The co-ordination and regulation of movements

Table of contents :
Chapter I. The techniques of the study of movements
Chapter II. The problem of the interrelation of co-ordination and localization
Chapter III. Biodynamics of locomotion
Chapter IV. Some emergent problems of the regulation of motor acts
Chapter V. Trends and problems in the study of investigation of physiology of activity
Chapter VI. Trends in physiology and their relation to cybernetics

Citation preview

The

MOVEMENTS by N. Bernstein

PERGAMON OXFORD TORONTO

- LONDON - SYDNEY

- EDINBURGH - PARIS

PRESS - NEW

YORK

- BRAUNSCHWEIG

Pergamon

Press Ltd.,

4 & 5 Fitzroy Pergamon

Headington

Square,

London

Press (Scotland)

Hill

Hall,

Oxford

W. 1

Ltd.,

2 & 3 Teviot

Place, Edinburgh

Pergamon

Press Inc., 44-01

21st Street, Long

Pergamon

of Canada,

6 Adelaide

Pergamon

Press (Aust.)

Pergamon

Press S.A.R.L.,

Vieweg

Ltd.,

& Sohn GmbH,

Pty. Ltd.,

Island

New York

Street East, Toronto,

20-22

Margaret

24 rue des Ecoles, Burgplatz

City,

1 ill

Of

CONTENTS

Ontario

Street,

Sydney,

Paris 5 "

N.S.W.

FOREWORD

TO

THE

ENGLISH

EDITION

PREFACE

1, Braunschweig PREFACE

TO THE

ENGLISH

CHAPTER

I.

TECHNIQUES

THE

Emarzon op

THE

STUDY

op 1

MOVEMENTS

Copyright @ 1967 Pergamon

1 , The

Press Ltd. ..

'

-',..:',. ..,.

i

-

i

,

h/ la /"',""li '';i 0-0179 0-4270

0-0712 00324 00181 0-0084 0-1118 0-0439 0-0183 0-4630

JOINT

op GRAVITY

(LENGTH

Thigh Lower leg Upper arm Forearm

given

individual

different important hold Tlie

for

would

living

subjects. human

author

of

solved

It

tliis

for by

and the centres

to present

plicated

and

leagues problem

for

the

in this

delicate

measurements and

volume

to

O. Salzgeber

of gravity of

even

employed

of this related

Scheidt

type.

to the

moments

by the

autlior

It can only

of the limbs

on

after

TABLE

tlie

most

3. THE RADII op THE CENTI(E op GRAVITY Fron'i our data hccoruing

imMean value

to the study of living

is im-

Thigh

of the com-

Lower

leg

Upper

arin

and

be said body

Mean square deviation

to Fischer

sub-

It

his colthat

measurements of tlie

values

to weigh

Hebestreit. account

tliese

mean

appeared

P. Pavlenko

were

of the limbs

planimetric

all

only

to proceed

a brief

that

be made

and

which

and

of

most

of methods

business It was

problems

it was possible

chapter

method

is ultimately

the volumes

ideas

of

absence

measurements

with

the

relationships

analysis

piecemeal.

persons

beg

subjects.

the complete

auxiliary

that

for

they the

subject

on special

of the radii of the centres of gravity of the long to be much closer to tl'iose obtained by Fischer than to those by Harless (I term as tlie radius of the centre of gravity the distance from the centre of gravity to the centre of the proximal joint with tlie lengtli of the limb taken as a unit). We may recall thpt Fischer's material was obtained on 3-5 subjects, wliile our material provides information oii about 150 persons; because of this the reliability of the present data is many times greater than that of the old figures. I append a list of the means we obtained for comparison with tliose obtained by Fischer (Table 3). The

limbs

vary

of live

of tlie

positions

obtained.

to be an impossible

together

purpose

possible

extent

necessary

the

may

Finally,

experimental

been

as it were,

paper

employing

they

what

to

the

being,

this

of tlie weights

all-to

appeared

experimentally

portant

ways structure.

recently

permit

0-467 0-36 0485 0-44

are characteristic

obstacle

has until

which a living

of

cadavers

primary

what

body

1)

