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Leonardo da Vinci and Perpetual MotionAuthor(s): Allan A. MillsSource: Leonardo, Vol. 41, No. 1 (2008), pp. 39-42Published by: The MIT PressStable URL: http://www.jstor.org/stable/20206515 .Accessed: 09/07/2014 05:13

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Leonardo da Vinciand Perpetual Motion

Allan A. Mills

ABSTRACT

Leonardo da Vinci illustratedseveral traditional forms of"perpetual-motion machine" insmall pocket books now knownas the Codex Forster. He waswell aware that these designs,based on

waterwheel/pumpcombinations, mechanicaloverbalancing hammers orrolling alls, would not?andcould not?work.

JL. JLumankind has always sought to reduce the

need for its own manual labor. Draught animals were one

solution, but much more beguiling was the concept of ma

chines that would work "by themselves," with no obvious primemover [1]. Even in ancient times, it appears that at least two

categories had been proposed: the self-pumping water wheel

and the mechanical overbalancing wheel. None of course

worked, and as science and technology progressed it became

apparent that any such device was theoretically impossible.However, before this understanding was fully achieved and

became well known, many technologists and hopeful inven

tors [2] felt obliged to devote time to this hoary problem.Among the former was Leonardo da Vinci. Well aware of the

futility of all suggestions for achieving "perpetual motion," he

simply recorded?and refuted?ideas that were prevalent in

his time.

the same wheel, then the machine

might turn "forever."

A number of empirical attemptsto achieve such a hydraulic chimera

perhaps were made but went un

recorded because they never worked.

Drawings and plans of self-pumpingwheels persisted into the 18th cen

tury and even into modern timesas amusing artifacts of linear per

spective [3]. Progress in the under

standing of efficiency, friction and

the conservation of energy gradu

ally vindicated the practical knowl

edge that, no matter how ingenious,such devices simply could not work.

The Self-Pumping WaterwheelWheels turned by flowing water were well known in the an

cient and medieval world and were sometimes used to drive

bucket wheels to raise water for irrigation. The Archimedeanscrew was another form of pump. It must therefore have oc

curred to many speculators that, if only the two could be com

bined, with the waterwheel driving a pump to supply water to

Leonardo's ContributionThe papers of Leonardo da Vinci bear witness to the semi

quantitative understanding of machines that was emerging in

the late 15th century. Perhaps the least known of his extant

works are three tiny notebooks collectively referred to as the

Codex Forster, now in the Victoria and Albert Museum in London. They are believed to have been compiled between 1495

and 1497. A facsimile edition has been published, accompanied by a transcription of Leonardo's mirror-image text in its

archaic Italian [4]. (The facsimile drawings are in their origi

Fig. 1. Leonardo's pump/waterwheel combination in Codex Forster I, folio 42v.(Giunti facsimile)

i-i?-.-.-. ,.. r f.4i

???Hbi*?*??*,

i

Fig. 2. The "overbalancing wheel" of Villard deHonnecourt (13th century).

AllanA. Mills (retired niversity hysics ecturer), 1Thatch Meadow Drive,MarketHarborough, Leicestershire E16 7XH,U.K. E-mail: aa.mills@hotmail.co.uk>.

?2008ISAST LEONARDO, Vol. 41, No. 1,pp.

39-42,2008 39

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3T

Fig. 3. Overbalancing hammer wheel shown in Codex Forster n, folio 90v.(Giunti facsimile)

nal mirror-image form.) Unfortunately,no complete English translation of this

difficult material is available, although ex

cerpts and discussions have appeared in

various works on Leonardo.Codex Forster /, folio 42v, contains the

drawing reproduced here as Fig. 1. The

accompanying text says that "Screw A liftswater to screw B, and screw B with the

same water moves screw A." Leonardo

emphasizes that this is impossible in still("dead") water and heaps scorn on the

designers of such machines. The best thatcan be said in defense of the latter is that

