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Anthropomimetic Soft Robotic Forearm with Independently Articulated Carpal Bones Enabling Human-Like Adaptive Stiffness Modulability

Yoshinobu Obata, Yinlai Jiang, Hiroshi Yokoi, Shunta Togo

arXiv:2609.29176v1cs.RO

TL;DR

The morphological factors underlying human wrist stiffness modulation remain unclear despite evidence that muscle co-contraction can reorient wrist stiffness. This study compares carpal configurations and activation patterns using an anthropomimetic forearm, finding human-like stiffness modulation with the normal skeleton and opposing muscle-coupling patterns at the proximal carpal row.

  • Problem

    Although muscle co-contraction can reorient human wrist stiffness, carpal morphology’s contribution had not been quantitatively verified.

    Source: §1.1 · p. 3, §1.2.2 · p. 4

  • Method

    The study used an anthropomimetic forearm to compare wrist stiffness across skeletal morphologies and muscle activation patterns.

    Source: §2.4 · p. 8

  • Results

    The normal skeleton reproduced human-like stiffness modulation, and wrist and finger muscles produced opposing inter-carpal coupling patterns, significantly at the proximal row.

    Source: §5 · p. 19

  • Takeaways & Limitations

    Carpal morphology, including the capacity for differential proximal-row motion, is a key factor in adaptive wrist stiffness modulation.

    Source: §4.2 · p. 18, §5 · p. 19

    Measurements were quasi-static and came from a single prototype, leaving dynamic behavior and inter-build variability unevaluated.

    Source: §4.4 · p. 18

Abstract

from arXiv · show

The human wrist exhibits adaptive stiffness modulability: joint stiffness anisotropy can be actively regulated through muscle co-contraction. This functionality is essential for stable manipulation, yet the underlying morphological factors remain unclear. To identify these factors, we developed an anatomically accurate anthropomimetic soft robotic forearm comprising eight independently movable carpal bones interconnected by ligaments, 22 actuated muscles, and compliant fingertips. We measured wrist joint stiffness under four muscle activation patterns across three skeletal configurations: anatomically normal carpal bones, a fused proximal carpal row, and a geometric ellipsoidal skeleton. The stiffness ellipse exhibited low stiffness along the dart-throwing motion (DTM) direction when finger muscles were activated, but high stiffness along the same direction when wrist and finger muscles were activated simultaneously. These results agree with previously reported human measurements, demonstrating that precise anatomical replication reproduces human-like stiffness modulability. Fusing the proximal carpal row eliminated the low DTM-direction stiffness under finger muscle activation, while the geometric ellipsoidal skeleton showed poor stiffness ellipse reorientation across all conditions. Carpal bone motion analysis revealed significantly opposing coupling patterns between wrist and finger muscles at the proximal carpal row, accompanied by a consistent but non-significant trend at the midcarpal joint, providing a mechanical explanation for this modulation. These findings demonstrate that carpal bone morphology plays a dominant role in human wrist stiffness modulation and provide design principles for humanoid robot wrists.

1 Introduction

The human wrist can reorient anisotropic stiffness through muscle co-contraction, but the carpal morphology behind this capability has not been quantitatively established. This study uses an anthropomimetic forearm and comparative skeletal experiments to investigate that gap.

1.1 Background

  • Human wrist stiffness is anisotropic, with its minor axis aligned to dart-throwing motion (DTM), and muscle co-contraction can reorient the stiffness ellipse.Low DTM-direction stiffness is associated with grasping, while the ellipse can rotate to increase DTM stiffness against disturbances.Source: §1.1 · p. 3

1.2.1 Wrist Joint Stiffness in Humans

  • Human measurements found the stiffness ellipse’s minor axis aligned with DTM, but could not establish the morphological mechanism because skeletal structure cannot be experimentally altered.A cited simulation suggested co-contraction can modulate stiffness orientation, but consolidated the carpal bones into one rigid body.Source: §1.2.1 · pp. 3–4

