lecture 04 [rigid mechanisms]-1
TRANSCRIPT
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2.000: Rigid mechanisms
Laptop checkup~ Internet capable?
~ Notes downloadable?
Mechanisms/linkages
~ Linkage fundamentals
~ Examples
~ Position synthesis and analysis
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Mechanisms
Actuators
Electronics
Sensors
Machines
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Announcements
Problem set 1
Make sure you get a camera
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What is a linkage?
x
yInput or Output
Grounded(Held motionless)
Input or Output
Input or Output
What is a linkage?
A mechanism used to define motion (kinematics)&/or transfer energy using links & joints
Link
Joint
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Ubiquitous mechanical modules
http://smithstuff.net/albums/
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hotogarry.c
om
Generic 4 bar mechanism
Ubiquitous building block
Aim to combine nano 4 bars
to create complex nano devices
Complex motion example
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Compliant mechanism: All/part of motion due tocompliance
Given that we can engineer
compliant 4 bars more
complex machines can
be built by combining 4 bars
Major types of mechanisms
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hotogarry.com
Linear
Rotary
Conventional rigid mechanism Compliant mechanism
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Linkage components
F1 =f(F2) what is it?
Input or Output Input or Output
Input or Output
Linkage components:~ Links = rigid components or groups of rigidly connected
components between joints
~ 2D joints can either be pinned, sliding or rolling contact
x
y
F1
F2Grounded(Held motionless)
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Linkage classification
Input or Output
Grounded(Held motionless)
Input or Output
Input or Output
Linkages are classified by:~ The number of links (we will deal with 4-bar linkages)
~ Type of links (we will deal with bars and sliders)
~ Connection between links (we will deal with pinned, spherical and
sliding joints)
x
y
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Example: 4 bar door damper linkage
1
1= Wall or Link 1 This is the grounded (held still)
2
2 = Bar 2 or Link 2
3
3 = Bar 3 or Link 3
4
4 = Door or Link 4
Pin or rotary joints
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Mechanisms relationship to the 5 Fs
Actual machine design
Nominal machine design
Modeling
Dominant
Application
Fysics
Limiting
Momentum
Information
Mass
Flows
Energy
Who?
Where?
What?
Function
Why?
Motion
Constraints
Geometry
Form
Interfaces
Quality
Cost
Processes
Fabrication
Rate
A. What is
engineered?
B. What is
realized?
Modeling
Dominant
Application
Fysics
Limiting
Momentum
Information
Mass
Flows
Energy
Who?
Where?
What?
Function
Why?
Motion
Constraints
Geometry
Form
Interfaces
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Example: Stewart platform
Grounded (Constrained in 6 DOF)
How to identify links and jointsStep 1: Find the link that is not moving (ground)
Step 2: Find a feature that experiences relative motion (joint)
Step 3: The next link lies between this joint and the next pt ofrelative motion
Step x: Continue through links/joints to shortest path to ground
This sounds easy, but
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Example: Automotive suspension
Tie rod
Rotor
Spherical joint
Control arm
Frame
SteeringKnuckle
Rack Pinion
Spherical joint
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Example: Automotive suspension
x
y
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Example: Automotive suspension
x
y
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Effective 4-bar linkage
x
y
Appears that there are only 3 linksLink 4 is an effective link
This linkage can be modeled as a 4 bar linkage
Length of link 1 varies with linkage position
An effective link is characterized by a rigid non-changing lengththat is needed to define the motion of the mechanism
1
23
4
1
23
4
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Common 4-bar linkage types
1
2
4
3
1
2
4
3
4 BAR SLIDER-CRANK:
Consists of 3 links and slider:
- 1 = Ground- 2 = Crank- 3 = Coupler- 4 = Slider
Crank is link driven by Force/torque
Link # 4 can be:- A pin, block, or tube
Link # 4 slides in/on one of these:- Another part, rod or tube
Links can cross each other
4 BAR COUPLER:
Consists of 4 links:- 1 = Ground- 2 = Crank or follower- 3 = Coupler- 4 = Crank or follower
Crank is the link driven by force/torque
Links can cross each other
x
y
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4-bar pin slider linkages
24
3
Pull
32
4
11
x
y
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Simulation: Working model
Backhoe Piston assembly
Automotive suspension
Credit: http://workingmodel.com/simulations.htmlx
y
1
2 3
4
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Graphical synthesis of 4-bar, 2 positions
Situation: Want coupler to hit 2 specific positions~ Q: Location of ground link and length of crank/follower
9Know points A & A and B & B
~
A: Obtain these by following this procedure9 1. Draw lines (chords) between points A & A and B & B
9 2. Connect A & A and B & B ends with desired arc of motion
9 3. Construct perpendicular bisector to each chord
9 4. Joints to ground lie on bisectors
9 5. Ground joint positions defined by tangent to arcs
9Note: Your choice of arc radius affects position!!!
1
24
3
A
A B
B
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Graphical synthesis of 4-bar, 2 positions
A
A B
B
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Analytic method: Vector analysis
1Rv
2Rv
3Rv
4Rv
Analytic position/velocity method~ Represent links as vectors between joints
~ Works for 2D and 3D, we will use 2D to illustrate the point
~ Vectors form a closed loop; vector sum = 0
~
jiRRRR 0004321 +==+++vvvvv
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Analytic method: Vector analysis (2D)
jiRRRR 0004321 +==+++ vvvvv
( ) ( ) jRiRR sincos 11111 +=vvv
( ) ( ) jRiRR sincos 22222 += vvv
( ) ( ) jRiRR sincos 33333 +=vvv
( ) ( ) jRiRR sincos 44444 +=vvv
( ) ( ) ( ) ( ) iRRRRi coscoscoscos0 44332211 +++=vvvv
( ) ( ) ( ) ( )( ) jRRRRj sinsinsinsin0 44332211 +++=vvvv
in x:
in y:
jiRRRR 0004321 +==+++ vvvvv
1Rv
2Rv
3Rv
4Rv
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Parallel link 4 bar mechanism
Parallel 4 bar linkage:~ Opposing links have equal lengths
~ 1 = 180o |R1| = |R3| |R2| = |R4|
~ Opposing links remain parallel
x
y
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Linkage competition [ 10 pts ]
In groups of 4, use LeggosTM to experiment~ Design a linkage(s) which inverts a sketch (turns it upside down)
~ Hand in a sketch of your linkage geometry, the sketches it made
and an few sentence explanation before the bell sounds
~ Describe the logic (bulleted points and/or mathematics) that explain
why the device works
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Minutes
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14
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