Page 441 - Marks Calculation for Machine Design

P2: Sanjay
P1: Shibu/Rakesh
15:34
January 4, 2005
Brown˙C10
Brown.cls
423
MACHINE MOTION
Therefore, for crank angle (φ) equal to 0 , the angular velocity of the connecting rod
◦
(ω rod ) is also zero, the velocity of the slider (v slider ) is a maximum to the right, the angular
acceleration of the connecting rod (α rod ) is a maximum counterclockwise (CCW), and the
acceleration of the slider (a slider ) is a maximum to the right.
For the slider-crank linkage shown in Fig. 10.14, the crank angle (φ) is 90 .
◦
f = 90° C
A B
L AB L BC
FIGURE 10.14 Slider-crank linkage at φ = 90 .
◦
It is obvious from the geometry in Fig. 10.14 that the angle (β) is zero.
From Eq. (10.10) the angular velocity of the connecting rod (ω rod ) becomes
◦
L AB sin 90
ω rod | φ=90 ◦ = ω crank
L BC cos 0 ◦
L AB
= ω crank (10.29)
L BC
and from Eq. (10.11) the velocity of the slider (v slider ) becomes
◦
◦
◦
v slider | ◦ = (L AB ω crank )(cos 90 + sin 90 tan 0 ) = 0 (10.30)
φ=90
and from Eq. (10.22) the angular acceleration of the connecting rod (α rod ) becomes
2
◦
L AB ω crank cos 90 + α crank sin 90 ◦
α rod | φ=90 ◦ = ◦ − ω 2 ◦ tan 0 ◦
rod φ=90
L BC cos 0
L AB
= α crank (10.31)
L BC
and from Eq. (10.23) the acceleration of the slider (a slider ) becomes
2 ◦ ◦ ◦ ◦ ◦ ◦
a slider | φ=90 ◦ = L AB ω crank (sin 90 − cos 90 tan 0 ) − α crank (cos 90 + sin 90 tan 0 )

◦
◦
◦
+ L BC ω rod φ=90 ◦ (cos 0 + tan 0 sin 0 )
2
2

= L AB ω 2 L AB
crank + L BC ω crank
L BC

2 L AB
= L AB ω 1 + (10.32)
crank
L BC
◦
Therefore, for a crank angle (φ) equal to 90 , the angular velocity of the connecting rod
(ω rod ) is a maximum, the velocity of the slider (v slider ) is zero, the angular acceleration of
the connecting rod (α rod ) is a positive value counterclockwise (CCW), and the acceleration
of the slider (a slider ) is a maximum to the left. Note that if the angular velocity of the crank
is constant, meaning the angular acceleration is zero, then for this crank angle the angular
acceleration of the connecting rod will also be zero.