the arrangement would demonstrablywork for a while if holding tank were in

corporated at the top of the pump [5].All that it would require would be to elim

inate friction and improve the efficiencyof the machine to 100%

The Overbalancing WheelThe first recorded

representationof

the popular "overbalancing wheel" ap

pears in the sketchbook of Villard deHonnecourt, an enigmatic figure who

traveled extensively in Europe in the

13th century [6]. In Fig. 2, it can be seen

that he is struggling to depict a wheelmounted upon an axle turning within a

stoutly braced frame. Around the cir

cumference of the wheel are pivoted an

odd number (here seven) of mallets hang

ing from their rigid wooden handles. The

lowermost mallets hang vertically, but the

upper ones rest against the rim of the

wheel. The implication is that the four

mallets on the left of a vertical throughthe center of the wheel will always over

balance the three on the right, causingthe wheel to perpetually turn in a coun

terclockwise direction. It must have been

thought that the blows of the descendingmallets would assist this motion.

The simplest model soon proves that,as depicted, the uppermost mallet fallsover too soon: a manually started wheel

rapidly comes to rest in equilibrium. To

day, we understand that the turning ef

fect ("moment") of any mallet is given bythe product of its mass times the distance

of its center from a vertical through the

center of the wheel. The wheel comes torest with the sum of the moments on the

left equal to those on the right, and no

external work can be done. It makes no

difference if there are an odd or an even

number of mallets.

Da Vinci's Hammer WheelsCodex Forster IL measuring only 9.5 x 7.0

cm, depicts on folio 90v the overbalanc

ing hammer wheel shown in Fig. 3. The

circumference of the wheel bears ratchet

Fig. 4. A more complex hammer wheel shown in Codex Madrid I, folio 145.Leonardo's drawing has been digitally contrast-enhanced and rectified.

t *

^??jVisi iift>A >^?Ua^?W*** &T*v?v*y^HW^W^y^^ii^

l^MU -??Aft.Ci(?M^'OP%'?P^pHhA^ft?v**j(l?A?SI?

r^i^m^j %tr*nr?M^******

f^*f* f^^ffV^cuW- *?> v?^r>?^*t*

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Vs

s

Fig. 5. A model of the "overbalancing hammer wheel." (? Allan A Mills)

teeth, and a pawl permits counterclock

wise rotation only. The pivoted hammers

have therefore been positioned aroundan inner disc, where coarser teeth sur

rounding the pivots prevent the rigidhandles from hanging vertically excepttoward the bottom right-hand side. Ca

sual inspection of the drawing might im

ply that the wheel will continuously rotate

counterclockwise, but Leonardo is well

aware that it will, in fact, soon assume a

stable, stationary equilibrium just like de

Honnecourt's mallet wheel.

Another drawing in Codex Forster II (folio 90r) is of a hammer wheel with addi

tional arcs upon its face. This particular

drawing is cramped and unclear but is re

peated in CodexMadrid /, folios 144 and145. (Dated to 1490-1496, this work is

now available in facsimile with an ac

companying commentary by Ladislao

Re ti [7].) The second drawing has been

rectified and is copied here as Fig. 4. Thearcs upon the face may represent initial

attempts to construct the loci of the cen

ters of gravity of hanging weights as the

wheel turns, but they neither are symmetrical nor serve to position the hammers around the rim of the wheel rather

than hanging vertically?as shown once

they leave the lowest point. Simple peglike stops are the simplest way of ensur

ing this, as shown in the model illustrated

in Fig. 5. The most significant part of Fig.4 is the way in which Leonardo has com

pounded the moments inmobile-like [8]chains to prove that, as drawn, the wheel

is resting in equilibrium about an imaginary vertical line through its axis. Many

examples of this diagrammatic construc

tion are to be found in this codex, which

has an emphasis on mechanics.

