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

Tutorial 6:Mechanism Fundermenta

lsZhengjian, 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=3 J1=2 J2=1 M= 1

(a) N=6 J1=7 J2=1 M=0

(d) N=7 J1=7 J2= 1 M=3

(c) N=4 J1=4 J2=0 M=1

Classification of four-bar linkage Grashof condition

PQSL Where: L: length of shortest link S: length of longest link P: length of one remaining link Q: the length of another remaining link

Classification of four-bar linkage

Position analysis of 4-bar linkage: graphical method

O2O4

A

2=45°

B1

B2

3

4

Position analysis of 4-bar linkage: graphical method

O2

A

2=45°

B1

B2

3

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

cd

abdc

2

)(cos

222

4

4

4

d

c

a

b

a

bc

Transmission angle

bc

abbctrans 2

)(cos

222

AO1

B

O2

AO1

B

O2

(3.1)

(3.2)

bc

adcbtrans 2

)(cos

222

Two limited status:

trans

trans

a

b

b

a

c

d

Four-Bar slider-crank mechanismThe output range:

Inverted slider-crank mechanism