Effect of handwheel sizes on the turning speed.: NA

Calhoun: The NPS Institutional Archive
Theses and Dissertations
Thesis and Dissertation Collection
1952
Effect of handwheel sizes on the turning speed.
Viana, Paulo Viriglio Didier Barebosa.
Purdue University
http://hdl.handle.net/10945/14092
- .'.-"n^iMar.
i:
EFFECT OF HANDWHEEL SIZES ON THE
TURNING SPEED,
PAULO VIRGILIO DIDIER BARBOSA VIANA
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by
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In Partial l^af Ulnant of tha
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of
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Th« author is
grttatljr
indebted to Doctor M. £• Mundel
for his assistanee in shaping up the ideas leading to this
thesis, and to Professor H* T. Aiarine for his cooperation
and Tery eapable supenrision in the subsequent tasks leadittg
to the present outcome*
To Doctor I« ^. Burr the author is grateful for his
suggestions on the statistical analysis of the observed
data.
The author also wishes to express his appreciation to
Carl Kromp, H« M« Sousa, Oscar Eroaberg^ J* B» Maehado,
R« H, Doolittle, J* House, C. Borba, S* G« Lindquist, A. A*
Caalnada and George Serban, Jr« whose cooperation enabled
the author to collect the experirsental data on which the
present work is based*
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TABIE OP G0JIT1SKT3
ABSTaAC?
mrr
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i
PURPOSE
3
SQUIPMSHT AHD PROCKDU
4
JE
RS3ULT3
10
COIiCLOSIOHS
19
APPIHDIX A. COMPLETE DATA
HAHIWHBKLS AHD
fO'd
AU, OPSRilTOaS,
20
TOftsiUES
APPSHDIX 3. STATISTICAL ANALYSIS 0? Riu3ULTS
26
APPfiimiX C. AJPPLICATIOH Of LAGRAKQE»S INTSHPOLATIuH
FORMULA 70 iSSTXMATE
MAIimZIMG THS
TH?.
fURillllO
aADII
Oi*"
HAJIDWiiKKLS
SPEED
29
APPKHDIX D. SAMPLE OF XTHOaaAPH PAPER
32
AK»8»DIX B. PHYSICAL GHAftACTlSaiSTIGS OF OPSKATOHS
33
BIBLIOORAFHT
34
0^
6
T'"''."
^J^:,i^«GJ:
A.
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,
LISTS Of /iaU.B3 AND TABUiS
Liat of Fl^»r««
1*
Tho ^xperiaeiitaX S«t-up and the ICjrwograph
2«
7h« Hoadwheels* •».•
>•
Operators Average Tiaa p«r Eiiirolutlon versus
Iladil of Handwhselfl
,
4«
5
•.•••
16
Rslatlonship Between Torques end Grenkliif; tadll
of H&adwheele for the Condition of Maxiimm
Turning Speed
•
17
Ust
of Tables
Table
1*
2«
?•
Page
l^eans and littdges of Obsenred ?!«•••
Torqtiet 0»9 lii'^lb
11
Means and Ranges of ObserTed
Torque: 10,7 ln*lb..
12
Tlcies.
Means and Ranges of Obserrred Times*
Torques ?$• 2 in«lb« .
•
.
4«
$9
6*
7«
13
Means and Ranges of Observed Times*
Torques 57*4 in«lb, «.*....
14
Means and Ranges of Observed
Torque: ^4*6 in*lb.,«...
15
riiaes.
