Computer Aided Engineering Design

20 COMPUTER AIDED ENGINEERING DESIGN

Squared-ends ⇒ Na = Nt – 2

Squared-Ground-Ends ⇒ Na = Nt – 2 (1.23)

The total number of coils Nt is calculated using the above.

Step 9: The shut (or solid) height Ls of the spring is calculated from

Ls = dNt (1.24)

Step 10: The initial deflection and the clash allowance are calculated from

y

F

k

initial = initial, yclash = 15% of the = 0.15δδ (1.25)

Step 11: The free length Lf of the spring can now be determined from

Lf = yinitial + δ + yclash+Ls (1.26)

Step 12: Determine the maximum force at the shut height deflection Fshutto check for the shear stress
in the coil at this force

FkLL K

FD

d

shut f swshut

shut

= ( – ), = 3

8

τ

π (1.27)

Verify if the factor of safety N
Ssy
shut
shut

= > 1.

τ

If not, another iteration may be required.

Step 13: The buckling of the spring has to be checked.

L D

d

critical(buckling) 2.63≈ , < LLf critical (1.28)

Step 14: Now, the complete spring specifications can be written as:
Spring Material: A227 (or as selected)
Wire diameter: d Free length: Lf
Mean diameter: D Total number of coils: Nt
Outer and inner diameters: D 0 = D + d,Di = D – d Ends: As specified

Weight of the spring: W

d

= DNt

2

,

π^2

⎛ γ

⎝

⎞

⎠

where γ = material density.

Exercises

1. A four-bar mechanism is shown in Fig. P1.1. Fixed pivots are given to be O 2 and O 4 20 cm apart. The input
   crank O 2 A is of 10 cm and AB = BO 4 = 25 cm. Trace the point path of point P for AP = 50 cm. All links are rigid.


2. A Chebychev’s straight line linkage is shown in Fig. P1.2. Fixed pivots are given to be O 2 and O 4 20 cm
   apart. O 2 A = 25 cm, AB = 10 cm and BO 4 = 25 cm. Determine the path traced by the point P for BP = 5 cm.
   All links are rigid.


3. A film advance mechanism is shown in Fig. P1.3 for a 35 mm camera. Link 2 is attached to the dc motor and
   rotates at a constant angular velocity. O 2 O 4 are fixed pivots. Link 3 is extended and has a pin-end, which goes