=

Harless

0-44 0-42 0-47 0-42

in

age and

question

true

questions

jects

and

sex,

op THE LIMBS

op LIMB

Fischer

weighing

trolled

Harless

11

in numerous carefully determined Calltwin-support scales (see Fig. 12). From analyses of the figures obtained in this way and by comparison witli data obtained from tlie most accurate microscopic examination of photographic plates of tlie positions assumed during the weighing, data on the locations of the centres of gravity of the limbs and on their masses could be obtained. An analysis was undertaken of material obtaiited from 152 subjects of both sexes with an age range of 10-75 years. This study did not include investigation of tlie locations of the centres of gravity of head, liands or feet such as were determined by Braune and Fisclier; ratlier, we investigated the locations of the centres of gravity of the upper arm, forearm, thigh and lower leg and the masses of all the major limbs of the body. The locations of the centres of gravity of the trunk and of the body as a who]e were also included in the program of investigation. I append below some of tlie data from the results we have tlie

1)

=

Fischer

OF THE CENTRES

FROM THE PROXIMAL

Techniques of Study of Moveinents

and

the

Forearm

of

In the material

to

does a significant

0-3880 0-4175 0-4746 0-4145 as a wliole,

* -l ,,l *

therefore,

differencefromthe

0-0332 0-0224 00338 0-0309 only

position

of the thigh determined byFischer

in tlie case

12

Co-ordination and Regulation of Moveinents

occur, but the second column of figures in Table greater importance indicating that the spread of tlie words tl'ie variation, is considerable. If we take tlie deviation as a measure of tl'ie variation, it appears whelming majority of cases fall between tlie following Thigli Lower leg Upper arn'i Forearm

3 is of data,

mucli

Tliere

are only

in other

tliis

cliaos

square

ing

witli

mean tliat

tlie

over-

limits.

0-3548-0-4212 0-3951-0-4399 (14408-0-5084 0-3836-0-4454

two

possible

of variations.

Eitlier

tl'ie

subject

wliom

anthropometric will

enable

radii

of

our

of our

OF THE Liuns

Men

Mean value

Thigh Lower Ieg Upper arm Forearm

0-3857 0-4130 0-4657 0-4124

(IN MEN AND WOMEN)

Women Variations due to the mean square deviation 0-3543-0-4171 0-3942-0-4318 0-4394-0-4920 0-3850-0-4398

Mean value

0-3888 0-4226 0-4840 OA174

turn

in tliis

women.

to tlie

respect

unreliable.

Tlie

different

vahies

obtained

of

latter

TABLE

5. RELATIVE

masses tlie

to

new

find

such

(correlations)

accuracy

tlieir

the

general

wliicli

of tlie

data

as

probable

liabitus

and

we set as the objective

sample

picture,'*

even

of tlie and

op THE LIMBS

we may were

even

we examined

if we consider of any

body,

Harless

of material

independently

MASSES

limbs

of Fisclier

massive

qriite

only

variation

(MASS OF THE BODY

gives

tlie

mean

(Table

5).

AS A WHOLE

1)

=

Our Data Men

Lower

leg

Foot arm

Hand

Tlie Table

following 5. In

first

these

presented data

available

human

body.

In the

characteristic ratio

of the

Male

tliighs

legs and

mean

question second

place,

be observed

are mucli been

for

we liere

lighter the

tlie

smaller

than

40 years

observe differences

than

female

same

' The figures given here are only preliminary undergo small changes.

for

is re-

the

only in the

significant

and

giving

most

thighs

men

for

masses

of masses column

tliese

from

figures

In fact,

distribution

the sexes. The

illustrates

are almost

0-1158 0-0527 €10179 00336 00228 0-0084

overestimated

the feet.

have

of tlie

between

masses

arms

limbs

whicli

are significantly

upper

0948 0961 1-126 1-021 1-000 1-279

may

greatly

except

of tlie

A4ass according to Fischer

I10-00642

limbs

differences

M/W

circumstances

figures,

on tlie

mean

Fisclier

of tlie

extremities

Ratio

I

001295 oozboo 0-01820 0-00550

place

by these

General

0-12485 C104731 , I 001313 i 002632 I 0-01819

0-12815 (104845

interesting

tlie

all the extremities of all

Women

0-12213 €104655 (101458 0-02655 001818 0-00703

Thigli

Forearm

and

sufficient

basis

devery

attempt

investigations.

