AN ENCHANCED KINEMATIC MODEL OF THE HUMAN THUMB

FOR AN ARTIFICIAL HAND

Marc Franke and Martin Bogdan

Department of Computer Engineering, Institute for Computer Science

University of Leipzig, Johannisgasse 26, Leipzig, Germany

Keywords: Thumb, Motion, Scaphoid-Trapezium-Trapezoid, Joint, Workspace, Prosthetic hand.

Abstract:

Hand prostheses need to be lightweight, robust and forceful and should replace the function and range of

performance of the human hand in the best possible way. Furthermore, their look and appearance should turn

up as naturally as possible. The prostheses and anthropomorphic robot hands known today often lack one or

more of those aspects. We assume that the kinematic function of the thumb is additionally supported by the

kinematic function of the STT (Scaphoid-Trapezium-Trapezoid) joint, which builds the radial carpal column.

Our study is based on a previous work by Essers (Essers, 2006) determining the speciﬁc movements of the

STT joints. In this study, these results were combined with a kinematic 3D model of the human hand with

focus on the kinematic of the radial carpal column. We set up a kinematic chain of the radial carpal column

and the thumb bones to analyse the data gained from the measured movements. The simulations revealed,

that the joint movement of the STT joint supports up to 1/3 of the motion range of the adduction, abduction,

ﬂexion and extension. Based on these results, we integrated the previous ﬁndings into a real kinematic model

of the human thumb.

1 INTRODUCTION

The opposability and circumduction of the thumb is

in medical-anatomical literature usually contributed

to the biomechanical function of the CMC (Car-

pometacarpal) joint between the trapezium and the

1st metacarpal. The CMC joint of the thumb en-

joys great freedom of movement due to its saddle-

shaped articular surfaces. It’s movements are ﬂex-

ion and extension, abduction and adduction, prona-

tion and supination. Hence, previous robot hands

are commonly based on CMC joints providing a sim-

pliﬁed kinematic with up to 2 DOF (ﬂexion and

extension, abduction and adduction). Anatomically

more precise the CMC joint is synonymously named

trapeziometacarpal joint because of the os trapezium

which connects the 1st metacarpal with the carpus.

In this approach, an enhanced kinematic model of

the human thumb is presented, based on our analy-

sis of a detailed morphologic-kinematic model of the

carpus and the thumb. We state that the kinematic

function of the thumb is supported by the kinematic

function of the STT (Scaphoid-Trapezium-Trapezoid)

joint, which builds the radial carpal column. Our

study is based on a previous work by Essers (Essers,

2006) determining the speciﬁc movements of the STT

(Scaphoid-Trapezium-Trapezoid) joint in a set of ca-

daver hands. In our study, we combined these re-

sults with a kinematic 3D model of the human hand,

with focus on the kinematic chain of the radial carpal

column. We set up a kinematic model of the radial

carpal column and the thumb bones to analyse the

data gained from measured motions. Based on these

results, we set up a real kinematic model of the human

thumb and integrated the previous ﬁndings. Our ob-

jective is the development of more sophisticated pros-

thetic hands to reconstruct the function of the natural

hand in the best possible way.

2 ANALYSIS OF THE

ARTICULATION OF THE

THUMB AND THE RADIAL

CARPAL COLUMN

The hand’s function and grasping capabilities are

fundamentally supported by the complex articula-

tion of the thumb. The posture of the thumb

has a main contribution to the elementary grasp

206

Franke M. and Bogdan M. (2010).

AN ENHANCED KINEMATIC MODEL OF THE HUMAN THUMB FOR AN ARTIFICIAL HAND.

In Proceedings of the Third International Conference on Biomedical Electronics and Devices, pages 206-210

DOI: 10.5220/0002749202060210

 SciTePress

types of the hand (McKenzie, 1994). In medical-

anatomical literature the carpometacarpal articulation

of the thumb is commonly explained by the func-

tion of the trapeziometacarpal joint between the ﬁrst

metacarpal (os metacarpale pollicis) and the trapez-

ium. The trapeziometacarpal joint is synonymously

and more commonly named carpometacarpal (CMC)

joint. The CMC joint of the thumb enjoys great free-

dom of movement due to its saddle-shaped articular

surfaces, as described in (Dornblueth et al., 1998),

(Rauber and Kopsch, 2003), (Frisch, 2001), (Speck-

mann and Wittkowski, 1998), (Cooney et al., 1981).

It’s movements are ﬂexion and extension, abduction

and adduction, circumduction and opposition. Hence,

artiﬁcial hands with more complex kinematics are

commonly based on CMC joints with 2 degrees of

freedom (DOF) (Butterfass et al., 2001), (Liu et al.,

2007), (Lovchik and M.A.Diftler, 1999), (Wilkinson

et al., 2003), (Wilkinson et al., 2003), (Schulz et al.,

2005) which rotate around ﬁxed joint axes.