Torque 0.9 in-lb. Gomplete Date for All
Operators and Randiflieels
Torque 10.7 ln«lb« Oof^lete Dat« for All
Operators mid Handnmeels
*
#•
6
21
• « •
22
Torque ?d«2 ln*lb« Co^lete Data for All
..•••• 23
Operators and i^«[id«rheels
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Tabl«
9*
10,
11«
P«t«
Torque 57*4 in-Ib« CoiBpI«t« Data for All
Oporators &iid HaBdnSuiala
Torqua d4.6 in^-Ib, Gonpleta Data for All
Operators and Handifieiaals
Physical Character isties of Operators
24
•
25
••• 33
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AaSTRACT
Til*
purpose of this thesis is to inyestigsts th« offset
of the dlsneter of hsiuliihools on the mtotlmm speed of turnlac that an operator ean inpart to a handwheel for different
tor^ttos applied to the handwheeX shaft*
Five ha&dwheels ware studied ranging in eranking radii
froa 1.625 to 6*375 i&ehos*
FITS different torques v^re used rattgiag fron 0*9 to
^4*6 in-»lb*
f«a subjects were tostod*
fresi
The subjeets were volimteers
the aale population of Purdue University*
Based upon the results a fanily of curres was drawn
•iMwing the relationship between the tiae per reTolution
and the radii of handwheels for different torques*
iniaa of these eurreSy
The
aa obtained by loeans of Lagrange's
interpolati^i formula » w«re used to draw a graph showing
the relationship between torques and radii of handwheels
for the condition of aaTtJimm turning speed*
The analysis of the results led to the following con-
clusions :
For each individual the maxiaaia speed of turning
(MMM
to be affected, within the range of the present esqperii&enty
by two factors; a} The auseular force required for turning
the handwheeli b) The radii of the handwheel*
There is a strong indication, statistically
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so%o«Mutl ow4
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•ignlf leant at th« 1% l^val, that, for a glTen torque,
«n« apooifle hanchrhaal among thoAa tastad producas tha
ttaxiamm turning apaad*
xkBm
of tba
aaxionfie
Thla faet appaara to juatlfy tha
turning apaa4 aa an objaetlya eritarion
for the selection of handwheals.
Tha eunre showing tha relationship between torquea and
radii of handwhaala for the condition of auuciaua turning
•paad should provide an approximate solution for the prob«
las of selaeting that handwheel whioh should allow for the
•axisuB spaad for a p&rtioular torque*
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SrFSCT OF
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THE TUKUUIQ 3PBED
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laTRQDUCTIOX
The study of tho performance of aaehlne control de-
lees
first caught the attention of inveatigators aa early
aa 1926.'
'
«lth the outbreak of World
.^ar
II a concerted
drive waa aade to eliminate nmeh of the uncertainty impair*
ing the utilisation of
•qiii|»Mnit«
hvmm abilitiea
in the o{>eration of
To thia end, isany inYeatigationa have been
pw^
foraed on control deyicea aueh aa iaioba» XcTers and hand«
wheels
In 1946 Hainea and Eoaenblooa^
'
atudied the perfor*
aanee of handiflieela operating at aaxlwiw apeed and alao at
a Moderate c<m8tant apeed*
In this
itfork
they arrived at a
graph showing the relationship between the turning speed
and the turning force required when several subjects oper»
ated at BaxiaRa speed a handwheel 1.5 inehea in diameter.
Thia graph indicates an approxinate linearity between the
turning speed and the turning force and also a wide varlai»
bility awBAg individuals.
However » because of the wide
variability SAoag indivlduala, Rain«a and Eosenbloos felt
(1) Kuhne, w, P.^ Studies Concerning the Optiauffl Determination of v^eaetions of Force on Controls of Machines . Indus*
trielle Psychoteehnick, v3, n6y pl67*172» June 1926*
(2) Haines f 4. and Eosenbloon, J. K., Ideal Torques for
Handidieels and Knobs , Machine Design 9 vld^ August 1946.
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that it w«8 worthless to pursue further inTestlgstlon of
the operstlon of h«ietwheels et ae«iwmii s]>eed«
laTesti^ation
In their
at a aoderate ooastant speed , they attenpted
to introduce a seleetiTO criterion for handwheels based on
tkm sabjeetive feelings of the operators.
In 194^ en extensive study was undertaken b^ Heed^^'
OB the faetors influencing rotary perfomanoe.
ieed's work
is a step forward froia that of Eaines and Rosenbloom in the
MMiee that it provee the existence of a definite relaticaship between the cranking radius and the maglmwt turning
speed of handtfheels*
In his eseperiaent Reed used handwheels
ranging in cranking radii from 0*394 to 7*^(1 Inches snd
torques ranging ttom sero to 4»34 in<»lb*
Based upon this prerious research there appears to be
m Aeed for further investigation and the introduction of a
basis for an objective selection of handwheels to operate
at Baxittun speed*
O) Reed^ J* D,, Factors Influencing Ilotary Performance
The John Hopkins University » Fh«D* Dissertation » 194^*
,
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PURPO^iB
Th« purpose of this th«si« is to InTestigat* thm
f«et of the eranking r«dii of
•p««ol
whoal*
handnrtitt^Xs
•f<»
on th9 aaxiMiui
of tiirning that an oparator can i^art to tha hand*
»
S4UIPMS1IT AHB Fm)C£DU,HE
Tlui
apparatus (Fig* X) uaad consisted of a shaft to
•«^port the handi^eal and a bait arr«ig«aaiit daaignad to
pansit tho application of different torques to the shaft
of tha handi^eel*
The torques ware aet by var/lag tlM belt
tension with the aid of tumbuekles, (see Fig* 1}«
The
shaft was supported by self-aligning bearings to alalalse
any possible effects resulting from the deflection of the
shaft under h^ary belt tensions*
FITS handwheels (Fig. 2) were used, with cranking
radii of 1.625, 2.250, 3.062, 4.500 and 6.375 inches,
TiMse handirheels will be
r^fem^
to as handwheels 1,2^3
4 and 5» respectively.