1.2.2 Biomimetic Wrist Robots

  • Existing biomimetic wrists simplified or consolidated carpal bones, while the authors’ earlier prototype lacked flexing fingers and had actuator-control limits.These constraints made quantitative verification of stiffness modulation during grasping difficult.Source: §1.2.2 · p. 4
  • Consequently, carpal morphology’s contribution to adaptive stiffness modulation had not been quantitatively verified.The study targets the unresolved contribution of carpal structure and joint-surface geometry, as well as muscle arrangement.Source: §1.2.2 · p. 4, §1.3 · p. 4

1.3 Research Purpose

  • The study extends an earlier forearm robot with independently movable carpal bones, 22 actuated muscles, articulated fingers, and compliant fingertips.Comparative experiments vary skeletal morphology and muscle activation to evaluate morphological factors in stiffness modulation.Source: §1.3 · p. 4

2 Materials and Methods

The methods combine an anatomically based forearm robot with controlled comparisons of skeletal morphology and muscle activation. Wrist deflections are measured across directions and summarized as stiffness ellipses.

2.1 System Overview

  • The forearm reproduces 28 bones actuated by 22 servo motors and can grasp objects while actuating its wrist.The system includes eight carpal bones, five metacarpals, fourteen finger phalanges, the radius, and the ulna.Source: §2.1 · p. 5

2.2 Wrist and Forearm Design

  • Carpal ligaments use polyethylene wire, while tendon-driven muscles route through PTFE sheaths to anatomically appropriate insertion sites.The design also implements the TFCC with four radioulnar ligaments and a TPU-printed fibrocartilage disc.Source: §2.2 · pp. 5, 8

2.3 Finger Design and Soft Fingertips

  • The fingers include three intrinsic thumb muscles for opposition and dual-layer elastic fingertips designed for stiffness experiments during grasping.The fingertips combine a hard silicone outer layer with a soft inner layer and an integrated fingernail.Source: §2.3 · p. 8

2.4 Wrist Stiffness Measurement

  • Stiffness was compared across three skeletal types and four activation patterns while current-controlled motors generated identical 0.6 N muscle tension.Uniform tension was used to isolate skeletal morphology from differences in muscle force distribution.Source: §2.4 · p. 8

2.4.1 Comparison Skeletons

  • The comparison used an anatomically normal skeleton, a fused proximal carpal row, and a geometric ellipsoidal skeleton.The fused and ellipsoidal designs share a joint-axis count, allowing the comparison to test whether axis count or morphology better accounts for stiffness differences.Source: §2.4.1 · pp. 8–9

2.4.2 Experimental Setup

  • A force gauge deflected a disc attached to the proximal phalanges, while motion capture tracked the force-gauge plate in wrist-centered coordinates.The coordinate system places its origin at the midcarpal joint, with X pointing palmarly and Y radially.Source: §2.4.2 · pp. 9–10

2.4.3 Experimental Procedure

  • Four activation patterns—relaxed, wrist muscles, finger muscles, and combined—were tested at 12 loading directions, with eight trials per condition and direction.The plate was pushed to 3 mm displacement at each direction.Source: §2.4.3 · p. 10

2.4.4 Analysis Method

  • Stiffness was calculated from force and displacement, then directional means were fitted as ellipses; a stratified permutation test assessed activation-related reorientation.Negative values and values below 5 N/m were excluded before ellipse fitting.Source: §2.4.4 · p. 10

2.5 Carpal Bone Motion Measurement

Carpal bone motion was measured during loading in the DTM direction to examine the mechanical basis of stiffness differences across conditions. Elevated marker pins enabled capture of small relative motions among selected carpal bones.

2.5 Carpal Bone Motion Measurement

  • The motion measurements targeted the mechanical basis of stiffness differences across skeleton types and muscle activation patterns.Relative carpal motion was measured during DTM-direction loading.Source: §2.5 · p. 11
  • Pins inserted into the scaphoid, capitate, and lunate elevated markers above the bone surface to improve capture of their small relative displacements and rotations.Loading was applied at 330°, the direction with the largest stiffness variation among conditions.Source: §2.5 · p. 11, Figure 7 · p. 11
  • Three-dimensional relative displacement and rotation were recorded during slow plate loading for 20 repetitions per condition under wrist, finger, and combined muscle activation.The relaxed condition was not included in this motion-measurement protocol.Source: §2.5 · p. 11

3 Results

In the normal skeleton, muscle activation reoriented wrist stiffness so resistance along the dart-throwing motion (DTM) was low with finger activation and high with combined activation. Changing carpal morphology reduced anisotropy or stiffness-ellipse reorientation, while carpal motion varied with activation, especially at the proximal row.

