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This article presents a model of a novel 4-DOF kinematically redundant planar parallel grasping manipulator. As distinct from the traditional 4-DOF manipulator, the proposed design includes an extensible platform, which provides kinematic redundancy. This constructive feature is used for grasping. The article discusses the inverse and forward kinematics of the proposed manipulator. The inverse kinematics algorithm provides the analytical relations between the platform coordinates and the driven (controlled) coordinates. The forward kinematics algorithm allows defining different assembly modes of the manipulator. Both algorithms are demonstrated using numerical examples. The article discusses different designs of the manipulator in which its links are placed in one, two, or three layers. Based on these designs, we performed their workspace analyses.