The handwhaels had f laced handles which had different
shapes as can be seen from Fig. 2.
Fixed handles were not
desirable for the present experlaestt because of the variable
friction between the hand of the operator and the handle of
the handwheel;
this difficulty was overcome by providing
the operators with a cotton glove*
Five torques were used: 0*9 » 10.7 » 2{(.2, 57.4 snd
These were d^amlc torques as estlnated
<t4*6
inch-pounds.
fros^
the readings on the tension sealea when the handwheel
ahaft was being turned at the Esaxlmum speed by an operator
•f ai^proxlitately average strength.
The dynaaio torques
mmmA^jsOi
9
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ad IK
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fig, 1
TSI
UmonTAL
SET.UF
AffO
THS KWOiXUVU
Pig. 2
THE
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w«r« foimd to be r^ry close to the static torques as ean be
seen from the following tablet
Zfeft
IMM
DyTiande ?02*que8:
10,7
20 ,2
57*4
^4*6
Static Torques:
10.1
2«,2
59.0
09.0
liifiXiSt
The K]rmogx*eph^^' (^ig«
Bp—d of turning of the
tisins dSTice a
buaB|>er
D
was used to measure the
handwheel.
In order to use this
was attached to the hanMieel shaft
la saeh a war t^^t ia each revolution this bu^^er operated
a niero switch which closed the circuit for the Iqrasgrapfe*
The time for each revolution oould be measured then by tlM
distance between each pair of pips in the kyasgraph paper*
(See appendix ? for 8aB9>le}
One eentizBeter of kynosrapli
paper represents 0*0436 seconds of tins*
at, tf ^ft^lffia at
yyb.1e9^ff
The subjects used in
trom the
siale
thet
experiment were voluateers
population of Purdue University.
All were
right handed and had no injuries to their hands or aras*
Thegr
varied in age from 29 to 39 years with im average of
31.9 years.
Their averace height was
fro« 5 ft-0 in to 6 ft-2 in«
5
ft-10 in sad ranged
The elbow height of the
operators varied froa 40.5 to 46 in with an average of
43*2 in, (for the physical characteristics of each operator
see Appendix B)
For each eicperiamit the han(h#heel shaft was adjusted
(4) For a discussion of the Kyaograph, see Barnes, H.M,.
University of Iowa Studies » Bulletin n-^^ (February 1936
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to b« at th« halght of th« operator* a olbo*r bocauso It was
aasuBiod that th« albow Is the natural esnter of rot st ion
for ths forsarm in tho oparation of handwhsals*
Tha opar-
ator was raqulrad to stand in front of the handwhaal with
tha right are aad the tip of tha right foot in tha vartieal
plans oontaining the handwhaol shaft.
?he Lxpy of tha fast
ware 15 inchss apart and d inohas away
fro29
plana containing?; tha handwhool,
ator was instructed on how
-uo
tha vortical
^'sfore each run the or>er-
srasp u.
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quired to parfonn one or two revolutions to gat the fselias
of that torque which was sst for each run.
Than,
ator was encouraged not to attais^t to reach the
tlio
opsr*
aaaciwiMi
spssd of turning in tha first two revolutions but froB than
on ha should apply his maxinnim r^hysleal exertion in order
to iapart the saximusi speed to the hsftdntissl.
The objective
of this presaution was to reduce the muaoular strain usually aasociatsd with the instantaneous application of a great
macular force*
iCach
operator perfor^t&d 20 runs in which
the different handwheels and torques were rendosly dis-
tributed*
These 20 runs, except for the randomisation
followed tha scheciQ illustrated in tha table below:
•»••
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yfuffft
?tnr»r
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•vJt^&9tdo
»f:
Torques
HandwhMls
0.9
10.7
2d.2
57.4
^4.6
1.625
1
2
3
2,250
4
5
6
3 •062
7
d
9
10
4.500
11
12
13
14
15
6.373
16
17
Id
19
20
tlui rttasea
for th« blank eella In tho tabla abova
la that It waa found l«praetioal to uaa aoma of tha aiaallar
haadwliaala for hoaT/ torquaa.
