According to the topology design method of parallel mechanism based on sub-kinematic-chain generating sub-workspace and its superposition principle, a pure three-translation parallel mechanism with symbolic positive solution and motion decoupling was designed. Through the topology structural analysis of the mechanism, it was found that the mechanism was composed of two sub-kinematic-chains, and the coupling degree of the mechanism was 0. Then, using the mechanism position analysis method based on topological characteristics, the forward and inverse position solutions of the mechanism were solved and verified. And it was found that the mechanism had the characteristics of partial motion decoupling and symbolic positive solution. Finally, the singular configuration of the parallel mechanism was analyzed by using the singular analysis method based on the sub-kinematic-chain element, and the regular and non-singular rectangular workspace of the parallel mechanism was solved. Using this singularity analysis method, all singular configurations in the sub-kinematic-chain can be found, and it was conducive to solving the regular workspace without singularity. The research result can provide a theoretical basis and specific method for the design of a class of parallel mechanisms with regular workspace, and it played a guiding role in the design of three-translation parallel mechanism based on the superposition principle of sub-workspace generated by sub-kinematic-chain, and provided an idea and method for singularity and workspace analysis of complex parallel mechanism with multiple sub-kinematic-chains.