Direct kinematic analysis of a family of 4-DOF parallel manipulators
1.How to draw a kinematic diagram 2. The Mechanism DOF 3. The Planar four bar linkagesHow to draw a...
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Transcript of 1.How to draw a kinematic diagram 2. The Mechanism DOF 3. The Planar four bar linkagesHow to draw a...
1.How to draw a kinematic diagram2. The Mechanism DOF3. The Planar four bar linkages
Chapter Two Planar Linkage
Chapter Two Planar Linkage
General Character of a four-bar linkage
2.1 )Basic Form of Four-bar Linakage
2.2 ) Grashof Criterion (Conditions of a Crank)
2. 3)Inversions of Four-bar Linkage
2. 4)Kinematic Design of Four-bar Linkage
•Character of Planar Linkage
1.Advantage–Bar form link, the distance of kinematic
transmission can be longer
–Low pairing, Force Transmitted be very large
–Can got a very complex curve
–Different motions
2.Shortage:Low Efficiency, Inertia force,
Not easy to design•Problem to be Investigated
–Kinematic analysis
–Kinematic design
2.1 Basic form of four-bar linkage
2.1.1 Crank rocker
2.1.2 Double crank
2.1.3 Double rocker
2.1.1 Crank rocker mechanism
1)Constitution2)Quick return Character 3)Pressure angle and transmission angle4)Dead point position
Crank Floating
linkOr coupler Side links Frame
Constitution of four bar mechanism
Diagram of quick return principle
Quick return2.1.1 Crank rocker mechanism
Quick return character of a crank rocker
Definition Coefficient of Advance return time ratio K=Vmb\r/Vma>=1 K= ( 180º )) 180º- ) Limit position : Extreme position of the
driven bar crank angle between extreme positions
Quick return is used to describe the characteristic of the driven bar
If that is:then the mechanism has quick return character
Pay attention to the direction of prime mover when analyze the quick return characteristic
Quick return Character of crank-rocker
Pressure angle : without consideration of friction force, The acute angle between the acted force line of driven link and the velocity direction of acted point.
Transmission angle : the component angle of pressure
Represent its transmission performance. The bigger the ) the better performance to trans
mit force.When Design a mechanism ) min
Where is the smallest ?
Pressure angle 、 transmission angle
Extreme position of the transmission angle
When the transmission angle is zero, this position is called dead point.
You must know which is the prime move when analyze the dead point.
Dead point is a special position of the mechanism. It is different from the DOF equals zero. Or the mechanism is self-locking.
How to avoid the dead point? Duplicate a linkage out of 90 degrees
phase With the help of a flying wheel Acting a outer forceHow to use the dead point Landing mechanism in airplane Clamping device on machine tool
Dead point
Use the quick return character of driven crank
Parallel linkageanti-parallel linkage
2.1.2 double crank
The formation
crane
landing mechanism of a air plane
2.1.3 Double rocker
2.2 Grashof Criterion1 ) The question asked why there is a c
rank2 ) Grashof criterion ( Conditions for h
aving a crank)Suppose: l1=min{l1,l2,l3,l4} l4=max{l1,l2,l3,l4} l1+l 4 <=l2+l3
the crank should be the shortest link bar l1
2.3 Inversions form of a four-bar linkage mechanism
1) Changing the kinematic pairing a. The crank slider mechanism2) Changing the fixed linka) guide bar mechanismb) Rocking block and fixed block mechanis
m3) Enlarge the size of a pairinga) eccentric wheel mechanism
1 ) graphical design–Know the positions of a coupler ,–Know the positions of side likns
–Know the quick return coefficient
2 ) through the experiment
2 ) analytical design–Know the positions of side links
–Know the trace point of a coupler
4 ) Optimization
2.4 Kinematic Design of planar four-bar linkage
To realize the motion of a driven link
To Realize certain trace curve
2.4.1 Given the movement of driven link
Given : the quick return coefficient K , the length of a rocker l3 It’s rocking angle , Design this mechanism!Steps :1 ) Calculate the value of 2 ) draw an equilateral triangle with side length l3 and the top angle 3 ) draw a right angle triangle , the right angle side has a angle 90- 4 ) take the hypotenus as the diameter, draw a circumcircle5 ) Taka an appropriate point, decide the length of crank and coupler
Know the speed ratio of driven link
Design a door for heat-treatment oven
1 ) Analyze the problem2 ) The optimization of the results3 ) Given the three positions of a
coupler, How to solve the Problem?4 ) Given four or more positions of a
coupler, How to deal with the problem?
Know the positions of a coupler
2.4.2 Give the movement of driven link
Exm.1 Concept design of a door
Gas d
oor
Fliu
d d
oor
Magnetic fluid
door
Mech
anical
door
Biological door
Exm1. Mechanical Ways of a Door
Soft door
Folding door
Push-pull door
Rotating door
Horizontal axis Vertical axis
single
double
The open methods of vertical axis doors
、、Inward or
outward?
2.4 Kinematic Design of planar four-barlinkageGiven the trace points of a coupler
graphical method, Experiment method, Virtual experiment method, Analytical method, synthetic method
Steps to optimization 1 ) Describe the problem with mathematic model
and the constraint equations
2 ) Select a appropriate method and software package
3 ) Analyze the calculate results.
Homework today
1) Exercise book, pp 42, Prob. 2.162) Design a door operating
mechanism, Analyze the given Conditions and How to solve it. Please give the size of your design