Chapter 7
Problems
7.1 Problem Set: Mechanisms
The dimensions of the planar mechanisms, shown in Figs. 7.1–7.15, are given in
Tables 7.1–7.15, respectively. The angle of the driver link 1 with the horizontal axis
is
φ
. The constant angular speed of the driver link 1 is
n
and is given in the tables.
1. Determine the type of motion (rotation, translation, and complex motion) for
each link, the connectivity table, the structural diagram, the contour diagram, the
independent contours, the number of degrees of freedom, the dyads, and the type
of the dyads.
2. Find the positions of the joints and the angles of the links with the horizontal
axis when the angle of the driver link 1 with the horizontal axis is
φ
. Write a
MATLAB
R
±
program for the positions of the mechanism for the given angle
φ
.
3. Write a MATLAB program for the positions of the mechanism for a complete
rotation of the driver link 1,
φ
∈
[
0
◦
,...,
360
◦
]
, using different methods.
4. Write a MATLAB program for the path of a point on a link with general plane
motion.
5. Write a MATLAB program for the animation (movie) of the mechanism for a
complete rotation of the driver link 1,
φ
∈
[
0
◦
,...,
360
◦
]
.
6. Find the velocities and the accelerations of the mechanism, using different meth
ods, for the given position when the driver link 1 makes an angle
φ
with the
horizontal axis. The constant angular speed of the driver link 1 is
n
. Write a
MATLAB program for this.
7. The link bars of the mechanism are homogeneous rectangular prisms with the
width
h
=
0
.
01 m and the depth
d
=
0
.
001 m. The sliders have the width
w
Slider
=
0
.
050 m, the height
h
Slider
=
0
.
020 m, and the same depth
d
=
0
.
001 m. The links
of the mechanism are homogeneous and are made of steel having a mass density
ρ
Steel
=
8000 kg/m
3
. The gravitational acceleration is
g
=
9
.
807 m/s
2
. The driver
link 1 has a constant angular speed
n
. The external force or moment applied on
the last link 5 is opposed to the motion of the link and has the value:

F
5
ext

=
275