(Essers, 2006) describes detailed experimental

results of examining the STT (Scaphoid-Trapezoid-

Trapezium) joint of the human hand using a set of ca-

daveric hands. In this experiment the motion of the

scaphoid and trapezium during abduction, adduction,

extension and ﬂexion of the CMC joint has been mea-

sured and recorded by the use of a 3D tracking sys-

tem. Fig. 2 shows a model of the radial carpal column

and the skeleton of the thumb.

We conﬁgured a kinematic model of the carpal

bones to simulate the joint movements. The kinematic

transformation of the thumb including STT joint is:



0 1



(1)

(2)

(3)

(4)

(5)

(6)

. (7)

where (2) describes the scaphoid’s abduction-

adduction, ﬂexion-extension, and supination-

pronation kinematic axes.

(3) describes the trapezium’s abduction-adduction,

ﬂexion-extension, and supination-pronation kine-

matic axes.

(4) describes the metacarpal’s abduction-adduction,

ﬂexion-extension and supination-pronation.

(5) describes the ﬂexion-extension of proximal

phalanx.

(6) describes the ﬂexion-extension of distal phalanx.

(7) describes the constant translation from distal

phalanx to TCP 1 (Tip Center Point).

3 SIMULATION AND ANALYSES

OF THE WORKSPACE WITH

FORWARD KINEMATICS

3.1 Experimental Short-description and

Simulation Basics

The experimental setup from Essers (Essers, 2006) is

displayed in Fig. 1. The thumb’s TCP has manually

been moved in a circumduction with a deﬁned diam-

eter of 100 mm by using the maniplation bar and the

guidance ring. During this circumduction, the coordi-

nates of the scaphoid and trapezium in the radial col-

umn have been measured and recorded by a 3D space

track system.

In the kinematic chain, the movements of the

scaphoid and trapezium measured by Essers describe

a contribution to the movement of the TCP. The MCP

and IP joints are in this case assumed as to be ﬁxed

and the motion of the CMC has not been recorded.

The data in (Essers, 2006) has been taken on a set

of 7 cadaveric hands, average and deviation were cal-

culated and documented. Using the kinematic model

we simulated the circumduction by forward kinemat-

ics, using the recorded coordinates (x,y,z,rx, ry,rz)

for scaphoid and trapezium. The circumduction di-

ameter and the distance between TCP and CMC have

been taken from the experimental setup documenta-

tion. The simulation of the kinematic chain revealed

the motion of the CMC joint. Hence, the contribution

of STT motion and CMC to the circumduction move-

ment of the TCP in workspace could be calculated.

3.2 Setup of the Kinematic 3D Model

The kinematic model has been conﬁgured by combin-

ing 3D data of an average sized adult hand skeleton

with the forward kinematics given in (1). The ma-

nipulation guidance ring Fig. 2 (a) has been posi-

tioned aequivalent to the experimental setup in (Es-

sers, 2006). It’s diameter is required to determine the

corresponding TCP circumduction diameter. By ro-

tating the complete thumb around the radius given by

the guidance ring, the TCP circumduction workspace

is generated. The data for scaphoid and trapezium

movements documented in (Essers, 2006) has been

integrated into the 3D model to generate the partial

AN ENCHANCED KINEMATIC MODEL OF THE HUMAN THUMB FOR AN ARTIFICIAL HAND

207

Figure 1: Experimental setup from (Essers, 2006) (printed

with permisson) The experimental setup: Prepared cadav-

eric hand and sensors. a) Manipulation guidance ring. b)

Manipulation bar. c) Space track sensors, attached to ra-

dius, saphoid and trapezium.

Figure 2: Setup of the kinematic 3D Model: a) Manipula-

tion guidance ring. b) Manipulation bar. c) TCP (tip center

point) of the thumb. d) TCP circumduction plane. e) Os

metacarpale 1. f) CMC joint. g) Os trapezium. h) Os

scaphoid. i) Os trapezoid.

trajectories of the scaphoid and trapezium during cir-

cumduction. The combined and seperated adoption

of the data generated different combined and decom-

posed trajectories for trapezium and scaphoid articu-

lation during circumduction of the thumb.

4 SIMULATION RESULTS

Workspace simulation and decomposition relvealed,

that the STT joints articulation contribute 22% ±

11,47 of the TCP circumduction workspace of the

thumb. Fig. 3 visualizes the results of the simula-

tion. The combined partial workspace of scaphoid

and trapezium (Fig. 3 (a)) can be decomposed

into the scaphoid’s and trapezium’s component. The

scaphoids partial TCP workspace (Fig. 3 (d) and (e)

) turned out as more elliptical shaped.

5 ENHANCED ARTIFICIAL

THUMB PROTOTYPE FOR A

PROSTHETIC HAND

How can the previous results be used to improve the

function of an artiﬁal hand?

