Uploaded by Emmanuel Agyekum

# Theory of machines questions

```ASSIGNMENT ONE
1. Four masses A, B, C and D revolve at equal radii and are equally spaced along a shaft.
The mass B is 7 kg and the radii of C and D make angles of 90&deg; and 240&deg; respectively
with the radius of B. Find the magnitude of the masses A, C and D and the angular
position of A so that the system may be completely balanced.
A rotating shaft is to carry four discs, A, B, C and D, whose masses are 15 kg, 25 kg,
20 kg and 18 kg respectively; they are to be spaced at intervals of 300 mm, 375 mm
and 225 mm along the shaft. The centres of mass A, B and C are at 36 mm, 12 mm and
18 mm respectively from their axes of rotation.
a. The three discs A, B and C are first attached to the shaft, at the spacing specified
above and with their centres of mass in positions which give static balance. Find
the relative angular positions of their centres of mass.
b. The disc D is then attached to the shaft in such a position as to nullify the outof-balance couple, when the reference plane passes through A. Find the
eccentricity of the centre of mass of D and its angular position relative to that
of A.
2. Four masses A, B, C and D revolve at equal radii and are equally spaced along a shaft.
The mass B is 7 kg and the radii of C and D make angles of 90&deg; and 240&deg; respectively
with the radius of B. Find the magnitude of the masses A, C and D and the angular
position of A so that the system may be completely balanced.
3. The rocker of a crank-rocker linkage is to have a length of 500 mm and swing through
a total angle of 45&deg; with a time ratio of 1.25. Determine a suitable set of dimensions for
π1 , π2 πππ π3 .
ASSIGNMENT TWO
1. If link CD shown in Figure 1 has an angular velocity of ππΆπ· = 6 πππ/π , determine the
velocity and acceleration of point E on link BC and the angular velocity and angular
acceleration of link AB at the instant shown.
Figure 1
2. At the instant shown in Figure 2 rod AB has an angular velocity ππ΄π΅ = 4 rad/s and an
angular acceleration πΌπΆπ· = 2 πππ/π  2 . Determine the angular velocity and angular
acceleration of rod CD at this instant. The collar at C is pin connected to CD and slides
freely along AB.
Figure 2
3. The&quot;quick-return&quot; mechanism shown in Figure 3 consists of a crank AB, slider block
B, and slotted link CD. If the crank has the angular motion shown, determine the
angular motion of the slotted link at this instant.
Figure 3
ASSIGNMENT THREE
1. In the epicyclic gear train shown in Figure 4, shaft A is stationary. If gear 2 rotates at
800 rpm cw. What are the speed and direction of rotation of shaft B?
Figure 4
2. Find the speed and direction of rotation of gear 8 in Figure 5. What is the speed ratio
of the train?
Figure 5
```