3.1 Wrist Stiffness for Normal Skeleton

  • The normal skeleton’s minor stiffness axis aligned with DTM under finger activation, while combined activation aligned its major axis with DTM, indicating a reorientation toward higher resistance.The measured axis shift was unlikely to arise from chance alone (permutation test, p = 0.0038).Source: Table 3 · p. 11, Figure 8 · p. 12, §3.1 · p. 13

3.2 Comparison of Skeletal Configurations

  • Kmin rose from 80.1 to 149.5 N/m under finger activation after proximal-row fusion, which removed the normal skeleton’s low-DTM stiffness and reduced anisotropy.The fused skeleton’s eccentricity fell to 0.186 under finger activation.Source: §3.2 · pp. 13–14, Table 4 · p. 13
  • The geometric ellipsoidal skeleton barely reoriented across activation conditions and had the highest absolute stiffness, although its ellipse scale is not directly comparable in Fig. 8.Its major-axis stiffness exceeded that of the normal and fused skeletons in every activation condition.Source: Figure 8 · p. 12, Table 5 · p. 13, §3.2 · p. 14

3.3 Carpal Bone Motion

  • Proximal-row translation peaked under wrist activation and ranked inversely with wrist stiffness, consistent with an inverse compliance–stiffness relationship.Translation under wrist activation significantly exceeded finger and combined activation.Source: §3.3 · p. 14
  • Proximal-row rotation differed between wrist and finger activation, while midcarpal rotation showed the numerically opposite but nonsignificant pattern; combined activation co-stiffened both joints.The combined condition produced the highest wrist stiffness, significantly exceeding wrist-muscle activation alone (p = 0.0016).Source: §3.3 · pp. 14, 16, Figure 9 · p. 15

4 Discussion

The anatomically normal skeleton reproduced human-like stiffness modulation under uniform muscle activation, while comparisons and carpal-motion measurements implicate carpal morphology and muscle arrangement in that behavior. The discussion identifies three morphological design factors and notes that the study tested quasi-static behavior in one prototype.

4.1 Validation and Consistency Across Skeletons

  • The normal skeleton reproduced human-like stiffness modulation under uniform activation, consistent with prior human measurements and predicted stiffness-ellipse reorientation.The measurements used identical muscle tension rather than differential force tuning.Source: §4.1 · p. 16

4.2 Mechanistic Role of Carpal Morphology

  • Opposing wrist- and finger-muscle compression pathways shift proximal-row coupling, while combined activation co-stiffens the wrist and reorients its stiffness ellipse.Proximal-row changes were significant; accompanying midcarpal changes were directionally consistent but non-significant, and the robotic measurements support prior biomechanical theories of differential carpal rotation.Source: §4.2 · pp. 16–17, Figure 10 · p. 17
  • Equal joint-axis counts did not predict equivalent modulation: fusion removes differential rotation, while symmetric ellipsoidal surfaces distribute forces isotropically.The normal proximal row resembles a consolidated unit under wrist and combined activation but differentiates under finger activation; its retained translation also distinguishes it from the fused row.Source: §4.2 · pp. 16, 18

4.3 Summary of Morphological Factors

  • The proposed design factors are independently movable proximal carpal bones, orthogonal wrist- and finger-muscle routing, and asymmetric convex-concave joint surfaces.The authors propose that these principles can produce task-appropriate stiffness responses with reduced control burden in humanoid wrists.Source: §4.3 · p. 18

4.4 Limitations of the Present Study

  • The study measured stiffness quasi-statically in a single prototype, leaving dynamic manipulation behavior and variability across builds unevaluated.The authors identify inertial or impact loading and between-build reproducibility as areas for future investigation.Source: §4.4 · p. 18

5 Conclusion

The study concludes that the normal robotic forearm reproduced human-like adaptive stiffness modulation and that carpal morphology helps explain the differences between skeletal configurations. Future work will test dynamic tasks, varied finger use, and simplified humanoid wrist designs.

