In previous studies on 4-DOF parallel mechanisms with four sub-chains, only symmetric arrangement of those four chains connected to the top plate was considered. Such symmetric shape sometimes falls into a sort of architetural singularity. This work demonstrates that an asymmetric placement of the four chains on the top platform is desired to minimize the effect of such architectural singularity. A new 4-DOF parallel mechanism exhibiting 4-DOF motion (3-DOF translational motion and one rotational motion) is examined as an exemplary device. This device consists of a base plate, an upper plate, and four hybrid subchains connecting those two plates together. The position analysis and kinematic modeling for this mechanism are performed, and an optimal design with respect to the workspace size and the kinematic isotropic characteristic is conducted. A set of offset angles on the top platform is found, which significantly minimizes the architectural singularity problem within the valid works...