Chapter 1
Problems 1-1 through 1-4 are for student research. 1-5
Impending motion to left E

1 f A

1 f B G Fcr F
cr

D

C

Facc

Consider force F at G, reactions at B and D. Extendlines of action for fully-developed friction D E and B E to find the point of concurrency at E for impending motion to the left. The critical angle is θcr . Resolve force F into components Facc and Fcr .Facc 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 E E

1 f A d D

1 f BG Fcr C
cr

F Facc

Consider force F at G, reactions at A and C. Extend lines of action for fully-developed friction AE and C E to find the point of concurrency at E for impending motion to theleft. The critical angle is θcr . Resolve force F into components Facc and Fcr . Facc is related to mass and acceleration. Pin accelerates to right for any angle 0 < θ < θcr . When θ > θcr , nomagnitude 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 accomplishes this quickly.It is important 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 isa good way to begin a course. What is the role of pin diameter d? Yes, changing the sense of F changes the response.

2

Solutions Manual • Instructor’s Solution Manual to Accompany MechanicalEngineering Design

1-6 (a)
y F

Fy = −F − f N cos θ + N sin θ = 0 Fx = f N sin θ + N cos θ −
T r x

(1)

N

F = N (sin θ − f cos θ) T = Nr( f sin θ + cos θ) Combining T = Fr

T =0 r Ans.fN

1 + f tan θ = KFr tan θ − f

Ans. Ans.

(2)

(b) If T → ∞ detent self-locking tan θ − f = 0 (Friction is fully developed.) Check: If F = 10 lbf, N= f = 0.20, θ = 45◦ ,

∴ θcr =... [continua]

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