1. How to draw a kinematic diagram 2. The Mechanism DOF 3
How to draw a kinematic diagram 2. The Mechanism DOF 3. The Planar four bar linkages

2. Chapter Two Planar Linkage

3. 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

4. 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

5. 2.1 Basic form of four-bar linkage
2.1.1 Crank rocker
2.1.2 Double crank
2.1.3 Double rocker

6. 2.1.1 Crank rocker mechanism
1）Constitution
2）Quick return Character
3）Pressure angle and transmission angle
4）Dead point position

7. Constitution of four bar mechanism
Crank
Floating link
Or coupler
Side links
Frame

8. 2.1.1 Crank rocker mechanism Diagram of quick return principle

9. Quick return character of a crank rocker
Definition
Coefficient of Advance return time ratio
K=Vmb\r/Vma>=1
K=（180º+q）/（180º-q）
Limit position：Extreme position of the driven bar
crank angle between extreme positions

10. Quick return Character of crank-rocker
Quick return is used to describe the characteristic of the driven bar
If q >0 , that is:K>0 then the mechanism has quick return character
Pay attention to the direction of prime mover when analyze the quick return characteristic

11. Pressure angle a、transmission angle
Pressure angle a: 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 g: the component angle of pressure
Represent its transmission performance.
The bigger the g，the better performance to transmit force.
When Design a mechanism，g gmin
Where is the smallest g?

12. Extreme position of the transmission angle

13. Dead point How to avoid the dead point?
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 force
How to use the dead point
Landing mechanism in airplane
Clamping device on machine tool

14. 2.1.2 double crank Use the quick return character of driven crank
Parallel linkage
anti-parallel linkage

15. 2.1.3 Double rocker The formation crane
landing mechanism of a air plane

16. 2.2 Grashof Criterion 1）The question asked why there is a crank
2）Grashof criterion ( Conditions for having 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

17. 2.3 Inversions form of a four-bar linkage mechanism
1) Changing the kinematic pairing
a. The crank slider mechanism
2) Changing the fixed link
a) guide bar mechanism
b) Rocking block and fixed block mechanism
3) Enlarge the size of a pairing
a) eccentric wheel mechanism

18. 2.4 Kinematic Design of planar four-bar linkage
To realize the motion of a driven link
To Realize certain trace curve
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

19. 2.4.1 Given the movement of driven link
Know the speed ratio of driven link
Given：the quick return coefficient K，the length of a rocker l3 It’s rocking angle f，Design this mechanism!
Steps：
1）Calculate the value of q
2）draw an equilateral triangle with side length l3 and the top angle f
3）draw a right angle triangle，the right angle side has a angle 90- q
4）take the hypotenus as the diameter, draw a circumcircle
5）Taka an appropriate point, decide the length of crank and coupler

20. 2.4.2 Give the movement of driven link
Know the positions of a coupler
Design a door for heat-treatment oven
1）Analyze the problem
2）The optimization of the results
3）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?

21. Exm.1 Concept design of a door
Mechanical door
Biological door
Magnetic fluid door
Gas door
Fliud door

22. Exm1. Mechanical Ways of a Door
Rotating door
Folding door
Soft door
Push-pull door
Horizontal axis
Vertical axis
double
single

23. The open methods of vertical axis doors、
Inward or outward?

24. 2.4 Kinematic Design of planar four-barlinkage
Given 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.

25. Homework today Exercise book, pp 42, Prob. 2.16
Design a door operating mechanism, Analyze the given Conditions and How to solve it. Please give the size of your design