ME 352  Machine Design I
Name of Student
______________________________
Fall Semester 2011
Lab Section Number
___________________________
Homework No. 2. Parts (i)(iv) due at the beginning of lecture, Wednesday, September 7th.
(20 points).
Part (v) due at the beginning of lab, Monday, September 12th, or Tuesday, September 13th. (20 points).
Section 2.12, see pages 7779, presents five different approaches for the position analysis of planar
single degree of freedom linkages. The approaches are illustrated by Example 2.5 which is a sliding
block linkage and Example 2.6 which is a planar fourbar linkage. This homework focuses on these
techniques for the position analysis of a planar fourbar linkage with the following link dimensions:
Ground Link 1:
20.0 cm
Input Link 2:
9.0 cm
Coupler Link 3:
15.0 cm
Output Link 4:
17.0 cm
The fixed X and Yaxes are specified as horizontal and vertical, respectively, and the origin is
coincident with the ground pivot of the input link 2. The orientation of the ground link relative to the X
axis is
1
15
θ= °
counterclockwise; i.e., oriented above the Xaxis.
(i)
For the input angle
2
30
θ=
D
counterclockwise from the Xaxis, choose a suitable scale and
accurately draw the fourbar linkage in its two possible configurations.
Measure the values of the
joint variables
3
θ
and
4
θ
for each configuration.
(ii)
Use the law of sines and the law of cosines to determine the joint variables
3
θ
and
4
θ
for the open
configuration.
(iii) Use the closedform solution to solve for the joint variables
3
θ
and
4
θ
. (Recall that the closed
form solution for a planar fourbar linkage is commonly referred to as Freudenstein's equation, see
Uicker, et al., Section 10.13, Equations (10.23)(10.26), pages 451 and 452. Note, however, that
these equations are for
o
1
0
). Compare your answers for the two joint variables
3
θ
and
4
θ
with
the answers from Part (i).
(iv)
Set up and carry out the NewtonRaphson iteration procedure (see Uicker, et al., Section 2.8, page
65) to solve for the joint variables
3
θ
and
4
θ
(for the open configuration) when the input angle
2
30 .
D
Use the initial estimates for
3
θ
and
4
θ
given by Part (i) above. Continue to iterate until
3
θ
and
4
θ
converge to within
0.01 .
D
Please show all the steps for each iteration.
(v)
Write a computer program using Matlab which uses the NewtonRaphson iteration procedure to
solve for
3
θ
and
4
θ
(for the open configuration) given initial estimates for these joint variables
(and the input angle
2
θ
and the link lengths). To check your program, use the initial estimates
given by Part (i) above and print out the joint variables
3
θ
and
4
θ
when the input angle
2
30 .
D
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Solution to Homework Set 2.
(i) The link dimensions and the joint angles that are specified in the problem statement are:
Ground Link:
R
1
= 20 cm
θ
1
= 15
˚
Input Link:
R
2
=
9 cm
θ
2
= 30
˚
Coupler Link:
R
3
= 15 cm
θ
3
= ?
˚
Output Link:
R
4
= 17 cm
θ
4
= ?
˚
For the specified input angle
2
30
θ=
D
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 Fall '08
 Staff
 Equations, Machine Design, Quadratic equation, Elementary algebra, Howard Staunton, Freudenstein

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