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For the needs of the mechanical components not limited by space when machines working in narrow spaces, according to the topology design theory and method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations, a set of 12 spatial single-loop two-translation PMs, each propelled by two actuated prismatic joints, was designed and the degrees of freedom of each PM were calculated. A comprehensive kinematic modeling effort was undertaken, focusing on eight select PM configurations. Through meticulous analysis and computation, the univariate eighth-degree polynomial equations (i.e., closed-form solution) were derived for each configuration. Symbolic inverse solutions were also derived respectively, Additionally, numerical examples were employed to validate the accuracy and efficacy of these solutions. Leveraging the differential evolution algorithm, an exhaustive effort was made to maximize the working space of the eight PM configurations under consideration. Through iterative refinement and optimization, the maximal operational envelopes of these PMs were meticulously determined, offering insights into their potential operational capabilities within varied working environments. Following a comprehensive comparative analysis of the maximal working spaces achieved by each PM configuration, two configurations boasting the largest working spaces were selected, which served as the foundational basis for subsequent endeavors, including the stiffness analysis, dynamic analysis and structural design of these PMs.