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The Cartesian Hand: In-Hand Manipulation with All-Linear Fingers

Boxi Xia, Bokuan Li, Ryan Shin, Zijiang Yang, Jiaxun Liu, Boyuan Chen

arXiv:2609.25696v1cs.RO

TL;DR

Parallel grippers are simple but offer limited manipulation after grasping, while articulated-object tasks often require another gripper or external support. The Cartesian Hand combines independent grasps and relative motion in an all-linear end-effector, demonstrating manipulation across varied objects and robot embodiments.

  • Problem

    Parallel grippers provide limited post-grasp manipulation, and operating articulated objects often relies on a second gripper, external support, or coordinated arm motion.

    Source: §I · p. 1

  • Method

    The 7-DoF Cartesian Hand uses two independently actuated parallel grippers and four translating fingertips to grasp and move different parts using linear motion.

    Source: §I · p. 2, §III · p. 3

  • Results

    Across 35 objects, the hand demonstrates varied manipulation tasks, transfers procedures to a humanoid, and supports bimanual laboratory manipulation.

    Source: §I · p. 2

  • Takeaways & Limitations

    The results suggest versatile in-hand manipulation can emerge from a mechanically simple architecture combining independent grasping with relative motion.

    Source: §VI · p. 8

    The reported 350 trials were successful once configured; new objects within an established category required up to five setup trials to determine parameters.

    Source: §VI · p. 8

Abstract

from arXiv · show

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.

I. INTRODUCTION

The Cartesian Hand addresses the limited in-hand manipulation of parallel grippers through a mechanically simple, all-linear design with independent grasps and relative actuation. It targets articulated objects and demonstrates manipulation across 35 objects, transfer between robot embodiments, and bimanual use.

I. INTRODUCTION

  • Parallel grippers offer simplicity but limited post-grasp manipulation, so articulated-object tasks often require another gripper, environmental support, or arm re-grasping.More articulated hands provide richer motions but bring greater mechanical and control complexity.Source: §I · pp. 1–2
  • The 7-DoF Cartesian Hand combines two independently actuated grasps and relative manipulation using only linear motion.Four translating fingertips and coordinated linear motion primitives support grasping, translation, rotation, and relative manipulation.Source: §I · p. 2
  • Threads, pivots, linear guides, plungers, and triggers suit the hand because their mechanisms constrain motion between object parts.Repeated release, reset, and re-grasp can extend motion beyond an individual actuator’s travel.Source: §I · p. 2
  • Across 35 objects, the hand demonstrates diverse manipulation tasks, transfers procedures from a fixed-base robot to a humanoid, and supports bimanual laboratory manipulation.Demonstrations include pipetting, pumping, screwdriving, trigger actuation, and in-grasp reorientation.Source: §I · p. 2
  • The hand’s configuration-independent fingertip kinematics let coordinated linear actuation be composed from reusable motion primitives.These controls do not require extensive optimization or human motion tracking.Source: §I · p. 2

II. RELATED WORK

Prior work pursues in-hand dexterity through articulated fingers, augmented grippers, or environmental contacts. The Cartesian Hand instead uses translating fingertips and two independent grasps to actuate relative motion between parts of an articulated object.

II. RELATED WORK

  • Articulated hands achieve in-hand manipulation through coordinated contacts, while augmented grippers add mobility at the contact interface through belts, rollers, wheels, vibration, or compliance.The Cartesian Hand keeps contact surfaces passive and translates the fingertips themselves.Source: §II · p. 2
  • Unlike approaches that exploit gravity, arm motion, or environmental contacts, the Cartesian Hand directly grasps and actuates two parts within one end-effector.This reduces reliance on a second gripper, external fixtures, or environmental contacts for the opposing grasp.Source: §II · pp. 2–3
  • Because an object’s mechanism constrains motion between its parts, the same linear motions can operate objects built around threads, pivots, guides, plungers, and triggers.Fig. 2 depicts the two stacked grippers and their four sliding fingertips.Source: §II · p. 3, Figure 2 · p. 3

III. MECHANICAL DESIGN AND KINEMATICS

The Cartesian Hand combines two independently actuated grippers and translating fingertips in a 7-DoF, all-prismatic design. Its fixed-axis kinematics support a compact library of coordinated linear motions for in-hand manipulation.