Tha duration of aaeh run waa about 3 aaaonda «nd Uia
Intaz^al botwean tha nana was 3 minutes.
Hit S^MP^JM ?*y9a*^"J^
For aaeh
nwi
6 obaarratlona wara nada of tha tlna ra«
quired to cooplate the rarolutiona fron tha 8th to tha 13tli
incltialya.
Therefore, for aaoh aubjeet 20 eella ware ob-
tained with 6 obaarratlona par call.
In all, 10 aubjeets
wara taatad aaking a total of 200 aalla with 6 obaanratioaa
aaeh.
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The
dftta
for nil operators » handwheola and torques
are mMBarlsed In Tables 1 to 5*
The ocuc^Xete data fttm
whieh these tables were prepared Is Included In Appendix A*
(For the hoaK>geneitr of aeasurenent error see Appendix B)
Using the aean tliM per reyolution sHrag all operators
the faallr of eiunres shoim in ?ig* 3 was obtained,
FroM
this fanil/ of otinres it ean be seen thatt
a) For ttiy giren sise of a handwheel, tho tiiae for
oespletion of one revolution inoreases as the torque inereases,
or,^
what aaounts to the saiM thing, the mpn^d of
turning decreases as the force required for turning in*
ereases
b) If the torque is sero» or nearly so, the time per
revolution increases with the radius of the handwheel*
Tables 1 to 5 thow a wide Tariabllity aoong individuals
in their abilities to iapart the
a hoQdi^eol*
maximm turning speed to
However, they show also a strong indication
that, for a given torque, one specific handwheel sneog
those tested produces the
wra»li«i«
turning speed regardless
of the physical strength of the operators involved* (The
significance test for speeds of handwheel s is presented ia
Appendix B)
On the basis of this fact a graph was con-
structed (Fig, 4) relating the radii of handwheels and
torques for the condition of aaxiauM turning speed*
The
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Fig.3
OPERATORS AYER.IGS TIME FEE REVOLUTION
VERSUS RADII OF HANFa^HEELS
70
34.6 in- lb
(0
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17
RELATIONSHIP BETWEEN TORQUES AND
CRANKING RADII OF HANDKfHEELS FOR
THE CGNDITIOK OF MAXIMUM TURNING
SPEED
o
M
s
5
en
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o
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20
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TORQUE IN INCH-POUNDS
1
60
TI
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04I
;-HOWI MI
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radii of hai4Mli««X« ua«d in plotting this graph vmrm obtalnad by alalaltliis hiLgrsmga* b Intarpolation formula ^'^^
aa appllad to the eunraa akatehad la fig* 3« {limt^r to
Appandlx C),
This graph probabl/ proTldaa an approxlnata aolutloa
to tha problan of aalaeting handwhaaXs with a eranklng
radii ranging fron 2 .46 to 5*07 inohas to operate at aaxl«
MM
apaad undar a conatant torqua In tha range lc«^ to
57.4 in^lb.
(5) Scarborough J J, B,, Kunsarlcal Mathamatlcal Analyaiai
Tha John Hopkins Press, 1930, pagae 72 and 116,
r?.5?'£;1'? •*^
19
CONCI.USIOIid
!• For •aeh individual tha Bmitiimtt 8p««d of turning
to bo af footed, within
tlio
raago of tho prooont ox-
porlnent, by two foetors:
a) tho muooular foreo roquirod for turning the handwhooX| «id
b) tho radii of tho handi^ool*
2* Thore ia a strong indication , statiaticiiilly aig*
nifioant at tho 1^ lovel, that, for a given torque, one
•pooifie handwhool
turning opood.
awmg
those tested produeoa the saxinwi
This fact appears to justify the use of tho
aximui turning spood
as an objective criterion for the so*
loot ion of handwhoola.
3* tfithin the Xioits of tho torques and haadwhool
radii indicated, the curve in Fig* 4 should provide an ap»
proximate solution for the probloa of soloeting that hand*
wheel which should allow for tho
a particular torque*
auudsaiia
turning speed for
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26
Ammoix
B
STATISTICiiL ASALXSIS OF R
3
To find out whether wo have hoaoctaelty of neesurement
error we take the rimge H, for each cell, and then we eaXeulate ^9 I.e. I the wean range for all eells*
Then we eaa eet
the Upper Control Lialt for raagee in aavplee of six observe^
tlonaj^^^
OCI^ -
D^ff -
2.00
f•
6.2dl
We want or hope that a not exeeaaive nuiober of the
200
11*8
la above the UCL^*
If ao, thert^ we have hoiaogenelty
of Bwaaureffient error.
