YLLABUS OF

OF

EXPERIMENTAL LECTURES

ON '!'HI!":

PRINCIPLES OF MECHANISM.

DY

ROBERT WILLIS, M.A., F.R.S., &c.,

JACKSON JAN PROFESSOR.

CAMBRIDGE: PRINTED AT 7'HE PITT PRESS,

BY JOHN w. PARKEH, PRIN1'EH. ·ro l'HE UNIVEUSITY :

FOR J & J. J. DEIGl-I'rON, TRINITY STR1'4;ET.

M.DC.:C '.XLI.

T e

r

.. n1mun1

and modif w n h 0 cl~".h~c.. ""~

these cla s i i mo · onY ni nt to b in

he l~ because i principle adnli of being

de eloped geometrically withol1t referen t tl1 po ers emplo ed or transmitted or to th resi tanr

or work to be done. The ordinar. principl f Statics and Dynamics ma be subsequently applied t.o the combinations thus obtained.

Of the second class of parts, nun1erous exampl

occur during this course in the machines sel et d f r the elucidation of the general principles of t.h t\v other classes

Finally, the first class of parts

of the second division of the cour

ehines considered with r p t to 1

f or1n tl1 ll j ' 11 f tl l. . i\ ~

r

PART I.

ON TRAINS OF MECHANISM.

8. MECHANISM may be defined to be a combi­

nation of parts, connecting two or more pieces, so

that the motion of one compels the motion of the

others, according to a law of connection depending

on the nature of the combination. The motion of

elementary combinations are single or aggregate.

SECTION I.

SINGLE MOTION.

4. THE motion of every piece in a machine is

defined by path, direction, and velocity.

5. Of these, the path is assigned to it by its connection with the frame-work, but the direction

and velocity are governed by the connection of th moving pieces with each other.

6. This connection is unaffected by th velocity and direction of the pieces,

governs only the relation of their dir,ection s.

7. I n a given path there arc hut two dircct i ns, nd between the directions of two pieces th ere exist

two relation s : In the first, while one pjece persevcr s in the sa1ne direction, the other also re tains a constant

direction , and when one changes the oth er changes ;

in which cases the directional relation is said to he.

constant:

In the second, while one piece perseveres in the

same direction, the other changes its direction, or

vice versa ; in which case the directional relation is

said to change.

8. 'fhe relations of vel9city divide themselves

also under two heads, according as the velocity ratio

is constant or varies. ,

9. By con1bining these relations of direction and velocity, three classes are obtained, under '\ivhich all

the elementary combinations of mechanisn1 inay be

conveniently arranged:

CLASS A. Directional relation and velocity ratio

constant.

CLASS B. Directional relation constant, velocitv

ratio varying.

CLASS C. Directional relation changino·, velocity .. ratio either constant or varyi110-.

10. The pieces in a train of m h ani "Ill nr,

connected in successive order eith r b < r

by intermediate pieces, so that when th ' Hr 1 i ,,. in the series is moved , it co1np ,l ~ t h ~ '" \ tHl ,

t • I

6

ino 'hicb . .

ao· Ill O'l \ ' ('.' inotion 0 th third , l n<l

n.

11. 'rl1 act of O'i ino- motion to a pi i.

rin dri in~· it and that of rec i\ino· 1notion froin

L pi i t r1n d jollou iu 0 • it. I o th pi, or

part f pi ce which i appropriat d to th tran _

ml• 1· on of motion to th n ·t i tl1 tl1J·1· 11 l ' '· <~ 'I', anc th t which r c i s motion i th jollo , 7r.

I . '1-,h law of 1notion f one pi e in a train

may diffi r in any way from th law f 1not.ion of another pi c , and th chan()' is IB ctcd by the

mod of connection. Th systematic examination of the different cases unde1· which these chanO' s may

be arranged constitutes the principles of mechanis1n.

13. The patl1 described by any point of a

piece, with respect to the frame may always be con­sidered as circular; for a· rectilinear path i a por­tion of a circle of infinite radius; and curvilinear paths

in practice are always effected hy ineth ocls that fall under the head of aggregate motion.

14. The motion in a circular path inay be either

capable of continuation to an unli1nited extent in on~ direction, or may be limited by the natur of th

contrivance.

15. The tnethods of communicatin · inotion fj nn one piece fo another, tnay b includ d und '· fly' heads: -

7

l () -' J,J ( ) ON'l'A 'I.

~~ L JN, ( )o TA 1 '1\

W lA]•p NG ;0 F. ,. T RH.

KS.

ATJON.

16. If on p·ec move another by the actual

contact of their surfaces, these surfaces are said to li'de togeth r when in passing from one position to

another th distances of the consecutive points of

·contact, measured upon the two surfaces, are unequal;

and they are said to roll together when those dis­

tances are equal.

17. If one piece move another by means of an

intermediate piece, the latter is termed a link when

its extremities are jointed to the two pieces, so as

to turn on a given point of each in the changes

of their relative positions.

