Robotic manipulation has increasingly pursued human-like dexterous hands with many articulated degrees of freedom, offering rich manipulation capabilities at the cost of mechanical and control complexity. At the other extreme, parallel grippers are simple and robust, but provide little ability to manipulate an object after grasping it. Operating articulated objects such as threaded containers, manufacturing tools, and laboratory instruments often requires a second gripper, an external fixture, or coordinated arm motion. We introduce the Cartesian Hand, a 7-DoF end-effector that rethinks dexterous manipulation by combining independent grasping and relative manipulation within a single end-effector using only linear motion. Two independently actuated parallel grippers hold different parts of an object, while four translating fingertips generate relative motion between the grasped parts. Its configuration-independent fingertip kinematics allow manipulation to be composed from simple linear motion primitives. The Cartesian Hand is particularly suited to objects structured around common mechanisms such as threads, pivots, linear guides, plungers, and triggers. We demonstrate cap opening and closing, pipetting, pumping, two-handle manipulation, screwdriving, trigger actuation, and in-grasp reorientation across 35 objects spanning laboratory, manufacturing, and household settings. The same manipulation procedures transfer from a fixed-base robot arm to a humanoid, where we demonstrate bimanual laboratory manipulation using two Cartesian Hands. These results show that versatile in-hand manipulation capability can emerge from a mechanically simple architecture when independent grasping and relative motion are designed directly into the end-effector. We will open-source all software and hardware design. Our website is https://generalroboticslab.com/cartesian_handv1.

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