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Tutorial 6: Mechanism Fundermentals Zhengjian, XU Oct 15, 2008

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Tutorial 6:

Mechanism Fundermentals

Zhengjian, XU

Oct 15, 2008

Fundermentals:

Design of Mechinary� Mobility:

Degree of Freedom (DOF),

In 2D mechanism every rigid body has 3 DOF.

� Link:

A Rigid body in the mechinary system

� Joint (Kinematic Pair)

Connect between different Links, the joints can restrain some DOF

of the links.

Analysis of the mobility (DOF)

� 2D mechanism

� 3D mechanism

Where: M is the DOF of the mechanism

N is number of links including the ground

J1 is number of 1 DOF joints

J2 is number of 2 DOF joints

Examples

(b) N=3J1=2

J2=1M= 1

(a) N=6J1=7

J2=1M=0

(d) N=7J1=7

J2= 1M=3

(c) N=4J1=4

J2=0M=1

Classification of four-bar linkage

� Grashof condition

PQSL +≤+

Where: L: length of shortest linkS: length of longest link

P: length of one remaining linkQ: the length of another remaining link

Classification of four-bar linkage

Position analysis of 4-bar linkage: graphical method

O2O4

A

θ2=45°

B1

B2

θ3

θ4

Position analysis of 4-bar linkage: graphical method

O2

A

θ2=45°

B1

B2

θ3

θ

4

Position analysis for Crank-Rocker

mechanism

� The calculation of out-put angle

Transmission angle

Example

� Given L1=12 ,L2=4, L3=8, L4=9;

� (1) Calculate range of output angle

� (2) Calculate range of the transmission angle

(1) , S=4, L=11, Q=9, P=8; therefore S+L<Q+P

(2) a=4, b=9, c=8, d=11

A

O1

B

O2

A

B

O1 O2

(2.1)

(2.2)

cd

abdc

2

)(cos

222

4

+−+=θ

cd

abdc

2

)(cos

222

4

−−+=θ

d

c

a

b

a

b

c

Transmission angle

bc

abbc

trans

2

)(cos

222+−+

AO1

B

O2

AO1

B

O2

(3.1)

(3.2)

bc

adcbtrans

2

)(cos

222−−+

Two limited status:

transθ

transθ

a

b

b

a

c

d

Four-Bar slider-crank mechanism

The output range:

Inverted slider-crank mechanism