287
Chapter 20
Gyroscopes
20.1
A pendulum mill is shown schematically in the figure. In such a mill, grinding is done by
a conical muller that is free to spin about a pendulous axle that, in turn, is connected to a
powered vertical shaft by a Hooke univer

115
Chapter 8
Synthesis of Linkages
8.1
A function varies from 0 to 10. Find the Chebychev spacing for two, three, four, five,
and six precision positions.
With x0 = 0.0 and xn +1 = 10.0 , Eq. (8.5) becomes:
x j = 5.0 5.0 cos
j\n
1
2
3
4
5
6
8.2
2
1.46447

7
Chapter 2
Position and Displacement
2.1
Describe and sketch the locus of a point A which moves according to the equations
y
x
z
RA = atcos ( 2t ) , R A = atsin ( 2 t ) , RA = 0 .
2.2
Find the position difference from point P to point Q on the curve y =

127
Chapter 9
Spatial Mechanisms
9.1
Use the Kutzbach criterion to determine the mobility of the GGC linkage shown in the
figure. Identify any idle freedoms and state how they can be removed. What is the
nature of the path described by point B?
n = 3 , j2

81
Chapter 6
Spur Gears
6.1
Find the module of a pair of gears having 32 and 84 teeth, respectively, whose center
distance is 92 mm.
mN 2 mN 3 (32 + 84)m
+
=
= 92 mm
2
2
2
92 2
m =
= 1.586 mm/tooth
116
R2 + R3 =
6.2
Find the number of teeth and the circul

19
Chapter 3
Velocity
3.1
The position vector of a point is given by the equation R = 100e j t , where R is in inches.
Find the velocity of the point at t = 0.40 s.
R ( t ) = 2.5e j t
R ( t ) = j 2.5e j t
R ( 0.40 ) = j 2.5e j 0.40
= j 2.5 ( cos 0.40 + j

41
Chapter 4
Acceleration
4.1
(
)
The position vector of a point is defined by the equation R = 4t t 3 3 + 10 where R is
j
i
in mm and t is in seconds. Find the acceleration of the point at t = 2 s.
(
)
R (t ) = ( 4 t 2 )
i
R ( t ) = 4t t 3 3 + 10
i
j
R

67
PART II
DESIGN OF MECHANISMS
69
Chapter 5
Cam Design
5.1
The reciprocating radial roller follower of a plate cam is to rise 50 mm with simple
harmonic motion in 180 of cam rotation and return with simple harmonic motion in the
remaining 180 . If the ro

107
Chapter 7
Mechanism Trains
7.1
Find the speed and direction of gear 8 in the figure. What is the kinematic coefficient of
the train?
N 2 N 4 N 5 N 7 18 15 33 16
5
=
=+
N 3 N 5 N 6 N8 44 33 36 48
88
8 = 8/ 2 2 = ( +5 88 )(1 200 rev/min ccw ) = 68.18 re

GAZI UNIVERSITY
FACULTY OF ENGINEERING
DEPARTMENT OF MECHANICAL ENGINEERING
MM305
MECHANISMS
PROBLEMS AND SOLUTIONS FOR POSITION,
VELOCITY AND ACCELERATION ANALYSIS OF
MECHANISMS
Ar. Gr. Abdurrahim DAL

283
Chapter 18
Flywheels
18.1
Table P18.1 lists the output torque for a one cylinder engine running at 4 600 rev/min.
(a)
Find the mean output torque.
(b)
Determine the mass moment of inertia of an appropriate flywheel using
Cs = 0.025 .
Torque data for P