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Sep 12, 2014
Kinematics of a slider-crank mechanism
Group Members:D PotterA Pirlo
Date of Experiment:15th August 2005
This report presents the results of a theoretical and experimental inves-tigation of a single-cylinder, four-stroke internal combustion engine. Atheoretical expression for the piston displacement as a function of crankangle is developed. Results from this expression agree with experimentalmeasurements to within 3.3% of the stroke of the piston. The timing ofthe opening of the inlet and exhaust valves relative to the piston motionwere also measured. Both valves are open at the same time over a 20
angular displacement of the crankshaft when the piston is near top deadcentre between the inlet and exhaust strokes.
1 Introduction 4
2 Theory 42.1 Four-stroke cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Kinematics of the slider-crank mechanism . . . . . . . . . . . . . 5
3 Apparatus 6
4 Procedure 7
5 Results and Discussion 9
6 Conclusions 13
A Apparatus measurements 14
B Raw experimental data 15
C Derived experimental data 20
The purpose of the slider-crank mechanism is to convert the linear motion ofthe piston to rotational motion of the crankshaft. One common application ofthis mechanism is in internal combustion engines.
The first aim of this experiment is to investigate and compare the theoreticalkinematic relationship between the displacement of the piston and the angle ofthe crankshaft with that measured for a single-cylinder engine. The other aimis to investigate the four-stroke cycle by simultaneously observing the motionof the piston and valves.
2.1 Four-stroke cycle
An internal combustion engine operates by burning a small amount of a high-energy content fuel, such as petroleum, and using the energy released to drivea shaft. The four-stroke combustion cycle, developed by Nikolaus Otto in1867, is commonly used in petrol-driven internal combustion engines.
Figure 1: Four-stroke engine cycle. Reproduced from the engines manual 
The four strokes in the Otto cycle are shown in Figure 1. These are:
Intake: The inlet valve is open and the piston moves downwards, drawing in amixture of fuel and air into the cylinder.
Compression: Both valves are shut and the piston moves upwards to compress the fuel-air mix. The spark plug fires just before the piston reaches its top deadcentre postion (the position where the piston reaches its maximum ver-tical location). This initiates the combustion of the mixture.
Power: Again both valves are closed. The hot gases due to the combustion of thefuel air mix drive the cylinder down. The connecting rod transfers thislinear motion of the piston to rotational motion of the crankshaft. Thetorque thus applied to the crankshaft can be used to drive a mechanism,such as the blades of a lawn mower.
Exhaust: The exhaust valve opens and the upward motion of the piston drives theexhaust gasses out of the cylinder.
Note: The terminology used to describe of the four strokes varies in differentsources  .
2.2 Kinematics of the slider-crank mechanism
The slider crank mechanism, shown in Figure 2, is a kinematic mechanism. Thepiston displacement from top dead centre, x, can be determined from the geom-etry of the mechanism, in terms of the lengths of the conrod, L, and crank, R,and the crank angle, . From the geometry and noting that = = 0 whenx = 0, x can be expressed as
x = RR cos() + L L cos(). (1)
Figure 2: Slider-crank mechanism.
Also from the geometry, it can be seen that
L sin() = R sin() (2)
[L cos()]2 = L2 [L sin()]2 . (3)
Substituting for L sin() from Equation 2 in Equation 3, leaves as the onlyvariable on the right hand side of the expression,
[L cos()]2 = L2 [R sin()]2 . (4)Equation 4 can be substituted into Equation 1 to obtain the kinematic equationfor the slider crank mechanism (Equation 5),
x = RR cos() + LL2 [R sin()]2. (5)
Equation 5 can then be rearranged by introducing another parameter, n, theratio of the length of the conrod, L, to the radius of crankshaft, R, as
x = R
1 cos + n1
)2 , (6)where
Equation 6 is the kinematic equation for the slider-crank mechanism given inthe practical handout . The values of parameters R and n are determined bymeasurement of the Briggs & Stratton engine.
A single-cylinder, four-stroke Briggs and Stratton Engine was studied in thisexperiment. A side view of the engine is shown in Figure 3. A top view of theengine, which shows a close up of the cylinder, piston and valves, is shown inFigure 4. The head has been removed and a dial gauges have been attachedto allow measurement displacement of the inlet and exhaust valves. The pistonand cylinder are also accessible for measurement. A protractor is attached tothe crankshaft to facilitate measurement of the crank angle.
