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In order to solve the strong kinematics coupling problem of parallel mechanisms obtained by the normal type synthesis approach, a systematic method for structural synthesis of the uncoupled spatial translational parallel mechanisms (USTPM) was presented based on the actuation wrench screw theory. Firstly, mathematic model mapping the relationship between the inputs and the outputs of USTPM was set up. Secondly, both the actuation wrench screw and actuated twist screw’s forms of the kinematical chains were obtained according to the condition that the velocity Jacobian matrix was a diagonal one. Then the rules to determine the non-actuated screws of the limbs were established in terms of the reciprocal product principle. Both criterion and steps of the limb’s type synthesis were proposed as well. Finally, the mechanisms with the expected motion characteristics were designed by selection three limbs synthesized above to connect the platform and the base. Totally 60 symmetrical USTPMs were designed. Among them, 47 mechanisms were nonoverconstrained and 29 mechanisms were composed of the open single kinematic chains with idle joints. The Jacobian was a diagonal matrix of the synthesized parallel mechanisms. It was more interesting that some mechanisms’ Jacobian was the identical matrix, in which there existed one-to-one linear mapping relationship between the input velocities of the actuated joints and the output velocities of the moving platform for these mechanisms, and condition number of their Jacobians was equal to 1. So these mechanisms showed fully-isotropic throughout their whole workspace. Meanwhile, they performed very well with regard to motion and force transmission. This work contributed to enriching and improving the structural synthesis theory of the parallel mechanisms.