5 Conclusion

  • The normal skeleton reproduced human-like adaptive stiffness modulation, while fused and geometric ellipsoidal skeletons showed impaired modulability.Carpal-motion analysis found opposing wrist- and finger-muscle coupling at the proximal row, significant there and a non-significant trend at the midcarpal joint.Source: §5 · p. 19
  • The identified morphological factors are independent proximal carpal degrees of freedom, orthogonal muscle arrangement, and asymmetric convex-concave joint surfaces.Source: §5 · p. 19
  • Future work will examine dynamic manipulation, diverse finger-use conditions, and simplified humanoid wrists incorporating the identified principles.Source: §5 · p. 19

Statements and Declarations

The statements report no required ethical approval, no declared conflicts of interest, and partial JSPS KAKENHI support. Study materials and supplementary notes are publicly available.

Ethical Considerations

  • Ethical approval was not required because the study involved no human participants, human data, human tissue, or animals.Source: Ethical Considerations · p. 19

Declaration of Conflicting Interest

Funding Statement

Data Availability

  • Publicly available materials include CAD and printable files, analysis and control code, and supplementary videos and notes.The repository also provides source data and files for the assembly jigs and fingertip casting procedure.Source: Data Availability · p. 20

Supplementary Material

The supplementary-material section contains the paper title and author names. The title identifies the work as a soft robotic forearm study focused on articulated carpal bones and adaptive stiffness.

Supplementary Material

S1 Jig-Based Assembly of the Skeleton and Ligaments

The assembly uses CAD-defined attachment geometry and dedicated jigs to make ligament placement, skeletal arrangement, and resting lengths reproducible between builds. Ligament lengths are set at target wrist angles to produce a designed passive range of motion.

S1 Jig-Based Assembly of the Skeleton and Ligaments

  • Dedicated jigs make ligament arrangement and resting lengths reproducible, reducing build-to-build variability that could otherwise confound morphological effects.The jigs were designed alongside the bone models and printed from the same photocurable resin.Source: S1 Jig-Based Assembly of the Skeleton… · p. 23

S1.1 Bone Models and Ligament Attachment Holes

S1.2 Chain-Knitted Artificial Ligaments

S1.3 Carpal Bone Holding Jig

  • Negative-cavity holding jigs seat the carpal bones, radius, and ulna so their spacing and orientation are fixed during ligament fixation.Palmar and dorsal jigs support fixing ligaments on the opposite side of the skeleton.Source: S1.3 Carpal Bone Holding Jig · p. 25, Figure S3 · p. 25

S1.4 Ligament Length Setting Jig

  • Ligaments are fixed just taut at target maximum wrist angles, making passive range of motion a designed quantity rather than a manual-adjustment outcome.A jig locks the radius and ulna at prescribed flexion–extension and radial–ulnar deviation angles; the target angles come from Japanese population mean values.Source: S1.4 Ligament Length Setting Jig · pp. 25–26, Figure S4 · p. 26

S1.5 Finger Joints

  • Finger-joint collateral ligaments are fixed with a joint-angle jig at the mean angle for a Japanese population.An elastic urethane film joint capsule is wrapped around each interphalangeal and metacarpophalangeal joint.Source: S1.5 Finger Joints · p. 26

S1.6 Assembly Sequence

  • The assembly sequence proceeds from printing bones and knitting ligaments to jig-based fixation, finger assembly, and tendon routing.The ligament-length jig is used to set each ligament just taut at the target maximum angle.Source: S1.6 Assembly Sequence · p. 26

S2 Fabrication of the Dual-Layer Elastic Fingertips

The compliant fingertips combine a hard skin layer with a soft subcutaneous layer, cast around the printed distal phalanx. A two-part mould sets the skin thickness, and the fingertip radius is based on Japanese adult male distal phalanx width.

S2 Fabrication of the Dual-Layer Elastic Fingertips

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