Solutions
\Step 1: Energy from the spring from phase 2 to phase 3
0.5
= 45 mm = 0.045m,
=45-26.4 = 18.6mm = 0.0186m, K = 20N/mm = 20e3 N/m.
0.5 20 3 0.045
0.0186
16.79
The rotational angle from phase 2 to phase 3 is 60-20 = 40 degrees. The work done by
DESIGN OF MACHINERY
SOLUTION MANUAL 3-14-1
PROBLEM 3-14
Statement:
Figure P3-3 shows a treadle-operated grinding wheel driven by a fourbar linkage. Make a
cardboard model of the linkage to any convenient scale. Determine its minimum transmission
angles. C
The Instantaneous Centre
Method . application
Keeping account .
For a mechanism of n
n links,
links there are:
F a mechanism
For
h i
of
f n
links,
li k there
th
are:
n (n - 1) / 2 instantaneous centres
n (n - 1) / 2 instantaneous centres
hence a 4 bar me
DESIGN OF MACHINERY
SOLUTION MANUAL 3-65-1
PROBLEM 3-65
Statement:
Design a fourbar mechanism to give the three positions shown in Figure P3-18. Ignore the points
O2 and O4 shown. Build a cardboard model and add a driver dyad to limit its motion to the ra
SUBJ ECT OUTLINE
Sub
bject Code: MECH226
Sub
bject name: MACHINE
E DYNAMIC
CS
Pre-requisites: E
ENGG152 Co-requisites
C
s: MATH1422 or MATH1
188 or MATH
H162
Cred
dit points: 6
O
Offered: Spriing Session 2014,
2
Wollonngong Camp
pus
CON
NTACTS
Sub
bject C
Sample solution using the analytical method (Unit Vector Method)
Mechanism type: 4 links pin joints
In the mechanism shown in Figure 1, link 2 is the driving link and in the position shown
is rotating counter-clockwise at 20 radians/second. It is also dec
DESIGN OF MACHINERY
SOLUTION MANUAL 7-48-1
PROBLEM 7-48
Statement:
Figure P7-18 shows a mechanism and its dimensions. Find the accelerations of points A, B, and C
for the position shown.
Given:
Lengths and angles:
Solution:
1.
Link 2 (O2 to A)
a
0.80
in
L
Tutorial Problems Week 7
7-21. The four-bar mechanism and its dimensions are shown in Figure P7-8a. Use graphical method
to find 4 and AB. Suppose 2=15 rad/s (CW) and 2=25 rad/s2 (CCW).
7-13 The linkage in Figure P7-5a has O2A=2cm, AB=5cm, AC=3.4cm, and o
Tutorial Problems for Energy Methods
Problem 1:
Based on 9.32 from M & R
For the slider crank mechanism shown in Figure 1, a spring provides the driving force on piston
4 with a spring constant of 20 N/mm. At phase II the spring is compressed 45 mm from i
DESIGN OF MACHINERY
SOLUTION MANUAL 6-21a-1
PROBLEM 6-21a
Statement:
The linkage in Figure P6-6b has L1 = 61.9, L2 = 15, L 3 = 45.8, L4 = 18.1, L5 = 23.1 mm. 2 is 68.3 deg
in the xy coordinate system, which is at -23.3 deg in the XY coordinate system. The
Week 12
Balancing Machines
(Ch 12 in Norton; Ch 10 in M&R)
Week 12
Balance .
1
1
Variations in the external loads on the mechanism would
be resisted by forces and torques applied at these
attachment points.
We also calculated inertia forces and torques re
DESIGN OF MACHINERY
SOLUTION MANUAL 6-12-1
PROBLEM 6-12
Statement:
Find all of the instant centers of the linkages shown in Figure P6-5.
Solution:
See Figure P6-5 and Mathcad file P0612.
a.
This is a fourbar slider-crank with n
4.
1.