18. The intermediate piece may be flexible, and

apply itself to curve surfaces attached to the driving

and following pieces; in which case it may be termed . .

a wrappzng connector.

(A . connector may be la link at one end, and

may wrap at the other.)

19. Reduplication ,. is the principle of the pully,

which, being principally employed for raising weigl1ts, is better studied as a m'odifier of force.

20. 'Axes of rotation may be : (a) parall l : (b) not parallel, but meeting in direction : t n .

parallel, and never meeting.

(a)

(b)

J

(c) H boloid or Do

pur Wheels. Pinion . Cogs. A nular Wheels. Racks. Face Geer. Crown Wheel. Bevil \ -\!heels.

kew Bevils. Hook's Geering.

2~. By Sliding Contact. Forms o d ~ 1 Tee-th of Wheels from Epicycloi · &c.

.Leaat numbers of T----

Odon~ . · . Ollivier'• Property of In olu Cam-PJaie.. Sorewa.

9

Endless screws. Hindley's Screw. Oldham's Coupling.

23. By Wrapping Connectors. Belts, Bands, &c. Flat Belts always run to the highest part

of a conical pull y.

The advancing portion of the Belt is the only one that governs its position on the

pully.

Management of Belts when the axes are not parallel, Geering C~ains, Guide Pul­lies.

24. By Links. Links in this class can only be employed

when the angular velocities of the Driver and Follower are equal, unless the mo­tions are limited in extent to a small arc.

Dead Points. Three methods of passing the Link over the

Dead Points. Cranks.

. .

Bell-Cranks.

25. EXAMPLES OF COMPLETE MACHINES.

Stationers' Ruling Machine. Balling Machine. Drawing Rollers. Clark's Blower. Covering Machine.

10

Piemont Silk Reel.

India Rubber Cutting. Veneering Saw.

Self-Acting Lathe.

CLASS B.{ DIRECTIONAL RELATION Co TSTA ... "T .

VELOCITY RATIO VARYING.

ELEMENTARY C01\1BINATI0.1. S.

26. By Rolling Contact, Ellipses. Logarithmic Spirals. Rolling Curves in general. Teeth applied to them. Intermitting Teeth. Eccentric Spm· Wheels. Roemer's Wheels. Eccentric Crown Wheel. Rolling Levers.

27. By Sliding Contact Pin and Slit Lever. Endless Screw with Varying Inclin. · Pinion of one Tooth, Geneva Stop. Oldham's Geering.

i8. By L ·nks, Cam-Plat.

, J . . 0 01 - •

. B

Hoo

~ PLETE fACHI~ ~E ·.

un-dial .facbine.

er rane.

EC I ~AL R ELATIO.t CHA_-GING.

ELEllE ... TARY CO fBINATIO ·s.

a .. By &!ling l0ntact, angle Wheel, angle RaclL seaping Geer.

32.. v Unit Work, Cranks and Excentrics . .1omplex motions by trains of Link-work .

etent and Click. ever of agarousse. ·1ent Click.

SS, By SU<Eng Contact, Cams. Screw returning into it elf.

wash Plate. olid' Cam. am with equidistant p rail l 'r i1 n .

apem nts.

12

3 . B:l/ TYraJJpin~" Connectors, Curvilinear Pully.

35. E XAMPLES OF ColVIPLETE MACHINE .

Pedal Harp Motion.

Arithn1etical Machine. \Vinding l\f achine.

Throstle. l\1 ortising and Grooving E ngine. Planing Engine. Boiler P unch.

Pumping Engine.

Buhl Saw.

SECTION II.

ON AGGREGATE l\1I OTION.

86. THE motion of a point, with respect either to its path or velocity, may be considered as th resultant of two or more component inotions. If i happen that the latter taken separate! are m · simple and practicable than the resultaut n1 · n,

this may be produced by communicatin · mul ously to the given point the compon '

37. To carry this principle into that we should be able to oommuni~. ·-~ &&&." ...... .... ,.~ a driver· to a f ollo , wb th I · their respecti \'· p th i ..

18

BXAMPLE \

Long Pinion.

Long Endless Screw. ]~picyclic Wheels. Bands.

Link-work.

38. EAMPLES OF MOTION IN A SIMPIJE PATil

WITH AGGREGATE VELOCITY:

By Link-u1ork, Compound ()urve Engine. Hank Machine: Copping Machine. Lazy 'l, ongs.

By Wrapping· Connectors, Chi11ese Windlass. Differential Pully.

By Sliding Contact, White's Screw. White's Screw and Nut. W ollaston's Odometer.

By Epicyclic Traina in ,.enerat, Sun and Planet Wheels. Ferguson's Paradox. Planetary Mechanism. Rope Making, by tluddart' Ma hin r . Differential Index . Equation Clock. •

89, EXAMPI,EN Ol• MoT 10 1

&T& 1ATR.

14

Writing Machine. "frammel.

Oval Chuck.

Scr~w Cutting and Boring. Cylinder Boring.

Block-scoring Engine. Geometric Pen.

Epicycloidal Chuck. Rose Engine.

