INSTRUCTI 0 N MANUAL
1ffM.17
Crank & Con-Rod
Apparatus
Crank & Connecting Rod Mechanism
INTRODUCTION
Early examplesof mechanisms
to convert an up and down motion to rotation were the treadle
drivesfor a wood turner'slatheor a tinker's grindingwheel on his barrow. With the inventionof
the steamenginethe needfor a well madeconnectingrod and crank was evidentin order to use
the reciprocatingpistonto drive rotating shaftsfor mills and railway enginesand other machinery.
Now the most commonuseis in the internalcombustionengine.
To designa crank. connectingrod and cross headit is necessaryto detenninethe velocity and
accelerationof the moving parts. Generallyit might be assumedthat the crank rotates at a
uniform speedaided by adding a flywheel to the crankshaft. A more accurateanalysiscan be
madeemployingtrigonometricaltermsto expressthe relationships,and by taking accountof the
fluctuatingspeedof the flywheel.
LIST OF PARTS
The standardset of itemssupplied(HTM.17) consistsof:
1 - Crankand ConnectingRod Apparatus
HTM.17. Page I.
Issue I. September. 1993.
APPARATUS
This experimentalsimulation of a crank uses a circular steel protractor with a central pivot
graduatedin 10° divisionsand numberedfrom 0° at the "outer deadcentre" in an anticlockwise
sense.The crank is a bar attachedto the protractor andwith tappedholesat threeradii, 25, 31.25
and50 rnm. Thereis a bar constrainedto slide along a centreline in the mannerof a pistonwith a
moveablelinear scalealongside. The connectingrod is pinnedto the piston at one end and at the
other end has three holesfor the crank pin, thus providing the different lengthsof 200, 225 and
250 rnm. The whole apparatusis mountedon a steelchannelbaseplate with a supportthat holds
the apparatusupright if requiredfor classdemonstrations.
EXPERIMENT
OBJECT
Therearetwo partsto this experiment
In the first placethe object is to determinethe relationshipbetweenthe rotation of the crank and
the piston stroke, and to see how this is affected by the crank radius and the length of the
connectingrod.
The secondobject is to studythe link betweenthe angularspeedof the crank and the velocity of
the piston.
PROCEDURE
Part 1. Crank & Piston Displacements.
Set up the mechanismwith the minimumcrank radiusand length of connectingrod. Note these
valuesandtheir ratio. With the crankat the outer deadcentreadjustthe pistonguideblock to put
the displacement
readingof zero againstthe piston mark. Turn the crankthrough 10°andnote the
displacement
in table 1. Repeatthis at 10°intervalsup to 180°.
Table I
n. rod I (mrn)
rank r (mm)
tion
Crank Angle
9 (O)
Displacementx
(mm)
(mm)
(mm)
0
to
20
Repeatthe aboveprocedureusing a connectingrod of 250 mrn with a crank radiusof 31.25 and
50 mm,recordingthe readingsin table 1.
HTM./7. Page 2.
Issue /. September./993.
Part 2. Crank and Piston Speeds.
Commencewith the connectingrod at 200 mm length and a crank radius of 50 mm. Zero the
displacementscaleasin part 1 andtake readingsat 20° intervalsof the crank arm from 0° to 360°,
enteringthe displacements
in table 2. Repeatthe procedurehavingchangedthe crank radius to
25 rnm(somepart 1 readingscanbe copiedinto table2).
Table 2
Con. rod
/ (mm)
Crank r (rom)
Ra .
bon:
:
I
Crank Angle
CO)
I
0
I
;
~
I
40
Increment
Dispt.
(mm)
(mm)
Dispt.
(mm)
Increment
(mm)
60
RESULTS
The analytical solution of the displacementsof a crank and connectingrod can be made as
follows:
Let x be the piston displacementfrom the outer dead centre point Q, and let the length of the
connecting rod I be nr.
x = 1coscj)- rcos9 - (/- r)
and r sin e = I sin <I>
This valueof coscI> canbe derivedusingthe binomialexpansion
cos 4>=
-.sm
1
. 29 --.sm 1
2n2
Sn4
.
4
9 -
HTM.17. Page 3.
[...sueI. September. 1993.
As n will alwaysbe severaltimesgreaterthan unity the third term andonwardare usuallyignored.
hence
r=r(1-cose)-nr{l-cos41)
,
:rt
-cos9-
sin2e1
~)
!~ ':iUmlQ""
;;;",...c~:;~j,"
{"'\{"f
';'~"
\
)
The velocity is obtainedby differentiationusing
.Q!= ~.~
dt de dr
Thus
= o>r(sin 6 - sin 26
(2)
~)
Comparethe experimentalresultswith the theory asfollows.
Plot the resultsof Part 1 on a graph of displacementx againstthe crank anglee. Checkthat the
ratio of the displacements
wheren is constant(that is n = 8) is 1.25,the scalebetweenthe two set
ups. At angleswhich are multiplesof 300calculatethe theoreticalvaluesof x to comparewith the
experiment.
In Part 2 it is necessaryto evaluatethe "velocity" of the piston. Assumingthe crankturnsthrough
200per second,then the changein displacementfor each200 interval is approximatelythe mean
velocity at the mid-point of the interval. Hence plot the incrementsagainstcrank angle in
accordancewith the rule
Xn+1 -Xn
against
9"+1+9"
2
noting that half of the incrementswill be -ve. Calculate the theoretical velocity at 900 for
comparisonwith the experimentusingthe conversion
(0=
~
60
rad./s
20 r.p.rn
where N= 60 x 360
OBSERVATIONS
How well did theory and experimentcompare? Would the accuracyof the approximationfor
cos havebeenpossible
to evaluate
by theapparatus?
<I>
/ITA/. 17. Page 4.
Issue I. .september.1993.