Determine the number
Prof. Weihua LI (WL)
School of Mechanical, Materials & Mechatronic Engineering
Office: 8.110
Phone: 4221 3490
E-mail: [email protected]
Week 1
Lecture/Tutorial Times
Lecture Time
Wednesday
14.30 16.30
Tutorial Time
Group 1: Wednesday
Group 2: Thursday
DESIGN OF MACHINERY
SOLUTION MANUAL 7-21-1
PROBLEM 7-21
Statement:
The linkage in Figure P7-8a has the dimensions and crank angle given below. Find 4, AA , and AB
in the global coordinate system for the position shown for 2 = 15 rad/sec clockwise (CW) and
Tutorial Problems Week 5
1. For the linkage shown below, link 2 rotates at a constant angular velocity 2 = 200 rad/s (cw).
(a) Determine VB and VC using the Unit Vector method;
(b) Draw the velocity polygon and determine VC, 3 and 4.
O2A = 15 cm
O4B = 10
Sample solution using the analytical method (Unit Vector Method)
In the mechanism shown in Figure 1, link 2 is the driving link and in the position
shown is rotating counter-clockwise at 55 radians/second. It is also decelerating at a
rate of 100 radians/
Tutorial Problems Week 2
2-1
Find 3 of the following common devices. Sketch careful kinematic diagrams
and find their total degrees of freedom.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
o.
2-7
2-8
An automobile hood hinge mechanism
An automobile hatchback
Week 5 & 6 Tutorial solution
Q1, solutions
Week 5
O2A = 15 cm, O4B = 10 cm, AC = 10 cm, O2O4= 30 cm
Step 1:
Setup both fixed and moving frames as above. Using geometrical configurations, find
the required angles. In particular, the angle DAB is used to re
Week 11
Virtual Work Method
(10.13 & 11.10 of Norton ;Ssection 9.9 of M&R)
Energy Distribution
Method
(10.13 of Norton ;Ssection 9.10 of M&R)
Week 11
Virtual Work Method
Based on equilibrium principles, and the
conservation of energy
Can be used to anal
Week 2
(1) 4 bar mechanism (cont):
Grashof condition (2.13, 3.3-3.5)
(2) Cams (8.1-8.4 of Norton, and ch
3 in Mabie & Reinholtz)
Week 2
Grashof condition
4 bar linkage is the simplest possible pinjointed mechanism for 1 DOF controlled
motion. Thus, it sh
DESIGN OF MACHINERY
SOLUTION MANUAL 6-28-1
PROBLEM 6-28
Statement:
The linkage in Figure P6-8b has the dimensions and crank angle given below. Find 4, VA, and VB
Given:
for the position shown for 2 = 20 rad/sec counterclockwise (CCW). Use the velocity dif
DESIGN OF MACHINERY
SOLUTION MANUAL 6-99-1
PROBLEM 6-99
Statement:
The linkage in Figure P6-33d has the path of slider 6 perpendicular to the global X-axis and link 2
aligned with the global X-axis. Find VA in the position shown if the velocity of the sli
MECH 226
P-8-43 Sample Solution
Design a cam to move a follower at a constant velocity of 100mm/s for 2s, and then return to its
starting position in 1s
Total revolution 360 => in 3s
2s at constant velocity =>240 or 4/3 rad
Total lift at constant velocity
Week 7
Acceleration analysis - graphical
method
(ch7, Norton; ch8, M &R)
Revision and Information on Midsession quiz
Week 7
Recalling the equations
Velocity (of some point P):
VP = Vo + V + R Equation 8.16
(M&R)
And acceleration:
AP = Ao + A + 2 V + R + (
Week 3
(1) Cam-follower design (cont)
(ref. video: https:/www.youtube.com/watch?v=KRnTXvjTeIA )
(2) Position and velocity analysis
of 4 bar mechanism
Week 3
Cam-follower example
Problem 8-43: (use Kloomok & Muffley Eqs)
Design a cam to move a follower at
Tutorial Problems Week 6
NB: the following two questions are extension of last weeks tutorial problems. The angular
velocities of 3, 4, for question 1, and 4, VA4A2 for question 2 were calculated in week 5. They will
be used for this weeks acceleration ca
Tutorial 4 Problems Week 10
Solve Problems 11.9 (fig 11.4 a) and 11.12 Fig 11.5 b) using (a) the analytical
superposition method, and (b) Matrix method.
11-9 All dimensions are in m, the crank and rocker (links 2 & 4) are steel cross section 50 mm
wide, 2