Curves of the Rose Engine. Shaping Engine. Anaglyptograph. Pentagraph. Cen trolinead. Green's Specular Engine. Dressing Brushes.

Parallel Motions.

ADJUSTMENTS.

40. The alterations and ~djustments of the com­munication of motion that may be required in a train are three:-

(a) To break off or resume at pleasure the com­munication of motion. (b) To reverse the direction of motion of the follower with respect . to that of the driver, that is, to change the directional 1-elation. ( c) To alter the ratio of ~elocity between driver and follower, either • by determinate or by r dual steps.

41. These changes may ·ith r b m d at any moment, or they may b

15

Cl(nss of organs esp -,.., •.•• ,N.ill . itself by means of a <Ii

Uy destined for that pur1l0se. .

4ii. (a) The communication of motion may be

i roken off.····· (l) By detaching pieces that remain united

during the action of the machine; as,

pullies or wheels fron1 shafts, or shafts

from each other by means of catches,

claws, couplings, or frictional adhesion.

(2) By disengaging the driver from the fol­

lower.

EXAl\IPLES.

In Wheels, by withdrawing the Teeth frorr1 con­

tact directly or laterally, or in the case

of contact without Teeth, by removing

the Pressure.

In Screws, by a Split Nut or Half Nut.

In endless Screws, by withdrawing the Wheel in the direction of _its Shaft.

In Pullies, by slipping the Belt laterally to a loose Pully; or by slackening the Belt.

In Link-work, by raising a Pin from a notch :

by dropping the fulcrum of a Lever, &c.

'··· 48. (b) The directional relation n1ay be chano,ed f)y a pair of Reversing Bevels, by Spur ,~n °1 lr . . ·v nee s, , J1 a pm of direct and crossed Belts, b shiftino-l ,Jiold>le hook in Link.. ork, c c .

. '6. (c) T he adjustm nt .. of th v I i ;~lilt either of (I) t' i·inin t .. b 11 It .11.0et part quirin · b

..

or of (") ( 1 •• \ l - •t.H ua ,·hauo·l'S 1 I . ~ . 'I :u H' l\ 0 t . \ . .

nac lllH' to lu.· st.o\>\ll'tl. · H qn11·1ue_· (1 t.ltt·

··~ x A M p I j I·~~ () F u n i\ l )\I A 1, ( '. II ,.\ N ( a;~ .

l )is'l\. nnd ltoller. l~qnitnugcntial ( ~ouoid.

~11ced Jlnllic~.

Pnir of (~on cl4.

(Jon~ nutl ( ~yll1ulcr. l~Xl)ttncliug lliggcr~.

Surface J_jnth ". A(ljnstnl>lc l.4cvcrs.

5. " · nm}llcs of mn ·hincs t~o11t:iini11~ ntljust-

m. nt for iiositiou, for limiting 111otio11s 1m<l self·

1dju tm · 11ts, &c. l~n rnv l" ltnliug l\fo ·hinc. 'utt'n · B11 -in • with J>i\itliug Pl:itc, or

•

T ·ni11 s of Chm1 r ' 'VJuds. Ill 1 1\' ]) iv id it l r h 11 ·i 11 c ·

W n · n in · n '1'1\1. .Ta qu rtl L~oom nutl Pund1i11. · 1\ pp1m1 t 11~ . ,- '} ()

t> A ll1' 1 I . (''f 'f () }~(J RC E.

,C)N JDl~;R~l> \,\TJTll ll};SPl~ 1

UT ~·~

•

6. Mov1N

their actions.

d Parts adapted to receive powers an

EXAMPLES.

Windmills. W aterwhc ls.

47. The Steam Engine. Newcomen's Engine. Watt's double acting Engine. Watt's single acting E11gi11e. Principle of working by Expansion.

The Marine Engine. The High-press11re Engine. Locomotive Engine. Rotative Engines.

48. Examples of the application of Statics to Machines.

Lagrauge's Demonstration of the Principle of Virtual Velocities. ·

Balances.

Printing Presses with variable Pressure. ~tting Rollers. Crushing Stones.

1~u,l.lies . and ·Tackle in general.

tl!" Jliction. Experimental Laws . . ,:Pn~ion increases by r t-i

18

to Prcs~ure: and independent of the \Te-1 oci ty, and of the Extent of Surfaces in <~on tact.

50. Employmen of Frie i n.

Brak .

Fricti n of rd wrapped ro' nd. a ylinder. Ca tan.

hitworth' Drilling lacbine.

51. Diminution of Friction. Perrault s Pully. Friction Wheels.

52. To measure the force exerted by Iachines, or required to move them.

Dynamometers of \Vbite Pron , . f orin, and others.

53. Dynamical Experiments of Atwood, mea­

ton, &c.

54. To govern the velocity of fachines.

Pendulums. Balances.

Escapements. Revolving Pendulum, or Governor.

Fly. Flywheel. Bottlejack. Striking parts of Clocks. General Construction of Clocks and

Watches.

THE END.