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