An Analysis and Synthesis of the Writing Control Mechanism

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Copyright © IF AC System Structure and Control, Prague, Czech Republic, 2001

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AN ANALYSIS AND SYNTHESIS 01' THE WRITING CONTJlOL MECHANISM

Hldeo Taluchi a.d AklDori Morltoh

1-1

Teikyo University Utunomiya, 320-8551, JAPAN

Toyosatoda~

Abstract: Human can perfoun synergic motions of bands and anns that require the OOIItlOl of delicate forces. These synergic motions of han~ and arms have not been aoalyzed from a kinematic mechanism viewpoint. In this paper, a new model for upper limb dynamics is constructed by analy2ing 34mensional motions in handwriting operations. And the writing control mechanism is mentioned from a dynamics viewpoint. Copyright· 2001lFAC Keywords: Arm movements, Tonpe control, Kinematics, Modeling. Brain models, Simulation

meI5Uring technicpe. In atHtion to this, an analytic model of an upper limb dynamics is OOIIstruc:ted on the basis of mcaswed data. In this model, the upper limb is reguded as a rigid linkage with multi-joints. On the basis of this dynamic model, each tonpe of upper limb joints is inverse-kinematically estimated from measuRld data. Finally, the writing calter model is proposed, aDd the haodwriting of Japaoese diameter .. ~ .. is simulated by using the estimated torques as output data of this writing calter model.

1. INfRODUcnON An analysis for the motion mechaoism of han~ and arms W15 a subject of study in physiology, anatomy, health ecbcation and physical edlcation (Fujiwara, 1973; Tagudli, et Ill., 1982; Igai, 1984). In kinetic analyses for the motions of han~ and anns , the motions in such the limited amensions as on the plane or in the line have ever been the objects of analyses. For the writing wolk of characten, the wave analyses of haodwriting and pen power in a time
2. MEASUREMENT OF THE WRITING WORK

2.1 Measuring System The measuring system is composed of an dcc:trogoniometer (Fig. 1). a stylus pen with inner force sensors (Fig. 2). a dgitiZltl and a peDOnal computer that ~rds and anal)'2lCS data. The measu~ data ~ stored in a fODD of a data file at every trials.

2.2 Measurement of Upper Limb Dytuunics The writing walk is complex motions of a shoulder,

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an elbow, a wrist, a palm, and fingas. The CUlter of

So a rotation angle of the inside ring for the outside ring can be deteded. The angles (81 , ~ , •••• , 8,) of the upper limb joints can be calrullled from a set of gooiograms ~., ~·, ..... ,elo·, that are output data from these potentiometers. The calwlated results ~ plotted by solid lines in the Fig.8 (b), in the case of writing Japanese script "~".

a shoulcZr joint, in gmeral, is regudcd u the origin of this dynamical coordnate system. If the CUlter of a shoulder joint is fixed, and if fingers and a palm ~gion Ire ~garded as a rigid body when a pen is held, the writing wolk is mUlti-joint linked dynamiC5 with 7 degrees"f-freed>m (Fig.1 that ~ 3 degreea"f -fr=d>m for a shoulder joint, 2 degr=s for an elbow joint and 2 degrees for a wrist joint. However, as the center of the shoulder joint is not fixed on I(tual amdition, an electrogoniometer with more degreea"f -fr=d>m thm 7 degreea-of-freeam1 is recpired (Fig.1 Therefore, a hancmade goniometer with 10 degrees-of-frecdJm has hem used for measurements (faguchi, et aL,l990). Ten potentiometers (PI' Pz, ••., PlO) ~ located in the goniometer. The position of PI is located on the origin of the coordnate of the goniometer. P, and p. ~ sliding potentiometers with oouble rings. A brush attached to the inside ring contacts a re5istancc wire on the out5ide ring.

