Mechanical Engineering Design 7th ed (SOLUTIONS MANUAL) - S. Mischke, R. Budynas (McGraw-Hill, 2003) WW.pdf

6/5/03 12:11 PM Page 1
Chapter 1
Problems 1-1 through 1-4 are for student research.
1-5 Impending motion to left
E
11
ff
A B
G
F
cr F ␪
␪
D C cr

Consider force F at G, reactions at B and D. Extend lines of action for fully-developed fric-
tion DE and BE to find the point of concurrency at E for impending motion to the left. The
critical angle is θcr. Resolve force F ponents and Fcr. is related to mass and
acceleration. Pin accelerates to left for any angle 0 <θ<θcr. When θ>θcr, no magnitude
of F will move the pin.
Impending motion to right
EЈиE
11
ff
A B
G
d
FЈ
cr FЈ␪Ј
␪Ј
D C cr
Ј

Consider force F
at G, reactions at A and C. Extend lines of action for fully-developed fric-
tion AE
and CE
to find the point of concurrency at E
for impending motion to the left. The
θ
.


.

critical angle is cr Resolve force F ponents and Fcr is related to mass
<θ
<θ
. θ
>θ

and acceleration. Pin accelerates to right for any angle 0 cr When cr, no mag-
nitude of F
will move the pin.
The intent of the question is to get the student to draw and understand the free body in
order to recognize what it teaches. The graphic approach plishes this quickly. It is im-
portant to point out that this understanding enables a mathematical model to be constructed,
and that there are two of them.
This is the simplest problem in mechanical engineering. Using it is a good way to begin a
course.
What is the role of pin diameter d?
Yes, changing the sense of F changes the response.
6/5/03 12:11 PM Page 2
2 Solutions Manual • Instructor’s Solution Manual to pany Mechanical Engineering Design
1-6

(a) y Fy =−F − fNcos θ+ N sin θ= 0 (1)


F T
F = fNsin θ+ N cos θ−= 0
x r
T
x
␪ r F = N(sin θ− f cos θ) Ans.
T = Nr( f sin θ+ cos θ)
N
fN
Combining
1 + f tan θ
T = Fr = KFr Ans. (2)
tan θ− f
−1
(b) If T →∞detent self-locking tan θ−