The engine specifications are:
3 HP maximum power 127 cc capacity Model No: 81232 Type: 0209-01 Code: 79042603 Mechanical Engineering Catalog No.: M2820 Modifications:
The head has been removed allowing access to the piston and valves.
A dial gauge has been installed to measure the displacement of thevalves.
Figure 3: Briggs & Stratton engine that was used for the practical. Modifica-tions are shown.
A 360 protractor has been installed on the crank shaft to allowmeasurement of the crank angle
The measurements were made using these apparatus
Dial Gauge:Manufactured by Mercer, EnglandResolution: 0.01 mm
Vernier Calipers:Manufactured by TricleModel Number: P02270108ID Number: 4051904Resolution: 0.02 mm
360 Protractor:Generic School ProtractorResolution: 0.5
The experiment was completed in the following sequence:
1. The cylinder diameter was measured using the vernier calipers.
Figure 4: Top view of the engine, clearly showing the piston, cylinder and valves.
2. The inner diameter of the large and small ends of the conrod (Dlargeand Dsmall in Figure 5 respectively), and dimension F (also shown inFigure 5) were measured using vernier calipers. These numerical valueswere substituted into Equation 8 to determine the kinematic length of theconrod.
L = F 12(Dlarge +Dsmall) (8)
3. The crank was positioned such that the piston is at top dead centre,between the exhaust and intake strokes. Then the displacement of thepiston from the top of the cylinder was measured using vernier calipers.
4. The crank was rotated 15 anti-clockwise, and the new piston displacementwas measured using the vernier calipers and recorded in the logbook. Thisstep was repeated for 15 increments until one complete cycle (360 ofrotation) was completed.
5. Steps 3 and 4 were repeated twice and averages of these measurementswere calculated. The kinematic length of the crank, R, was then deter-mined from the average measurements using Equation 9.
R = 12 (x|BDC x|TDC) (9)
xTDC is the piston extension at top dead centre,
xBDC is the piston extension at bottom dead centre, and
Figure 5: Dimensioned sketch of conrod.
R is the kinematic length of crank.
6. The crank was returned to the top dead centre position between exhaustand intake stokes. The dial gauge was positioned over the inlet valve andthe reading on the dial gauge was recorded into the logbook.
7. The crank was turned 10 anti-clockwise and the the measurement on thedial gauge was recorded. (Note: It is necessary to correct the readingsfrom the dial gauge for the initial offset. This was done by subtractingthe reading on the dial when the valve was fully closed from the otherreadings (See Tables 4 and 5). This step was repeated for 10 incrementsuntil one complete cycle (720 of rotation) was completed.
8. Steps 6 and 7 were then repeated for the exhaust valve.
5 Results and Discussion
Figure 6 shows the displacements of the piston and the valves as a function ofthe angular displacement of the crankshaft from top dead centre (the raw dataused to generate this graph is given in Appendix B). The piston displacement ismeasured from the top dead centre position and valve displacement is measuredfrom the fully-closed position. It shows that the inlet valve is open primarilyfor every second downward stroke of the piston (increasing piston displacement)and that the exhaust valve is open primarily for every second upwards strokeof the piston. The upwards stroke when the exhaust valve is open precedes thedownwards stroke when the inlet valve is open. It is noted that the valves open
just before and close just after the piston changes direction. The intake valveopens 20 before the intake stroke and closes 40 into the subsequent upwardsstroke. The exhaust valve opens 40 before the exhaust stroke, and closes justafter top dead centre between the exhaust and intake strokes (exhaust valvedisplacement is 0.07 mm at top dead centre). Both the inlet and exhaust valvesare open for approximately 20, near and including top dead centre.
100 0 100 200 300 400 500 600 700 80010
50Fourstroke engine cycle valve and piston displacements
Crank angle from TDC ()Theoretical piston displacement Measured piston displacement Inlet valve displacement Exhaust valve displacement
Figure 6: Piston and valve displacements over an entire four stroke cycle.
The theoretical curve for p