Machine Design I (ME-4133)
Test I
Attempt all 21 questions, 5% each, and accumulate up to 105%
Time 80 minutes
Justify your answers with the applicable equation, or with a short sentence or two
All figures are drawn to their actual dimensions
Student Name
Machine Design I (ME-4133) - Test II - Solution
Student Name: _
1. Points A and B are attached to the ends of the link shown in the figure. The acceleration
diagram for the point B, with respect to an observer at A, is also shown. Find the magnitude
of .
Grueblers Criterion: DoF= 3(N-1)-2(P1)-(P2)
DoF=Unknowns-Equations
M=# of joints that must be frozen to immobilize
a mechanism
Newtons Method
X1=X0-[(Jacobian^-1)*f(X0)]
X2=X1-[(Jacobian^-1)*f(X1)]
Etc.
X0= Initial Values
X1=new values
F(X0)=function valu
4.1)
C
Given:
3
B
&
2 = 4rad / s 90
A
2
O2
4
= 2rad / s
30 2
O4
O2 A = 15in
O4 B = 10 in
AC = 10 in
O2O4 = 30 in
AB = 17.2 in (From figure)
Find v c and 3 graphically.
The velocity of point B can be found in terms of velocity of point using the equation
3.1)
C
Given:
3
B
90
A
2
O2
30
4
2 = 200 rad / s
O4
O2 A = 15in
O4 B = 10 in
AC = 10 in
O2O4 = 30 in
AB = 17.2 in (From figure)
Find v c and 3 graphically.
The velocity of point B can be found in terms of velocity of point using the equation
v B = v A +
2.2
B
B
75
O2
O4
The output angle in a four bar mechanism is at its extremes when links 2 and 3 are collinear.
From this
O2 B =l3 + l2 = 229
(1)
O2 B = l3 l2 = 229
(2)
and
Solving the linear equations in (1) and (2) we obtain
l2 = 63.5mm, l3 = 165.5 mm .
1.1)
Draw the common normal NN. Draw the line of centers. Note that point K coincides with
center O2, which implies that length of is zero.
Using the formula:
The follower angle is maximum when the point of contact P is farthest from O2. In this position
The gear train shown below has N 2 = 24 teeth, N 3 = 18 teeth, N 4 = 30 teeth, and
N 6 = 36 teeth. The gears are all of the same module, and are supported on a carrier 5.
(a) If the speed of gear 7 is 150 rev/min clockwise, and the input shaft a is
driven
Equation for cam with flat face follower
Parametric equation for the cam
x = (C + f ( )cos f ( )sin
y = (C + f ( )sin + f ( )cos
Minimal radius
C + f ( ) + f ( ) > 0 for all angles 0 2
Length of followers face
L > max( f ( ) )
Inertia force
FI = maG
Mome
Instantaneous Center of Velocity
Consider two links, Link i , and Link j .
Definition. The velocity center ij is the common point on i (or its extension) and on j
(or its extension), which has the same velocity.
The velocity center ij is sometimes called