The STT and CMC joints are located in the

metacarpus and they provide a very compact mor-

phological structure. Therefore, a compact func-

tional model of anatomic size can not easily be imple-

mented. According to (McKenzie, 1994), the grasp-

ing function of the hand is mainly determined by 4

main areas in the thumb’s workspace:

• Pad opposition

• Palm opposition

• Side opposition

• Virtual Finger

We combined this issue with our further results

and implemented an artiﬁcial thumb based on an ac-

tuated STT joints with 1 active rotation DOF and 1

passive elastic rotation DOF. The active rotation DOF

combines the ulnar and opposition-reposition axis

(abduction-adduction and supination-pronation) mea-

sured in (Essers, 2006). As a result, the metacarpal

articulation is supported and the thumb’s workspace is

enhanced. The passive elastic rotation DOF is under-

actuated and combined with the thumb’s CMC, PIP

and DIP ﬂexion and extension. The corresponding

kinematics is given by the transformation:

∼



∼

0 1



(8)

∼

AASP

(9)

(10)

(11)

(12)

. (13)

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208

Figure 3: Simulation and decomposition of the Workspace

of the thumb’s metacarpal motion during circumduction:

a) Workspace of TCP circumduction movement, combin-

ing CMC and STT articulation. b) Simulated TCP (µ+ σ)

workspace resulting from STT articulation with ﬁxed CMC.

(Partial scaphoid and trapezium movement.) c) TCP µ

workspace of the same articulation.

d) TCP (µ+σ) workspace resulting from Scaphoid articula-

tion with ﬁxed Trapezium and ﬁxed CMC. (Partial scaphoid

movement.)

e) TCP µ workspace of the former articulation.

f) Os trapezium.

g) Os scaphoid.

h) TCP of the thumb in center position.

where (9) describes the simpliﬁed STT articuation

with combined abduction-adduction and supination-

pronation kinematic axes.

AASP

describes the

passive ﬂexion-extension DOF.

(10) describes CMC (metacarpal base) articula-

tion abduction-adduction, ﬂexion-extension, and

supination-pronation kinematic axes.

(11) describes the ﬂexion-extension of proximal pha-

lanx.

(12) describes the ﬂexion-extension of distal phalanx.

(13) describes the constant translation from distal

phalanx to TCP 1 (Tip Center Point).

The partial TCP workspace resulting from the active

DOF is represented in Fig. 4. Experimental postures

of the enhanced artiﬁcial thumb prototype based on

the kinematic chain (13) are displayed in Fig. 5. Pos-

tures in 5 a) - c) are based on the simpliﬁed STT joint.

The extension posture (Fig. 5 d)) is positioned by a

combination of the simpliﬁed STT joint and the pas-

sive extension joint.

6 CONCLUSIONS

This investigation revealed, that the carpometacarpal

articulation of the thumb must be differentiated into

the contribution of the trapeziometacarpal joint and

the contribution of the STT joints. The simulation

Figure 4: Enhanced artiﬁcial thumb model for a prosthetic

hand. An active DOF in the region of the radial column

articulates the main axis of the STT joints. It combines

opposition-pronation and reposition-supination. It’s cor-

responding TCP workspace crosses the TCP’s neutral po-

sition and intersects the partial scaphoid-trapezium TCP

workspace in Fig. 3 (b). a) TCP trajectory along simpli-

ﬁed STT DOF.

b) TCP workspace combining CMC and STT.

c) Combined scaphoid and trapezium workspace (σ).

d) Combined scaphoid and trapezium workspace (σ+ µ).

e) Passive ﬂexion-extension DOF.

f) Active DOF combining opposition-pronation and

reposition-supination.

Figure 5: Experimental postures of the enhanced artiﬁcial

thumb prototype: a) Retroposition, b) Opposition, c) Neu-

tral position, d) Extension.

results revealed, that the joint movement of the STT

joints supports up to 1/3 ( 22% ± 11,47 ) of the mo-

tion range of the adduction, abduction, ﬂexion and ex-

tension. The workspace of the thumb is signiﬁcantly

enhanced by the motion of the STT joints. Hence

we propose, that adequate anthropomorphic models

of the thumb should simulate the kinematics of the

STT joints to approximate biomechanically correct

movements. Currently simpliﬁed kinematic concepts

of the articulation of the thumb - as presented in state-

of-the-art robot and artiﬁcial hands - commonly dis-

regard the fact, that the joint axes of the scaphoid and

AN ENCHANCED KINEMATIC MODEL OF THE HUMAN THUMB FOR AN ARTIFICIAL HAND

209

trapezium affect the trajectory of the thumb and it’s

TCP workspace.

The fact, that the rotation centre lies deeper in

the radial carpal column corresponds to an extended

workspace of the thumb. In the artiﬁcial thumb pre-

sented an STT joint with 1 active DOF and 1 pas-

sive, underactuated DOF is applied. As a result, the

thumb’s workspace is enlarged and biomechanically

more adequate. Some examples for extreme postures

of the thumb are given in Fig. 5 a),b) and d).

In combination with robust and forceful ﬁnger

kinematics (Franke and Bogdan, 2009) biomechani-

cally effective hand prostheses can be realised. We re-

sume, that these properties are excellent qualiﬁcations

for applications in the ﬁeld of future hand prosthe-

ses, for example for biologically inspired neural pros-

theses (Bogdan and Franke, 2001) with an extended

range of performance.

ACKNOWLEDGEMENTS

The authors would like to thank Dr. Essers and Priv.

Doz. Dr. Jantea for providing further details about

their experimental setup.

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