(a»,

2.3 Measuring HandwriJing andPen PCWtIer The structure of the stylus pen is shown in Fig. 2. (faguchi, et d., 1989). Strain lJ.Iantities (el' e20 e3) are output data from strain gages SI' S20 S3 respectively. The strain quantity £3 is a romponmt of the aredion of the pen. 11 and 12 ~ two orthogonaI romponmts in a plane that is pe!pal -dwlar to the axis of the pen. The eledromagnetic inlilction roil IltadJcd on the tip of the pen outputs data about the position of the pen tip. Thme romponmts of pen power ~ shown in Fig. 3(a). One of romponents is a pezpendiwlar force romponent (f.) to paper plane, and the others are two orthogonal romponmts (r.. f,) of a force F in the progressive directioo of the pen. Three components of pen power (r.. £,. fa) are estimated by strain c,.umtities (el' 12' 13) as fonows (Uclriyama,1987). & shown in Fig. 3 (a), the pen is inclined at +-degree angle from the vertical line, and both a rel(tjon force fa and a force F with a 8-degree angle from an orthogonal projedion ~ applied to the pen. In this case, as shown in Fig. 3(b), the force actini upon the pen tip is cividcd into a force 0 1 in the aredion of the pen axis and • forae O2 in the petpeDCicu111' plll1e to the pen axis.

(b».

(a) Upper limb movements with 7 de~ freedcm N r0-

Il

.Jl

Sensor

strain) ( Gage •• 5 1 ---:"':'

52

t

Aluminum

• •

I

Bar

o

Ii C'IS

I

Posi tion Sensor (Coi l ) UnIt (mm)

(b) Exoskeletai-type electrogoniometer

Fig. 1 Upper limb movements and measuring

.... --./ ....1

Fig.2 Mechanical configuration of a stylus pen.

apparatus.

670

The relation between Q 2 X 10" [N] and a oomposite

Pe,n-axis

strain 'PIDtity tl1.2 can be estimated by using a multi

: J .7Y ~

f ;.

-regression analysis method (Kawaguchi.1982).

/ ('

Q:z=2.24+O.657 tl 1.2

, ..... /

11 I

i

t

~I

•

,

I

where tll.2={ZI2+tlllt'1. The estimated eqJation is in the accuracy of a coefficient of oorrelation 94.7%. The relation among QI' e 3• Q1> and COS+. also. can be obtained in the same mmner. The ccpation for 0 1 X 1O'3[N] with the aa::uracy of a coeffjcient of correlation 96.5% is.

'f/ fzcos~

:'

.:

!

;

P.per

I

plene

.' -1---..

fzsin . . '- .

1'"

8

f1I ~'-~::1'' ."

y

/

I F......----

~"

I

i .. ···'·, ... ... :'_Dlrectlon of '--""""---1 wr I tlnV r; progression I

Or t hogreph of pen-exls

Hereupon equations of the equilibrium of forces are as follows.


Q2

(3)

f.coS++Fcos9sin+=OI'

i

52 .....· \ ,\ fzsin-Fcose

(I)

•

{(f.sin+-Fcos8cosq, +(Fsin8)1}

112

=02'

(4)

The forces f. and F can be obtained by substituting 0 1, Oz into (3). (4) and solving these simultaneous equations. The force F is divided into the orthogonal oomponents (f.. £,) in the paper plain. By this way. the three components (f,.. 4. f.) of the pen power can be obtained from the strain quantities (Ill' el> e 3).

'. Fsine

51 -+----t"J---t-51 pen-exls

3. DYNAMIC MODEL OF UPPER 11MB AND ESTIMATION OF JOINT TORQUE (b) Force diagram from a viewpoint of pen axis.

In order to estimate forces and tonples to be reqJired to an upper limb in the writing work, a dynamic model for ID upper limb is oonstructed. Here. upper

Fig. 3 Force diagram with a pen.

limb movements are motions of a rigid body with 3 joints and 3 links in the coordnate system that the origin is on the shoulder joint. In this study. visoosity characteristics for tendons or muscles around joints are neglected. In this model, An upper limb dynamics is regarded as translational motions and rotational motions.

z

•

~r

(a) Translational motion of an upper limb

x-----~~

Alei. of rotati on ~I

(b) Rotational motion of forearm Fig. 4 Force diagram with motions of an upper limb.

671

The applied forces are estimated from the equilibrium of forces in trmsllllional motions. also tortples in the rotational motions are estimated by using these forces (Makino. 1983). A:> shown in Fig.4(a). gravities (RUt R,.. R~ extemal forces (FSI FE. Fw) and pal power Fp (f., f,. ~) act on each link in translational motions. SUbscripts U.F.H inc&cate an upper ann. a forearm and a hand respectively. SUbsaipts S.E.W.P mean that these forces act on a sbouldcr.an elbow. a wrist and a pen tip n=spectively. EcJwions of motion for the bmd, the foreann and the uppa- ann are as follows Fp+Fw+R~MtP~

(5)

-Fw+FE+R.,=M,G,..

