Abstract: Two kinds of 2R1T parallel mechanisms (referred to as mechanisms A (Z3), B) are taken as research objects to analyze the influence of branch chain layout on the attitude capability of the mechanism. Based on the screw theory, the motion/force transfer indexes are used to solve ITI, OTI and GTI of the PMs. A numerical method is used to establish a good transmission orientational workspace (GTOW) model when given Z-direction value of the PMs. Firstly, the boundary orientational performance curves of the PMs are drawn with the empirical dimensions, and the orientational abilities of the PMs are compared. From the above conclusions, the orientation of the PM B is slightly better. Then, the maximum inscribed circle radius (referred to as κ_GTOC) of the performance boundary curve when the allowable transfer index η_LTI equals 0.7 is maximized as the optimization objective, the GTI and the PM’s structure parameter are coordinated as constraints, and the DE is used to obtain the optimal dimensional parameters of PMs. Finally, the boundary orientational performance curve is drawn with the optimal dimensional parameters. After optimized, the orientation of the PMs are increased by 2.65° and 2.04° respectively. According to the example of optimizing the orientational ability of the PMs, the orientational ability of the PM B is reduced by 0.15 compared with PM A, which indicates that the orientational abilities of the PMs are not much different, but the orientational ability is affected by the branch arrangement.