say tliat

Upper

In the first place, it is apparent from this list that sex differences have very little effect on the radii of tl'ie centres of gravity. Generally speaking, tl'ie radii are slightly longer in women, tliat is, tlie centres of gravity lie closer to the middle of the limb and in tlie case of tlie upper arm they sometimes lie even lower wliicli is almost never observed in men. In tlie second place, the indication in the first table of the great variation of tlie radii as encorintered in practice is confirmed. Even if Fisclier's figures, for example, those for the upper arm, closely coincide witli our mean values (0-47 and 0-4746), it is possible to employ tliem in calculations, given tlie probability that for the overwhelming majority of subjects tlie values of tlie radius for the upper arm may vary in men between 0-44-0-49, and in won'ien between Oa45-0-52. Figure 13 provides a picture of liow the distribution of tlie va]ues of radii of tl'ie forearm appear for men

tlie

to measur-

develope

may

correspondencies

It was this

to analyse

ourselves

we have

witli

on

in order

resign

we

strrictural

data.

Variations due to the mean square deviation 0-3534-0-4242 C13983-04469 0-4484-0-5196 0-3835-0-4513

to clioose

we may

deal -or

determine

subjects

If we now

more

patlis

techniques we

and ris to

an entirely

4. RADII op THE CENTRESOF GRAVITY

complex

wit]i

antliropometric

, These variations are comparatively insignificant. Tlie deviations found with sex of subject, contrary to expectation, do not significantly affect the values of the radii obtained as Table 4 sliows. TABLE

13

Techniquesof Study of Movements

and

and

the

clearly. lower

women

(it

and after final revision

may

14

Co-ordination and Regulation of Movements

sliould

not

relative

masses,

weight are

be forgotten

taken

that

tl'iat

as the unit)

significantly

in

all

these

is to say masses

cases

are

with

; but

distal

portions

tlian

tliose

of women.

heavier

we

estimated

discussing

the total

of the

limbs

Both

body in men

for

the

legs

and for the arms tl'ie ratio M/W shows an increase from the proximal to' the distal

end

of the limbs

the

per

cent)

feet

(13

necessary limbs.

to

and

determine

So as not

TABLE 6. THE

to enter

GIVEN

IN

VARIANCE

for

the

variation

whicl'i illustrates

t4ble

becoming

into

tliis

OF THE

liands

OF

per

cent).

variation

MASS

is also

of human

only

a general

THE

II

PROBLEM

THE

LIMBS

OF

THE

op

THE

(THE

WHOLE

VALUES

BODY

OF

THE

INTERRELATION AND

6).

(Table

CHAPTER

for

OF

LOCALIZ

(Published

op

WEIGHT

MEAN

It

masses

we give

MASSES

THE

THE

significant

relative

complications

RELATIVE

OF

(28

in the

considerable

H[lNDRED-THOUSANDTHS PERCENTAGES

particularly

CO-ORDINATION

ATION

in Arch. biol. Sci.,

38, 1935)

ARE

AND

IN

t.ihyn)

1. The Basic Dijferential Equation of Movements

I

Men Foot Lower leg Tliigh Upper arm Forearm Hand

il620 *13-3% 507 109% 126 8-6% 312 11-8% 184 10-1% 84 11-9%

General figure

Women

*+tgo * 9-2% 389 80% 105 8-1% 344 13-2% 169 9-3% 98 178%

The :.tl480 -Lll-8% 469 9-9% 142 10-2% 322 12-2% 177 9-7% 117 182%

The

variation

the

upper

botli

lower arms

in the radii

legs,

feet

and

and in particular

and in tlie

forearms;

the

of the hands

relative

masses

is least

masses

of

thighs,

display

the

greatest

variance.

evoke

by no

means

univocal.

