Fixturing is an important requirement for many manufacturing and assembly operations. If flexible manufacturing and assembly system are to be truly flexible then the fixturing must also be flexible. A novel grasping strategy and gripper for fixturing in 3-D is presented for robotic assembly. The proposed fixture has three fingers, each equipped with a suction cup, to ease the grasping process and increase attaching flexibility. Using this method, the designed fixture is sufficiently general in order to fully grasp a variety of generic parts. To position suction cups, several linkage-based mechanisms are employed. Pneumatic cylinders and electrical motors are used as actuators to solve the space limitation and weight problem. Software has been developed to calculate the relative positions and angles in the mechanism as required for reconfiguration. A novel localization method is established to compensate for errors related to initial dislocation of the part due to low accuracy part bins from which parts are grasped. Several force and mechanism simulations are provided to verify the function and performance of the fixture.