A Model Hammer-WheelFor this model (Fig.5), I fastened 12brass

weightsto

phenolic-fiberarms. The as

semblies pivoted at equal intervals arounda 20-cm-diameter disk. Protruding pegswere positioned near each arm so as to

limit its swing. The resulting wheel was

supported by a low-friction axle throughits center and could be rotated manuallyin both clockwise and counterclockwise

directions. Either way, it soon came to

rest in equilibrium. As the weights were

equal, itwas expected?and confirmed?

that the sum of the distances of the cen

ters of the five weights on the left from a

central vertical was equal to the sum of

the corresponding distances of the seven

weights on the right.

Fig. 6. Leonardo, rolling ball wheel of Codex Forster II, folio 91r.(Giunti facsimile)

7 *, f

Fig. 7. Leonardo, rolling ball wheel of Codex Forster II, folio 91 v.

(Giunti facsimile)

?

Mills, Leonardo and Perpetual Motion 41

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3

Fig. 8. A model based on Fig. 7. (? Allan A. Mills)

Rolling-Ball WheelsLeonardo also illustrates in the Codex

Forster I (91r and 91 v) twowheels basedon balls rolling around guides positioned within the disc (Figs 6 and 7).

The second is perhaps the most aes

thetically pleasing: 12 compartmentsbased on arcs of diameter equal to the ra

dius of the main wheel givea

pinwheelappearance. Balls confined within the

closed compartments will tend to rollto the lowest points, which (as shown)fall upon the locus of a circle. Again it

may appear to casual visual examination

that a greater number of balls on the

right will cause the wheel to overbalance and turn clockwise, but a model

(Fig. 8) confirms that moments rather

than mere numbers of balls on either side are

the operative factors. It soon takes up a

stationary equilibrium position where

the moments about the axis on the rightare balanced by the greater distances

involved on the left. TheJ-shaped

chan

nels sketched in Fig. 6 are equally un

successful.

Itwould be possible to replace the balls

with globules of mercury, as used in the

14th-century mercury clock of the Libros

del Saber [9]. Such a construction, how

ever, would be no better as a perpetualmotion machine

Oh speculators on perpetual motion, how

many vain projects you have created in

this search. Go and be the companions ofthe seekers for gold

?Leonardo da Vinci [10]

AcknowledgmentsI am grateful to Pauline Mills for translations of relevant passages in the Codex Forster.

References and Notes

1. Hele Shaw, "Perpetual Motion," Nature 37 (1888)p. 254; Henry Dircks, Perpetuum Mobile (London,1861); Stanley W. Angrist, "Perpetual Motion Machines," Scientific merican 218 (January 1968) pp.114-122;Arthur WJ.G. Ord-Hume, Perpetual Motion(London: Allen and Unwin, 1977).

2. Charles F. Partington, The Century of nventions oftheMarquis of Worcester (London, 1825); G.K. Tall

madge, "Perpetual Motion Machine of Mark Anthony Zimara," Isis S3 (1941) pp. 8-14.

3. Maurits Escher's Perpetual Waterfall (1961 ) is wellknown example.

4. Leonardo da Vinci, // odice Forster, ugusto Marinoni, ed. and transcription (Florence, Italy:GiuntiBarbera, 1992).Available for consultation at the Victoria and Albert Museum, London.

5. Ladislao Reti, "Leonardo da Vinci the Technologist: The Problem of the Prime Mover," InternationalLeonardo Symposium, University of California, 1966.

6. See the web site of Carl F. Barnes at . He dates the work to 1220-1230 A.D.

7. Leonardo da Vinci, The Madrid Codices,LadislaoReti, ed. (McGraw-Hill, 1974) ; adislao Reti, ed., TheUnknown Leonardo (London: Hutchinson, 1974).

8.James J. Sweeney, "Alexander Calder (1898-1976),"in ive American Sculptors NewYork: Museum ofMod

ern Art, 1969).9. Allan A. Mills, "The Mercury Clock of the Librosdel Saber," Annals of cience 45 (1988) pp. 329-344.

10. Leonardo da Vinci, Codex Forster II, folio 92v.

Manuscript received March 2006.

42 Mills, Leonardo and Perpetual Motion

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