(6)

-FE +Fs+Ru=MuGUt

(T)

where M~ M. and Mu are mass. Cia. G. and G u are cmter positions of gravity. External forces (FSo FE. Fw) can be calallated by (5).(6) and (T). as assuming the values of MHo M .. Mu Gilt G.. GUt RUt R .. RH and Fp (Matui. 1966; Matui.1970). Rotational motions gmeJ'lle tortples around the orthogonal three axes at joints of the shoulder. the elbow md the wrist (Fig. S). Therefore the tOrtple coordinate is constNcted by 9 main axes. The unit vectors of the tortple coordnate axes are expressed by SI' Sl' "'S9' A:> shown in Fig. 4 (b), by using the tortple TI aro\.UId the main axis ~ (izl. 2 . .... 9), the ecpation of a rotational motion at the wrist is as follows.

where, i.o, 6. 7. The CIJIation of a rotational motion at the elbow is.

where, i=3, 4, 8. Also, the CIJIation of a rotational motion at the shoulder is.

TI-TIJ+T"uJ+T.~::d~(~)lti.

where, i=l. 2, 9. In these CIJIations. TWJ and T!'I are reactive torques around a parallel rotational axis to the main axis S;. that are genented by the tortple TI III the wrist and the elbow. T ..H.I' T....1 and T .. u1 are the tonpes around the main axis S. by the gravity at the blllld, the forearm and the uppa' arm respectively. TF" .I' T"wJ and T,,EJ are the tortples aro~d the m~n axis s; of the Qtemal forces on the pal tip. the wnst and the elbow respectively. ~ is the moment of inertia about the main axis s;. is an absolute rotational mgle around the main axis s; (Kato.et al .• 1972). The estimated results are plotted by solid li~es in the Fig. 8 (c), in the cue of writing Japanese scnpt

a.

"cII;". 4. SIMULATION OF TIIE WRITING WORK 4.1 CDuer Model for Upper Limb Dyruunics

By ad:>pting an assumption that the tonpe for the upper limb is oontrolled by the oenter in the macroscopic point ofview. the cmter model (Fig. 6) is constructed by using the upper limb dynanics model in sedion 3. Input is position vector of the paltip (r) with the origin on the shoulder joint cmter. Output is a vector 9 that show 7 joint angles of the uppa- limb. All signal lines are vectors. Notation [ ] in Fig. 6 sbows a ciagonal trmafer matrix with diagonal components of transfer elements dc$cn'bed in [ ]. The functional stru<1ure of the cmter (Fig.6) is constru<1ed by synthetically considering a related anatomic structure of the center. a transfer pass of oeuro-infoanation md some assumptions for functions of each system. Therefore, the writing work is executed in the process (I) through (V) IS follows (Taguchi.et al.• 1982),

e

- l - D Vector _ 7 - D Vector =--,-D vector

~----------------I

,-----------, o.r.bell_

,"

I I

"

I

: I

I

!

Fig. 6 Block diagram of a cmter model for upper limb motions

672

(10)

(I) A character image r is imagined from I...Inguage area, along with appearance of intention of writing down characters. (II) The deflection er between r and the visual data r of pen tip position is calculllcd in the parieto-ass area or the prefrontal area. The er is amt to the retiadar fonnation through the prdiontaI area. An incomplete integral (a+1/s, a: ~grec of tension) of the er is cxeaJtcd in response to the degree of tension in the reticular formation thlll is the centa' to control the degree of tension. Furthamo~ the incomplete integral of the er is modficd into advanced infounation Ar by projecting from a somltic seosory area, and it is sent to the premotor area. (ID) The premotor area is considered for a preprocessing system of a motor area. The premotor area transfonns Ar into adv.ocd infolD'lation AS of the upper Iim b joint angle in the fonn. A~rAr.

h can be given by the approximate ec:p1ltion as follows,

where " is a proportiooal allotment l'Ite (0<" ~ 1). The tonpe instJUc1ion T is calculated by using the above relations. (V) The muscles of the upper limb m:Qve the instJUc1ion T. dynamic motions appear It each joints as follows: For the wrist

(14) For the elbow

..

~8'I-TI+TwJ-T...~.T,.wJ=0. And for the sboulder

..