Design and Actuation

  • Seven prismatic DoFs provide independent grasping at two locations, relative translation between the grippers, and fingertip motion within each grasp.The base and auxiliary grippers each have an opening/closing DoF and two independently translating fingertips; a seventh DoF changes the gripper separation.Source: §III · p. 3

Fingertip Kinematics

  • All actuators move along fixed Cartesian axes, and the fingertip velocity mapping remains full-rank and configuration-independent throughout the feasible workspace.The fingertip slides move along x, grippers open and close along y, and the auxiliary gripper translates along z.Source: §III · pp. 3–4

Design and Actuation

  • The assembled hand weighs 850 g, measures approximately 166 × 100 × 76 mm when closed, and uses joints with 52–65 mm travel.The fingertip slides travel 65 mm; gripper opening and inter-gripper separation each travel 52 mm.Source: §III · p. 3

Fingertip Kinematics

  • The linear joints give each finger an axis-aligned box workspace, with the auxiliary gripper gaining reach through inter-gripper translation.The base and auxiliary gripper workspaces meet at each gripper’s closing midplane.Source: Figure 3 · p. 4, §III · p. 4

Manipulation Primitives

  • The design groups motions into five reusable joint-action primitives and six compositions, forming a compact vocabulary for constructing manipulation procedures.The candidate actuation states are reduced by symmetry and by combining motions that produce the same functional interaction.Source: §III · pp. 4–5
  • Coordinated gripper closure establishes two grasps, while inter-gripper translation and fingertip motion produce pushing, pulling, pivoting, twisting, and squeeze-and-lift behaviors.The primitives can be sequenced for tasks such as multi-turn caps and syringes, whose mechanisms constrain relative motion between parts.Source: §III · p. 5

IV. CONTROL AND MANIPULATION PROCEDURES

Manipulation procedures combine position-controlled joint primitives with servo feedback to detect contact and adapt motions to object dimensions. Objects sharing an articulation reuse the same procedure with adjusted parameters.

Contact-Aware Joint Control

  • Contact is detected when commanded joint motion stays below a speed threshold for a set duration, after which the controller terminates or holds motion and saves the contact position.This lets grasping and contact-seeking primitives accommodate different object dimensions without specifying their geometry precisely.Source: §IV · p. 5
  • Contact-derived measurements such as object width or cap diameter are inferred during execution, while unobservable offsets such as relative part height are specified per object.Cap diameter estimates guide fingertip displacement and the number of re-grasp cycles for a requested rotation.Source: §IV · p. 5

Task Execution

  • Objects begin at known poses in a calibrated workstation, but the holder supplies no support or reaction force during manipulation and the arm remains stationary.The object is lifted from its holder after the initial grasp; subsequent manipulation occurs in hand.Source: §IV · p. 5
  • Objects with the same articulation use the same primitive procedure with different scalar parameters, and new-object adaptation required at most five setup trials in the experiments.Threaded objects use grasp, twist, release, and reset; two-handle mechanisms and plungers use relative translation; triggers use gripper closure and the object’s return mechanism.Source: §IV · p. 5

V. EXPERIMENTS

The experiments are organized around four questions about the Cartesian Hand’s primitive library, execution across object geometries, transfer between embodiments, and bimanual use.

Evaluation Questions

  • The evaluation asks whether a small set of linear primitives can operate a broad range of articulated objects.Source: §V · p. 5
  • It assesses how reliably procedures execute across objects with different geometries and whether those procedures transfer across robot embodiments.Source: §V · p. 5
  • The evaluation also asks whether two hands can compose their capabilities in a bimanual manipulation task.Source: §V · p. 5

A. Experimental Setup

The setup covers 35 objects across laboratory, manufacturing, and household settings, with trials conducted after grasping and lifting objects from their holders. Success is defined by completion of each task’s specified operation without manual intervention.

Experimental Setup

  • The 35-object set spans scientific laboratory, manufacturing, and household categories and includes threaded containers, pipettes, plungers, two-handle tools, screwdrivers, and triggers.Objects are grouped by manipulation type, including threaded rotation, pumping, pipetting, two-handle actuation, screwdriving, and trigger actuation.Source: A. Experimental Setup · p. 5, Figure 5 · p. 6
  • After an initial grasp at prescribed poses, objects were lifted from their holders and manipulated in hand without holder support or reaction force.Quantitative experiments used a Cartesian Hand mounted on a 7-DoF Franka Emika Panda, with the arm stationary during the procedure.Source: A. Experimental Setup · pp. 5–6
  • Each object received 10 trials from its prescribed initial configuration using the same parameters, with success requiring task completion without manual intervention.Completion criteria varied by task, and failure to establish or maintain the required grasp counted as unsuccessful.Source: A. Experimental Setup · p. 6

B. Manipulation Across Objects and Tasks

The Cartesian Hand applies a shared library of linear motion primitives across diverse object mechanisms and task categories. It achieved repeatable manipulation across the evaluated objects and also supported bimanual liquid transfer on a humanoid.

