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There is a wide range of industrial application for the 4-DOF parallel mechanism (PM) which can achieve SCARA type output motion (i.e., three translations and one rotation). However, due to the constraints of kinematic chains, most of them have small rotational capacity and cannot meet the actual demand sometimes. A type of 3T1R PM which can realize full cycle rotary motion was proposed. Firstly, a two-dimensional moving unit which consisted of revolute joint only was constructed. According to the mechanisms and machine theory, modular principle of the pantograph mechanism for scaling two-dimensional planar graph was explained as the mechanism can be divided into three types of modules which were all derived from the two-dimensional moving unit. And then a 3T1R PM with four legs was designed by taking the obtained pantograph mechanisms as sub-chains. Secondly, the structure coupling-reducing optimization design for this PM was performed, whose POC and DOF were unchanged with lower coupling degree (k=1)．Finally, the modeling method and the numerical solutions for forward and inverse position equations of the PM were established based on ordered single-open-chain (SOC) units. The working space and the rotational ability of this parallel mechanism were obtained and the rotational capacity map was drawn by using the inverse position equations. According to the map, the range of workspace that can realize the full rotational capability was selected which can be treated as a theoretical basis for the design and applications for this mechanism.