Aa can be aeen from Tables 1 to 5» five points are
above the UOL.
The probebllltiea of a point being above
and below the UGL ares
''^
P(a point above UCL) • 0.004 approximately
P(a point below UCL)
*•
0.996 approxiaately
Then, In 200 aaa^lea we expect 200 x 0.004 • O.d above the
UCL.
Observation of the data diacloaea five above » which
raiaes the question aa to whether thia la exeeaaivo.
(6) Grant, S. L., Statistical auality Control;
1949, p. 537.
MoGr^
Bill.
(7) Pearson I E, S«, The Percentage Liaita for the Distribution of Range In Samples from a Horeial Population , Bion^trikay
jZkt p404« Horenber 1932.
K
%XMh
^
.f.l
:.
^aiASBiii£mS^
Ml
1- !•
9lfO bf
U"
>
^«
%•*?.%
-
c^>
l./^. .»,-. (^
^
AiVdtiA 4»i
«i«e.
'JOS
.(/;
Tfi
-'^
J.
A
t
d90*n
»VO<lr.
-
nl jHwdT
'J*
^UXL^
•fit
'^JS'HJ
X
27
Th« binoMlal ooiild b« us«d to find the probAbllit/
of five points or sorv to bo obovo tho UCL^ or w« ean uoo
tho Poiooon as an spproximAtion*^
'
In our esso wo havos
up
• 200 X 0.004 * Q*B
P(4 or loss, np
• O.d) • 0*999
?i5 or aero, up
» 0«d) « O.OOl
This is signifioantly r^r^ and iadicatos soao dofinita
toodooey to non*hoiiiogonoit7'«
This tendoncy to non«hosiOgon«ity is a definito ono,
but not Tory strong*
^
3o wo will continuo to uso
but
wo sbould bo soiaswhat aoro consorratiTO in our Intorproto*
tlons boeauso of this*
s4iff^iAc¥*<?^
tff fftf
fgE
j^
ffpn4 Si ^m^ii>^nX§
To tost, for exaniplo, vhothor
or n*3
hsiutoirhool rfiz
givos lowor tiaos (or highor spoods) for a 10*7 in-lb
torquo wo find X2 * aosn tlao for all obsonrations asdo oa
haaibfliool
nS2 for tho torquo undor oonsidoration*
this is
to bo eoaporod to that for haadwhool nS3«
'4%
asko tho tost by using an astiiaatoo
(T^,
1*«*, tho
population standard doYiation for vfithln ooll variation*
For saaplos of siso 6 wo havos ^^'
{$)
Grant, E* L*, ibid*, p542*
(9)
Qpont, s* L*, op* eit*, p635»
.»,
tm motm
•1
.
:
.» i-'
tini;
2«
If t Is larger than 2»5d|^
^
In sls^^ th^n w* h«v« 0l»*
»%rw%d a t which bf chanoc alono would ooeur !••« oft«n thas
0B« tlK« la XOO and tha dlffaranea batwaen tha liaaaa of tha
obsanratloRs auula on haiiAwhaala 2 aad 3 la al^nifleant at
tha X% larel.
Aa can ba aaan fron th* eurvaa In Fig* 3t tha dlffaraaaa
juat tastad la about tba asallaat*
So It saans to ba hardXf
aaaaaaai*/ to apply tha t tast to any othar pair ot hand*
whaala*
(10) Tlppatt* L, G» H,, Taehnologlcel Applications of 3tatiatles; John ^^llay k Sons, 19 50, paga 8«
..N
w
•*
m4^
7
•Vftf< 9%f
tt^^
nA.t**f.-
Jf*af>i'
't;
•iawitl>
%t
xr
9aif««»«
"*i>£S£-
:;?,l:
q
)
t
29
APPBifDU C
getlaatiloo of th« mlnlmuw tiate v>er revolution ualnn;
a) Torquos
57 .4 in«-lb
Observed points
x^ - 3.062
r^ - 64.3d
x^ - 4.500
Tl - 53.77
Xj - 6.375
Xg • 5^.04
Lttfran^e's interpolation fonaula:*
'
fix) • A^(x«Xj^)(x-X2)^
Aj^(x-x^)(x-X2)*
A2(x-x^)(x-Xj,
fo
A^ o
(x^-Xj^jCXq-XjJ
.