this relationship this reason ments

a further

as

a

Whole.

gravity

of

problem

of

or of any or

of tlie

bility

If all

the the

discovering

particular wliole

is of

the system

leg)

presents

inestimable

ments

because

ments

of the whole

study

the

the loads

masses separate

on any

body of

centre (for no

importance

it opens

statics

and limbs

the

given

tlie

positions

of

tlie

of

gravity

example, difficulty for

the

and of its sub-systems group

and,

as lias

of muscles.

of

tliat

the are

known,

the

whole

of tlie

whatever.

the way to the dynamic body

of

body

System centres of

wliole of

move-

place,

tlffs

respect

already

here

only

us to above,

of tension

of its lengtli

this length

an analysis

of

of sucli

state-

at the present

time.

as an introduction

we may

to the joint

On tlie

other

to

momentum

tliat

and

In an intact

a function write

=

E, and,

of the velocity organism

place,

in the secwith

the lengtli

of the angle

of articulation

momentum

oF a muscle

tlie

/

doi.S

¥

at /

F I E, d,-1

we may by

assert

a given

of tl'ie muscle

of inertia

instant

over time.

in tlie first

condition

a; with

is

liand,

controlled

is a function,

and tonic)

at a given

changes

is in its turn

reason

of a limb moment

im-

is, moreover,

[8, 9, 14, 15] and for

summary

is to serve

of a muscle

(tetanic

F

tlie

undertaken

established

summary

innervational and

studies a sliort

as firmly

the

discussion.

of a muscle

of the move-

explained

of this

and

complex

of previous

present

object

The degree

for

I have

arm possi-

and also allows been

body

This

physiology analysis

tlie

movements is extremely

be regarded

of its innervational which

them

in a series

I sliall

as may main

ond

The Cerrtre of Gravity of the Entire Body and of the

between

which

The

for

relationship

pulses

that

muscle F and

of the limb

z

inversely

g I 15

tlie

angular

is directly

I. In tliis

dt2

(1)

.

acceleration

proportional

proportional

to to the

way (2)

a

16

Co-ordination

and Regulation

of

Movements

the muscleoperatingon complicated.Let us limit ourselves for simplicity to only one external force, namely gravity. In the simplest case wliich we liave just described,where we are considering tlie movement of a single limb segmentin relation to a 6econd fixed one, tlie momentum due to gravity G is, lilcethe momentum of tlie muscle, a function of tlte angle of articulation If tliere

tlie

limb,

are otlier

sources

tl'ie situation

of force

is a little

tlian

more

3 aO,; Qu ga" u,l N

G The

angular

of botli

acceleration

momenta

(la)

G(y.).

=

limb segmentunder the influence expressedby the equation

of tlie

together

is

m ,'-

k

0 00U) 004)

-E? D(d

,.a, ,E

.O 8 d2c

F + G

dt2

I

aha" G u

€

',a S) .o> ,' :jC:

If we introduce and G we obtain

into

d2c =

dt'

limb

equation

a relation I -

Tliis

expressions(1) and (la) for F of tlie following form :

tliis

/ dc '\ F l E, ct., -l ¥ df /

is the fundamental in a gravitational

eqriation field

+ (I(O'.).

(3)

for the movementof a single

tlie influenceof a singlemuscle

under

is E. In caseswherethe moving system consists not of one but of several limb segmentsand where we are obliged to take into consideration the activity of several

wliere

tlie level of innervation

muscles,

eqn. (3) becomes

extremely

complicated,not only quanti-

considerations of the mechanical effect of one muscle upon otliers also enter into the problem and the moment of inertia of the system becomes a variableterm. However, in spite of the fact that the complications which arisein this case are so great tliat equations of type (3) cannotalwaysbe written even in the most general form, tlie physiological aspectsof the problem differ only slightly, and tlie complicationsessentiallyin-

tatively

volve

but

also qualitatively

only the matliematical

as

and

mechanicalaspectsof movement.

context we may limit ourselvesonly to the consideration of the most simple equation (3). This basic equation is a differential equation of the secondorder whicli may be integrated if tlie functions F and G are known. Sohttions of an equation of this type, that is to say,the determinationof tlie movement wliich will take place in each given case,will be For

this reason

in the present

:2 !3 >A

..O(l)

€ a, a)(B 3>

2 u5 ,g ';; The;

a

€

O ':: ffi, '-zffl o-

H

2> a.j:: mal l-tz 51)+ Oi)l) d0 0-!:O aJ: Q (n ::{h 0g c.i0 1::0.1

5 g

,:) gf stC:

0P

-

,bd

Fia.

