1
ME 560 Kinematics
Fall Semester 2010
Homework No. 4
Wednesday, September 15th
Consider the sliding-block linkage shown in Example 2.5, see Figure 2.24, page 77. The
position solution for the input angle
o
2
135
θ
=
is presented on pages 78 and 79. The answers,
which
can
be
obtained
from
the
law
of
cosines
and
the
law
of
sines,
are
34
4
R
O
A
12.59 inches
=
=
and
.
o
34
3
4
104.64
θ
= θ
= θ
=
Assume that the input link 2 is rotating
with an angular velocity
2
5 rad s
ω
=
/
clockwise and an angular acceleration
2
2
10 rad s
α
=
/
counterclockwise. The length of link 4; i.e.,
4
O
C
20 inches
=
and the origin of the XY reference
frame is chosen to be coincident with the ground pin O
2
as shown in Figure 1.
Use the method of kinematic coefficients to determine the following
:
(i) the relative velocity and acceleration between links 3 and 4 (denoted as
34
R
±
and
34
R
±±
).
(ii) the magnitude and direction of the angular velocity and angular acceleration of links 3 and 4.
(iii) the velocity and acceleration of point C. Give the magnitude and direction of each vector.
(iv) the unit tangent and normal vectors of point C. Show the vectors on Figure 1.
(v) the radius of curvature of the path of point C. Show on Figure 1.
(vi) the X and Y coordinates of the center of curvature of the path of point C. Show on Figure 1.
Figure 1. The Sliding-Block Linkage.

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2
Solution to Homework Set 4.
(A). The vectors for the sliding-block linkage is shown in Figure 2.
Figure 2. The Vector Loop for the Sliding-Block Linkage.
The vector loop Equation (VLE) for the sliding-block linkage is
??
0
1
2
34
I
R
R
R
√√
√
+
−
=
(1)
The X and Y components of Equation (1) are
1
1
2
2
34
34
cos
cos
cos
0
R
R
R
θ
θ
θ
+
−
=
(2a)
1
1
2
2
34
34
sin
sin
sin
0
R
R
R
θ
θ
θ
+
−
=
(2b)
Differentiating Equations (2) with respect to the input position
θ
2
gives
2
2
34
34
34
34
34
sin
sin
cos
0
R
R
R
θ
θ θ
θ
′
′
−
+
−
=
(3a)
2
2
34
34
34
34
34
cos
cos
sin
0
R
R
R
θ
θ θ
θ
′
′
−
−
=
(3b)