(11)

~ 8'1-T1+TIJ -T..u~ -T.,IJ =0.

where r is Jaoobi matrix In (11). Ar is a three-dimensional vector• •d AS is a KYen.
4.2 DISCUSSION

By id:>pting the Japll1CSC saipt .. ~ .. of Fig. 8(a) as a character image input to the writing center m~. the rcprodlcibility of a joint tonpc, a joint angle and a character fonn is studcd in this m~. The effects of the parameter" arc stucicd unc the concition of ~ and W of (/.7) unit matrix. As the result of this,

e.

rlf

- - Real bandwritina .. .. . . Simulation

o

+5 X [an)

(a) Script

8

diffcrmtial gain) from the cerebellum.

--Eatimlted joint anale ..... . Simulation

[de. )

Eltimlfed torques .. . .. . Simulation

'1',

lOt....

'RH .•] -

=~.. -tJ:-c}" 20~ 92400t-t ... ________ ;--'-.. 4 2 0=

It';"r 'oL 5

rp;--------1

I

I

I

,

, I ,

I I I

I

I

I

I I

,

,

I , :,, I I L __ .:. _____ -',

I

I : I

r~---.B..h!l rf;---~.l:~

I I

_••• ___ .J

I I

: ....

, I

I

_------'

-fg

W1.J

W2.l

W2.l

W..,

Wu

W6,)

W,.J

1.28

U)

o:~

117

2m

1.8)

L99

Mean

V~ {SlIndIrd

$

~

: f

:

2

.]:

1

j

-:

E-- ----i -30~

67

p.o1S) fl,107) fl.2S7)

I

6~.1O~1:1 ~~ 6S:~f. la -

Table 1 Diapal weigbt mabix W,

flO12) fl,146) ~

-

-..v~' tOt 1

Fig. 7 Simulation results to a script "~".

(16).

This relationship is represented as 8=P(1') in Fig. 6.

A

Then. an additional vector S is tranafonncd into an absolute rotational .gle where 9 is an adtitional vector of AS in (11) and S in the somltic seosory area. We si~ply deaaibed as 9=0(9) in Fig 6. After that, 9 and 9 1ft seot to the motor area. (IV) The motor area issues motion instructions. In this case, it issues a torepe instJUction T for an upper limb joint. The torepe instNction T is detennined IIXOdng with the ec:p18tion (8) through (l0): Considering thlt the motor area receives the cxcitatory projection from the premotor area .d the inhibitory projection from cen:bellum. d~ Ilk in (8) though (10) is cxpresaed by the infonnation from the premotor area and the infonnltion @ : a

(IS)

i

'1'3

fl.B)

t[.. ~ "''--''?''

..t

..

•

•

12

!:s

.'

...

~ :7,~!

::U>1 o·t

~ i=

3

i ;4

'1',

-+'1

2b

3'

.'

~ 'l'7 ~~ 2~ 4 '1'. 0E

4= l

~

3'

r-

~

t=!

~

T

a

J4

'f-

of :

3

(c) Torques

Fig. 8 Simulation results in the catC of L-170[ms]. a=3. ~1 .8. ,,=0.8

deviation)

673

~

------z--r- -

\If

'1',

(b) Joint II1gles

'

1

.~

it has become clear that each joint of the upper limb is not controlled with unifonn aa:':U11IC)'. The farther joints are from the cenler of a body, the more they are oontrolled in high aa:uncy, in order to .quat a character size and 50 on. Next, the weighting diagonal matrix W is .qusted in order to improve a aa:':U11IC)' of oontrol for the upper limb. Here. the W is alfiusted by the following recurrmce relation.

model should be improved to an adIIptive modtl with a leaming functions for various actions.