2. One

of

Marey's

subjects

in a black

costume

with white tape. FIG. 4. Chronophotograph Right centre

side

or

of the

the body; picture

of movement

walking is from

is a superimposed per se.::.

FIG.

3. Chronophotograph from

left

to right.

of The

walking

frequency

taken is abotit

by

Marey.

20 exposures

Moveinent per sec.

is

taken

by

Braune

left to right.

and

Fischer.

The square

scale. Frequency-26

in tlie

exposures

Fia. their

6. Bulbs

used for

dimensions

Bernstein

cyclography,

may

be gauged.

bulb ; (right)

placed (Left)

for comparison, pocket

on a millim:tre

a Wolf thetype

grid

so that

socket ; (centre)

a Wolf-

of bulb commonly

usedin

flashlights.

(Bernsteinand Popova).Left sideof the to left. Trajectories from top to bottom : c, centre of gravity of the head; b, shoulderjoint of the left ann;a, elbow joint of the left arm ; m, radial side of thewristjoint of theleft hand ; gm, centre of gravity of the wrist ; f, hip joint of theleft leg; gy, a pointon the longitudinal axis of the left thigh; s, kneejoint or the let'tleg;.v", knee joint of the right leg ; p, ankle joint of thelei'tleg; 'rc,a point nearthe

FIG.

5. Cyclogram

body ; movement

of walking

is from

end of the foot.

right

Frequency-90 exposures per sec.

!0 N

FIG.

7. Camera

velocity the

witli

of rotation

rotating

shutter

cyclogram,

rotating

shutter,

may be estiinated. is semi-transparent

uniting

successive

equipped In a later ; this

points

with system provides

a siren

j:

so that

its

used by the author faint

lines on the

on the same trajectory.

y', ) lAi"a

J-

a

,+'/ Jj /l

Frc.

during cor8. Successive positions of the right hand and a hammer is with a chisel. The time interval between each phase shown a cyclogram. from made was sketch The ' /15 sec.

rect striking

at

of filing. The figure of the subject is visible FIG. 9. A kymocyclogram thetop of theillustration, with a standard cyclogram of a single cycle of filing. This can be seen to be quite unanalysable. of themovement Belowis a seriesof curves of the sa+ne movement, separated by being on a moving film. K, a control bulb; E, the elbow joint; photographed H, theradialside of the wrist joint; F, the fingers of the right hand;7', the frames per sec (1923). fingersof the left hand. Frequency-73

Fia. 10. Apparatus for mirror kymocyclography. The subjectisoperatmg a Powers perforator. On the left we have a mirror with a scaleandthe serial number (1929).

FIG.

11. A section

of a photograph on a ineasuring grid and the means by whicli it is studied through a lens.

&&k

FIG. 12. An of gravity

experiment

of the limbs

on the

determination

by Bernstein's

method.

of masses The

subject

and

tlie

centre

lies in a pre-

at two points, the placement supported on a platform position boards. byupright being determined of the head and the lower extremities extremity lower at the frilcrum, a upon fixed is At the end the p)atform scales. The asssistant by one of the pans of accurate it is supported the scales, the position of position a given of moment static the balances scale. on a predetermined at the saine instant being photographed determined

Fia.13.Distributionof the values for the radii of the centres of gravity of theforearmfrom data obtained by the author and his colleagues. Above:the}imitsfor men; below: those for women. The values of relativeradii areplotted along the abscissa. The number of cases observed

is plotted

along

the ordinate.

