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Mechanics of Machinery ?????????????????????

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... and size/shape of parts can then be determined Basic Mechanisms Linkages 4-bar linkage examples Slider-crank examples Cam Cam-follower examples Gears Gears ... – PowerPoint PPT presentation

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Title: Mechanics of Machinery ?????????????????????


1
Mechanics of Machinery?????????????????????
  • ??.??.?????????? ??????
  • Asst.Prof.Dr Monsak Pimsarn

2
  • ????????
  • ?????????? 40
  • ?????????? 50
  • ?????????????????? 10
  • ??? 100
  • ?????????????????????????????????
  • 1. Authur G. Erdman/George N. Sandor, Mechanism
    design (Analysis and Synthesis) Volume 1, 2nd
    Edition, McGraw-Hill, 1991.
  • 2. Mabie / Reinholtz , Mechanism and Dynamics of
    Machinery, Fourth Edition, John Wiley Sons,
    1987.
  • 3. Robert L. Norton, Design of Machinery, 2nd
    Edition, McGraw-Hill.
  • Class Web Site http//www.kmitl.ac.th/kpmonsak
    /Mechanism.html

3
  • ???????
  • ????????????????????????
  • ??????????????????????????
  • ???????????????????????????
  • ???????????????????????????
  • ?????????????????????????????????
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4
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5
Mechanism Analysis
Object is in motion
Object is motionless or moving with a 0
Mechanics
Dynamics
Statics
Mechanism Analysis
  • Kinetics
  • SFma
  • Kinematics
  • motion
  • position
  • velocity
  • acceleration

6
  • Object types
  • Particle a point mass, m
  • Rigid body a finite body that is not flexible.
  • Flexible body - a finite body that is flexible,
    not considered in this class.
  • Note In this class, we will look at how a
    particle and a rigid body move in two dimensional
    space(2D) or plane.

7
  • Motion types in 2D
  • Translation ????????????????????????????????????
    ??????????????????
  • Rectilinear translation ???????????????????????
    ???????????????????????????????
  • Curvilinear translation - ????????????????????????
    ???????????????????????????????
  • Rotation ?????????????????????????????????
    ????????????????????????? ??????????
  • Combined motion ???????????????? Translation
    ??? Rotation ??????????????????????????????

8
Translation motion(???)
9
Translation motion
Curvilinear translation
Rectilinear translation
10
Rotational motion
11
Combined motion or General plane motion
??????????????????????? combined motion ?????
????????????????????????????????
12
Mechanism Synthesis
  • Required Motion
  • Components types
  • Number/size/shape

Mechanism Synthesis (design)
Mechanisms are the basis of all machine design
13
Mechanism synthesis
  • In some devices, e.g. instruments, control
    mechanisms the correct motion is the most
    important thing. The power (force) transmitted is
    small and so strength/size of parts is not the
    prime concern.
  • In other machines, the kinematic analysis is only
    one step in the design process. Once we have
    worked out how parts should move together we must
    then calculate the forces that are produced. The
    required strength and size/shape of parts can
    then be determined

14
Basic Mechanisms
15
Linkages
2 - Rotation
4 - Reciprocating motion (back fore)
Slider-Crank Link 1 frame (reference) Link 2
crank Link 3 connecting-rod (con-rod) Link 4
slider
Crank-Rocker Link 1 frame (reference) Link 2
crank Link 3 connecting-rod (con-rod) Link 4
rocker
Kinematic diagrams simplified (but accurate)
diagrams showing geometry of motion
16
4-bar linkage examples
Crank-rocker
Double-rocker
17
Slider-crank examples
Inversion
Standard slider-crank
18
Cam
Cam rotates at constant angular velocity Follower
moves up and down
NB A cam can only push the follower (not pull)
the return action requires spring/gravity etc.
19
Cam-follower examples
Flat faced translating follower
Flat faced reciprocating follower
20
Gears
driver
driven
Gears trains can be used when a large overall
gear ratio is required
Gears are used to transmit motion from one shaft
to another with a constant angular velocity ratio
(gear ratio).
21
Gears
22
Definitions
23
Mechanism
  • A combination of rigid bodies connected so they
    move together with a definite (precise
    repeatable) motion

Examples Door lock, Engine
Machine
A mechanism or collection of mechanisms which
transmit power (force) from a source of power to
a resistance to be overcome
Examples Internal combustion engine, drill
24
Link
A rigid body having two or more pairing elements
(joints) that connect to other bodies for the
purpose of transmitting force or motion
Bell-Crank A simple link having three connections
used to for motion reduction
25
Frame
Joint (Kinematic pair)
Connection of 2 or more links allowing relative
motion
  • Fixed-Link reference frame, Link no. 1
  • (not always shown as a link)

