Two 3-DOF parallel mechanisms, a translational mechanism and a spherical mechanism, are analyzed. Each of two mechanisms commonly possesses three UPS serial sub-chains, and an additional passive 3-DOF PPP-type serial sub-chain and a passive 3-DOF RRR-type serial sub-chain are incorporated for the translational device and the rotational device, respectively. Such additional passive serial sub-chains act as constraints to restrict the output motion of the mechanism either in a 3-DOF translational space or in a 3-DOF spherical space. The position solutions of the proposed mechanisms and their first-order kinematic models are derived. Then their workspaces and kinematic characteristics are examined via the kinematic isotropic index