Multi-objective dimensional optimization of parallel kinematic manipulators (PKMs) remains a challenging and worthwhile research endeavor. This paper presents a straightforward and systematic methodology for implementing the structure optimization analysis of a 3-prismatic-universal-universal (PUU) PKM when simultaneously considering motion transmission, velocity transmission and acceleration transmission. Firstly, inspired by a planar four-bar linkage mechanism, the motion transmission index of the spatial parallel manipulator is based on transmission angle which is defined as the pressure angle amongst limbs. Then, the velocity transmission index and acceleration transmission index are derived through the corresponding kinematics model. The multi-objective dimensional optimization under specific constraints is carried out by the improved non-dominated sorting genetic algorithm (NSGA II), resulting in a set of Pareto optimal solutions. The final chosen solution shows that the manipulator with the optimized structure parameters can provide excellent motion, velocity and acceleration transmission properties.