Universiti Tenaga Nasional, 2006

Mechanical Design and CAD Laboratory

SLOTTED LINK MECHANISM EXPERIMENT

OBJECTIVE

The objective of this experiment is to investigate the motion of a slotted link and to see if

the piston rod moves with Simple Harmonics Motion

THEORY

Simple Harmonic Motion is defined as when a mass or point moves in such a way that its

accelerations is proportional to its displacement from a fixed point in its path and is

directed to that point, the motion is said to be simple harmonic.

The Simple Harmonic Circle enables us to establish a relationship between displacement

and accelerations. Consider the diagram below:

A B

t

O P

x

Q is a point which rotates at constant at constant velocity in a circle of a radius r. AB is

a diameter and O the center of the circle of rotation. Point P is the projection of Q upon

the diameter AB at any instant. The displacement of P from O is x. Clearly point P

oscillates between A and B as q moves around the circle. So P can only have velocities

along AB at any instant in time, similarly for accelerations. Now if we resolve the

centripetal accelerations into two components parallel and perpendicular to AB, then the

parallel components will represents the accelerations of P.

Universiti Tenaga Nasional, 2006

Mechanical Design and CAD Laboratory

BO

Q

Ptr cos.2

t

r

a

2

=

Acceleration parallel to AB given by this equation:

trAB .cos.2 =

Now displacement x is

trx .cos. =

So the accelerations of P is

aP =

xP 2=

Thus the accelerations of P is proportional to its displacement, x, from O and is clearly

towards O. Therefore the motion is Simple Harmonic Motions.

Alternatively we may consider the following method:

trx .cos. =

trdt

xd

trdt

dx

.cos..

.sin..

2

2

2

=

=

But: trx .cos. =

trdt

xd.cos..2

2

2

=

The minus sign indicates that the accelerations is to the left and thus the center of

rotations O.

Universiti Tenaga Nasional, 2006

Mechanical Design and CAD Laboratory

What do you note about the displacement, velocity and accelerations? They vary

sinusoidally

Periodic Time

This is the time taken for a complete oscillation from B to A and back again. The time

taken is also that for a complete revolution of particle Q which is an angular distance is

pi2 radians, so:

pi

2

=

However from previous analysis we know that:

21

=x

a

a

xpi 2=

Slotted Link Mechanism or Scotch Yoke

The apparatus is diagrammatically below:

It is clear that the driving pin which is fixed to the crank is similar to the point Q

on the SHM circle. The piston rod with a slotted link is constrained to move is a straight

line. The limits of the motions are either end of a diameter of the circle of the drive pin

rotations. So the motions of the slotted link and piston rod are identical to point P in the

foregone analysis. Thus the link and anything attached there to will move with SHM.

Universiti Tenaga Nasional, 2006

Mechanical Design and CAD Laboratory

APPARATUS

Slotted link Mechanism

Universiti Tenaga Nasional, 2006

Mechanical Design and CAD Laboratory

PROCEDURES

1. Set the crank at zero degrees. Record the piston displacement.

2. Move the crank by 10 and record the displacement.

3. Repeat steps 1 and 2 for one complete revolution of the crank.

4. Tabulate your results in the table given.

5. Calculate the theoretical piston rod displacement in the table.

RESULTS

1. Plot a graph of the experimental piston rod displacement versus crack angle.

2. Plot on the same graph the theoretical piston rod displacement against crank angle

3. From the experimental piston rod displacement data plot a graph of experimental

velocity and accelerations versus crank angle.

4. From the theoretical Simple Harmonic Motion equations, plot a graphs of

theoretical velocity and accelerations versus crank angle.

DISCUSSION

1. Prove the theoretical displacement ( )cos1= rx

2. Compare the experimental and theoretical piston rod displacement, velocity and

accelerations. How well do your experimental results agree with theory?

3. What is the motion produced by the Slotted Link mechanism? Explain your

answer.

4. Where do maximum displacement, velocity and acceleration on the slide occur?

Explain your answer

5. Where does the maximum force on the drive pin occur? Explain your answer

Universiti Tenaga Nasional, 2006

Mechanical Design and CAD Laboratory

RESULT SHEET

Slotted Link Mechanism Experiment

Crank Radius = 35 mm

Crank Angles, (degrees)

Experimental Piston Rod

displacement, x, (mm)

Theoretical,

( )cos1= rx (mm) 0

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