The basic parallel robotics principle of defining kinematic constraints as vector loops is transferred from the general 3T3R case to the 3T2R case by applying a nonlinear Tait-Bryan-angle rotation constraint using the intrinsic Z-Y′-X′′ convention. This presents an alternative way to the deduction of differential inverse kinematics by the theory of linear transformations. The resulting formulation is used in a permutational combined structural and dimensional synthesis. The modular approach allows to combine databases of serial and parallel robots without manual intervention. The validation shows the reproducibility of existing kinematic structures using the new kinematic formulation. The optimization scheme allows to obtain suitably dimensioned symmetric 3T2R parallel robots for a given task.