Baron, R., R. PlImonoon (1983). Aa:eleration measurement with an instnlmented pal for signature verification md hmdwriting lIlalysis. IEEE Tnas. on lnstnunent«ion tnd MellSllTD1le1lt, VoUS. No.'. 1136-1138. Crane, RD.. J.S.Ostrem (1983). Automatic signature verification using a ~-lXis fOJCe-seositive pal. IEEE Tnas. on Systems, M"" tnd Cybemetics, Vol.SMC-13, NO.3, 329-337. Fujiwara, T. (1973). Kine-~omy, pp. 184-224, Isbiyaku Publ. Co., Tokyo. Igai, M. (1984). Physiology of Hum". Bo4', Muscultr Physiology. Taishukan Co. LID., Tokyo. Kawaguchi, I. (1982). Inttotilction to multi-v";«e ".dysis, pp.27-30. Morikita Publishing Co., Tokyo. Kato, I., K. TlIlie (1972). The trial procilction of bipedalism machine. Tmn. of S ocidy of Biomeclumi.mt ofJapwa, 258-266. Makino, R, M. Tu-o (1983). Kinem«ic:s of mtrhinery, pp. 93-97. Corona Publishing Co., Lld., Tokyo. Matui, H. (1966). Hum". enginemng hflltIJook, pp.30-3S. Kanabara Publishing Co., Tokyo. Matui, R (1970). lntrotilction to Bo4t kiMm«ic:s, pp.l03-117. Kyourin Publishing Co., Tokyo. Tagucbi, R, K.. Fujii (1982). MovCIDmt oontrol function of the brain. Systems tnd Control (ISCIC ofJapwa), Vol. 2', No', 576-585. Tagucbi, H., K.. Kiriyama, E. Tanaka md K. Fujii (1989). Online m:ognition of baodwritteo signatures by feature extraction of pen movements. Systems tml Compul~ in JIfH'J, VoUO, No.lO, 1-14. Taguchi, H., K. Masuda and K. Tanaka (1990). Analysis of various fonns of hmdwritten characters caused by oentra1 prooessing differences.

(17),

W"l:A,.W.

where the initial matrix Wo is the unit ciagonal matrix of (1,7). The subsaipt n means the trial num~ of simulation, md A,. is a ciagonal matrix of (1,7) with elements A;.... A;... is as follows,

i:l,2,

., 7

where a6;.a is stmdard deviation of 9; in n-th trial, and o6s is standaId deviation of the measured data 9;. The .qustment under the rule of (17) ~rs until the condition of 0.95 ~ IA..I ~ 1 is satisfied. In the cue of J.L=O.8, the above ooncition has been satisfied at n=-3. And the weighting diagonal matrix W, is obtained as shown in Table 1. Using this W" the modification of the duuaaer form is shown in Fig. 7. It CID be seen that the bigger fJ is set, the more the motions are oontrolJed, and the character size has become small. In this CMe, time histories of the handwriting. joint _g1es _d toltfles are shown in Fig. 8(a), (b), (c) respectively. The solid lines in Fig. 8 show results of measun:ments, IIDd the cbtted lines show the simulllion results. Slightly gap bc:tweal measure -mmts IIDd simulllions is found in 860 8,. For the other mgles and toltfles, close agmment between measurements md simulations is obtained. The simulllion of the centCl' model based on fee&ack mechanism has mabled us to verify the physiological assumption that motions are derived by inner feedback such as the cerebrtH:erebellum interrelation.

5. CONCllJSION

In this paper, the writing work., that is one of examples of cognitive actions, has been malyzed. And each joint to~ of upper limb in writing works has been estimlled. In order to clarify the planning and the attainment of the writing actiODS, the mo~ of writing center oootrol has been oonstnlcted. HeR. the writing OCIIter is taken for the converter from SalSOty information to toltfle instructions for adions, md the upper limb dynamia is applied to the periphenl system. And then, the effects of parametas for Iq)rod1ccd chamc:ter.s is stucied by simulllion. Furthermore, it is clesr that the estimllled joint toltfles of the upper limb from measumi data is proper in writing works. Through the propoa:d model is constructed for the writing work., it CID be applied for other adions with force control by choosing proper model parameters. Hereafter, we think that this

Trrns. (D-O) of I.E.C.E. of JIfH'J, Vol.,J73-D·D, No.5, 756-766. Taguchi, R, T. Sakai lIld K. Fujii (1982). A structwal representation for the central OOI1trol organization of upper limb movements. Tnas(A)

of IEICE of JIfH'J, Vol. J65·A, No.12, 1286-1293. The Robotia Society of Japan (Ed) (1990). M ecJuaislll tnd COIItrol of _s, Robot HanJbool:. Corooa Publishing Co., Lld., Tokyo. UcbiymuI. M. (1987). Theory of system design for IObotia foroe-seosor. Systems tml Control (ISCIC ofJapwa), VoUt, No.l, 103-112. Yasuhara, S. (1972). A way to handwritten character recognition. Jou"" of the SICE of J."., Vol.ll. No.", 371-382.

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