26
Kinematic pairs (Joints or connections)
  • Have 2 basic types
  • Lower pair a joint connected 2 members having
    surface contact (e.g. bush, pin)
  • Higher pair a connection that takes place at a
    point or along a line (ball bearing, gear teeth,
    cam)

These classifications are not really important
for kinematic analysis
27
Types of pairs (joints)
Lower pairs
Revolute pair (1 dof)
Prismatic (sliding) pair (1 dof)
higher pairs
Rolling pair (1 dof) - without slip
Cams (2 dof) -with slip
28
Type of Joints, Higher Pairs
29
Type of Joints, Higher Pairs
Belt and pulley (no sliding) or chain and
sprocket 1 DOF
30
Common types of Joint
31
Degrees Of Freedom (dof) Mobility (F)
  • The number of motion variables (usually joint
    variables such as angles) which can be controlled
    independently to bring the device to a particular
    position (configuration)

If F 1 the mechanism can be driven by a single
input motion If F 2 the mechanism requires two
separate input motions to produce constrained
(definite) motion
32
Mobility of planar machanisms
Number of links n 6
Number of joint f1 7
Can we calculate the mobility from this
information?
33
2 links 3x2 6 dof
1 link 3 dof
1-dof-joint
2 links 1 joint 3x2-2x1 4 dof
34
q2 ??????????? q1
35
Formula for dof
To calculate the total number of dof for a planar
mechanism
  • F 3(n-1) 2f1 f2
  • F Mobility (dof)
  • n number of links
  • f1 number of joints with 1 dof
  • f2 number of joints with 2 dof

Kutzbachs criteria Or Grublers criteria
36
Implications of mobility F
  • F 0 motion is impossible and the mechanism
    forms a structure
  • F 1 mechanism can be driven by a single input
    motion (a constrained mechanism)
  • F 2 mechanism requires two separate input
    motions to produce constrained (definite)
    motion
  • F 3 etc.
  • F lt 0 mechanism has redundant constraints it
    is over-constrained and is called a statically
    indeterminate structure (the forces in every
    link cannot be determined)

37
Examples
F 3(n-1) 2f1 f2
n 3, f1 3, f2 0 F 0 motion is
impossible mechanism forms a structure
n 4, f1 4, f2 0 F 1 mechanism can be
driven by a single input motion constrained
mechanism
n 4, f1 4, f2 0 F 1 mechanism can be
driven by a single input motion constrained
mechanism
38
n 5, f1 5, f2 0 F 2 mechanism requires
two input motions (e.g. there must be two
controlled joints) to produce constrained
mechanism
n 4, f1 5, f2 0 (joint A has 2 dof) F
-1 mechanism is over-constrained statically
indeterminate structure
Slip/no slip?
n 3, f1 2, f2 1 F 1 mechanism can be
driven by a single input motion constrained
mechanism
39
f1
5
n 7 f1 8 f2 0
f1
4
F 3(7-1)-28-0 F 2
f1
6
f1
3
f1
f1
7
2
f1
f1
n 4 f1 4 f2 0
F 3(4-1)-24-0 F 1 mechanism can be driven by
a single input motion constrained mechanism
40
Degrees of Freedom (DOF) trench hoe
Number of links, n 12,
Number of one DOF joints, f1 12 (pins) 3
(slider) 15,
11, 12
Number of two DOF joints, f2 0
11
12
10
7
4
3 hydraulics are used to control the position of
the bucket.
1
41
Degree of Freedom (DOF) - example
Number of links, n 7,
Number of one DOF joints, f1 6 (pins) 1
(slider) 7,
Number of two DOF joints, f2 1 (fork joint)
Three input sources are needed to control the
mechanism
Fork Joint
4
3
2
5
Spring
Slider
6
7
42
Exceptions
Sometimes the Kutzback condition will give an
incorrect result.
n 5, f1 6, f2 0 ? F 0 Kutzbach formula
gives wrong mobility because 3 links are parallel
and equal length
n 5, f1 6, f2 0 ? F 0 Same result this
time is correct!
43
Kinematic Diagrams
A striped-down (simplified) drawing showing the
essentials needed for kinematics analysis. All
links are numbered while the joints are lettered.
44
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46
Example
47
Example
48
Example
49
Examples
X
C
1
B
4
3
2
E,F
A
6
5
D
G
50
Real life example
Myoelectric Elbow Prosthesis
51
Inversion same mechanism but different link
fixed
Four bar linkage link 1 fixed
For a 4 bar linkage there are 4 inversions
Coupler
3
2
4
(driven)
Input
(driver)
Output
1
1
Same mechanism inverted link 3 fixed
Input
3
3
Output
2
4
Links have same relative motion but different
absolute motion
1
Coupler
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