*2
^0
.
^
(Xg-x^ilXj-x^)
After substituting the nusierical values and rear-
rmsiiig tho terms we obtain t
ill) 3earborougn, J. B. op.oit.
oJacfiJi
'i'^ftf.V^
SSUu'
«•..'
**
ry^
30
f(x) • 2.95 rr - 29.9 x
This function has a mlnUnw at x
12«i.9
5*07 » as is ob«'
taiiMd by diffarantlating and aattlng tba darlvatlva aquaX
to laro*
b) Torquo:
2S.2 in«Ib
Obaarrad f3olnt8i
Crank In «^ radii
Av^raga tlaa par reYoluti<»|
%^ - 1.625
^o" 69.44
x^ - 2,250
5^1'• 55.t9
X2 • 3.062
^2' 46.14
X3 - 4.500
^3" 48.50
X|^
-
•
•
^'
• 6.375
•
54.69
Folloirinf tha procadura outXinad in tha praoaading paga wa
find:
f(x) - -0.2353x^
2.4598^ - 2.6622x^ - 32.2i23x
•^
120.0109
Thia function has a ainiBRm at x » 3.576.
c) Torqua: 10.7 in*lb
Obsanrad points:
Crankin;^ radii
Avarani^a
tiwa par ravoXution
x^ - 1.625
y^ - 46.61
• 2.250
j^ « 40.66
X2 » 3.062
y^ • 41.87
Xj • 4.500
y^ • 45.85
x^ - 6.375
y,.
Xj,
- 54.17
»
one
•
Bi&r!
m-:
"ti^^'^tf'"'"
«lfr
><>"'«»
A'
llUi
•»il^
«w mn^^
^XO.OSII
«*
•
?<
,1
•%nihmf.
'
1
ilO tfruffMV^t:
*^d:i
x>
di
Jfcfcf
•
«x*.
V '-^
«
,>•.-
«
.J.
5:^
31
For thi9 data w« get:
fix) « 0.5059x^ - d.254Qx^
This function has a
sainisois
4d.4284x^ - U8.5221x
at x • 2»45d«
143.2163.
i
.lb
32
APFSNDXZ D
89.3
imn
ftAMFU OF KINOGttAPH PAPEfi
)
33
APPEKOU X
T«bl« 11
PHTSICAL CHARACT&ftl3T203 or QFIHAT0R8
OPSRATOa
HSIGHT
«i&iaHT
pounds
ELBOW
HEIGHT
(inchsa)
(years)
(ft-in)
A
31
5-7
170
42
B
31
5
- 7
155
42
C
35
5
-U
165
44 1/2
D
32
6.2
210
46
1
2$
6-0
190
46
r
39
5
-10
175
44 1/2
31
5-7
160
42
H
34
6-0
205
44
I
29
6-0
190
44
4
29
5 - d
164
40 1/2
(
"
"•*"*"
1
5
«\X
M
i^A
UPI
I*; "^Hgt-
T
-J*-
a«j
xfS^
S\i
MWi«lta>
34
Biai...
at
!•
Kfhne, v/, F., 3tudl«a Oonceming th« Optimuni D«t«naination of Httaetlons of Foro« on Controls of liaohinos^
Industrielle rsychot«chnick, r^^ n6» pl67-172, June 1926,
2«
and Hotonbloos, J* H,, Idoal Torques for
Handnrhoola and Knobs, Machine Design, vld| August 1946*
3«
iieed, J* D., factors Influencini; Kotary Performanoe,
The John 'fopkins University, -h.D. Dissertation, 19id»
4*
Barnes, I:* K., University of Iowa "Studies, Balletin
n.6^ p37, February 1936,
5*
Scarborough, J. a», Nuaerieal Math^^Aatieal Analysis;
Tho John Hopkins Press, Baltiaore, IM., 1930*
6,
Grant, ^. L., itatistical quality Control ; MoCraw Hill,
Hew York, 1949»
7*
Tippett, i*. C, H,, Technological Applica ions of ita*
tistics; John Wiley k iions. Hew York, 1950*
$m
Pearson, '^.* 3., The Percentage Livits for the Distribu*
tion of ilange in "anples froM a Nomal Population,
Bloaetrika, v24, p404, November 1932.
i:ailn«s»
A*
•t
.>'
PlP^^itM/^^;rV..::.:vrVvV:/
IhrsV^S
1
limdwhrrl
st.-rs
on the turning
3 2768 000 99395
DUDLEY KNOX LIBRARY