B. Manipulation Across Objects and Tasks

  • The same primitive library supported threaded closures, syringes, pumps, two-handle tools, triggers, pipettes, and repeated screwdriving motions.Twist–translate procedures handled bottles, tubes, a marker, a glue stick, and a light bulb; relative translation operated syringes, pumps, and two-handle tools.Source: B. Manipulation Across Objects and Tasks · p. 6
  • A humanoid used two Cartesian Hands to open a centrifuge tube with one hand and dispense pipette liquid with the other.The tube-holding hand clamped the body and twisted off the cap; the other hand pipetted into the open tube.Source: Figure 7 · p. 7
  • The object set spans 35 objects, three domains, and seven task categories.Source: Table II · p. 7
  • 350 trials across 35 objects were completed successfully, with 10 trials per object.Given prescribed initial object poses, the procedures were highly repeatable across trials.Source: B. Manipulation Across Objects and Tasks · pp. 6–7
  • Grasping, contact, and relative motion produced both translational and rotational manipulation across different object mechanisms.A continuous sequence removed a threaded cap, actuated a pipette, and pulled a spray-bottle trigger using different axes and primitive combinations.Source: B. Manipulation Across Objects and Tasks · p. 7

C. Reuse Across Objects

Manipulation procedures were reused within object categories by adjusting scalar parameters rather than changing the primitive sequence. New objects required at most five setup trials to identify suitable parameters.

C. Reuse Across Objects

  • New objects across the evaluated categories required at most five setup trials to identify suitable parameters.The procedure and primitive sequence were established on a representative object, then retained for other objects in the category.Source: C. Reuse Across Objects · p. 7
  • Contact during execution supplied some parameters, while offsets and relative heights that could not be inferred from contact were specified during setup.For threaded caps, final jaw position estimated cap diameter and informed fingertip motion and repeated-stroke count; gripper closure similarly provided object width.Source: C. Reuse Across Objects · p. 7
  • New objects required parameter adjustment rather than changes to the primitive sequence, controller, or hand mechanism.Adjusted scalar parameters included grasp height, depth offset, stroke distance, force limit, and motion range.Source: C. Reuse Across Objects · p. 7

D. Humanoid Deployment and Bimanual Manipulation

The manipulation procedures transferred to a humanoid with the same hand hardware and primitives, adapting only robot-specific approach motion and grasp pose. Two Cartesian Hands also composed their single-hand procedures in a bimanual liquid-transfer demonstration.

D. Humanoid Deployment and Bimanual Manipulation

  • On the humanoid, the hand hardware, primitive definitions, and manipulation procedures remained unchanged; only approach motion and grasp pose were adapted.The same hand was mounted on the Duke Humanoid V2 for a subset of tasks demonstrated on the Franka platform.Source: D. Humanoid Deployment and Bimanual… · p. 7
  • Two Cartesian Hands demonstrated bimanual liquid transfer while each independently manipulated its own object.One hand opened a centrifuge tube by holding its body and twisting the cap; the other operated a micropipette, while the arms positioned tube and pipette.Source: D. Humanoid Deployment and Bimanual… · p. 8

VI. CONCLUSIONS, LIMITATIONS, AND FUTURE WORK

The Cartesian Hand combines two independent grasps with relative manipulation through an all-linear 7-DoF design. It completed configured trials across 35 objects and demonstrated reuse on a humanoid, while its current scope assumes structured objects and prescribed initial poses.

VI. CONCLUSIONS, LIMITATIONS, AND FUTURE WORK

  • The hand completed all 350 configured evaluation trials across 35 laboratory, manufacturing, and household objects.New objects in an established manipulation category required at most five setup trials, and procedures were also applied on a humanoid in a bimanual task.Source: §VI · p. 8
  • The current system is designed for structured mechanisms and experiments assumed prescribed initial object poses, using joint feedback without directly observing pose, contact location, or force.Its strongest capabilities arise when threads, pivots, linear guides, plungers, or triggers constrain relative motion between object parts.Source: §VI · p. 8
  • The results suggest that greater robotic dexterity need not require greater mechanical articulation.The hand combines independent grasping with simple relative motions to produce dexterous in-hand manipulation from directly controlled linear primitives.Source: §VI · p. 8
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