paper, we discussed about a kinamatic design of a 3-5R translational parallel manipulator with a large utility workspace. We defined the utility workspace as a closed area, from any point to other points in which the mechanism can move without suffering from singularity and workspace boundary. A computational algorithm of the volume of the utility workspace was proposed. We investigated the utility workspace of 3-5R translational parallel mechanisms having RRRRR, RRRRR and RRRRR chains with consideration of actuation and constraint singularities. Based on the theoretical results, we designed and built a 3-RUU translational parallel manipulator (one of the 3- RRRRR manipulator) and we conducted experiments to examine its performance.