Co-ordination different tliat

depending

and Localization

on tlie so-called

is, the initial

position

Problems

initial

of the

conditioi'is

limb

segment

17 of integration

determined

:

by the

angle Ao and on its initial angular velocity docoldt. By altering these initial

conditions

effects

of movement

for

tlie It

same

must

cyclical

in

functions

first

of

F and be 'iioted the

as a result

of effort

P and

clianges

tliis

may

the

same governing

that

relation

eqn.

obtain

of the

(3)

between

of the limb

very

upon

in its turn

oc. A cyclical

directly the

different

law

(3),

i.e.

bears

on

the

of

the

momentum

a. The limb

operation

momentum

in the angle

in tliis

we

and G.

of

F and the position

its position

ways

one

all

character

muscle

various from

chain

segment

changes

it of the momentum

changes

of cause

because

and

effect

of the operates

way.

Tliis

chain

would

be ideally

cyclical

if the momentum

(eqn.

(1))

depended solely on (X and drxldt, that is, if the movement were completely (l)

passive

and

degree from

(for

(3) given

example,

in this

of excitation

of the

the areas lying

It is apparent

that

of excitation

the falling

report,

outside tliere

E depends

tlie

of the arm).

value

muscle

E,

tlie circle

But,

of F also

whicli

appears

wliich

are two

possibilities

wholly

or partly

as in eqns.

depends

we liave just here;

on the

most

described.

either

on the values

clearly

the degree of

(X

and

of

daldt, or it is quite independent of tliem and is solely a function of time

t.

Tlie

choice

of great clarity

only

sliall

only

tlieses

between

the two

pliysiological

we have

If tlie

degree

velocity

with

discussion

in this

chapter.

tlie

some

of the

of excitation a function

differential

E is simply

initial

integrals

case,

proceed

are fulfilled witl'i

will

oscillate

position

and

then

2

F E cc,-1, dt / of which

a string

CRM

of each

sufficient moment

of the

I

hypo-

eqn.

of position

(3) will

take

and

tlie form

equation,

consequently,

conditions

it must

At

a function

tlien

da '\ =

d't In tliis

consequences

of time,

d2y.

I tlie partial

here is clearly

be revealed

raised.

and not

of a classic

indicated

as may

by further indicate

possibilities

significance

depend a movement (from

doe L ci, -l only

without),

released.

to

It is clear

(3a)

G((Xi

on tlie initial must

occur

regularity

a precisely that

conditions.

if the required

and once having

the same uninterruptable if displaced

+

dt J

this

witli

determined liypotliesis

begun wliich initial

does not

Co-ordination

and Regulation of Mouements

Co-ordination

18

physiological reality and in effect completely ignores the role of the central nervous system. On the otlier hand, it may be supposed thatthedegree of excitation E is a value which changeswith time and depends entirelyona predetermined sequence of impulses from thecentral nervous systeffi without any relation to the local conditions operating in the system of the moving limb being studied. If, asin thehypothesis formulated above for the elastic oscillation of a string, themuscle can be compared to some sort of independent springor rttbber baml, then in the second hypothesis it mayberepresented asasort of solenoid which attracts its core solely in relation to thepotential of the current wl'iich is supplied to the coil fromanexternal source. The law of the variation in this current mustberepresented in the system of eqn. (3) as a function of time; in fact,whatever maybe the real carises of these changes, the changes themselves arepresented to system (3) in a completely finishedandindependent form as quite unalterable data. Equation (3)in thiscase takesort correspond

to

the form d2o
'="" " properties of this motor field. and metrical

to assert statements that the physios"a.a-:aaraa:a,:a::"a'

(il

4 o

o

;="

Q o

-

A

o

0

p-

";

'

.

;. %

? ,,,'o-s

(5

o

Continuous

Ill

N

o

elements.

phenomena. vertical

,-,;=?S'=,

.i ::,

T!) o

elements.

corresponding

o

7

T. Ladoumeg's body, taken at a frequency of 187/sec in experiment

::=i:I ..2ffl"

'

3

=(D

No' of=.p"a'ses "R -

indicate

0

lines

"rl

heavy

FIG. 27 (a). Successive positions of the right side of No. 731. Heavy lines mark phases of the movement