tutorial 6: mechanism fundermentals
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Tutorial 6:Mechanism FundermentalsZhengjian, XUOct 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)
cdabdc
2)(cos222
4
cdabdc
2)(cos222
4
4
4
d
c
a
b
a
bc
Transmission angle
bcabbc
trans 2)(cos222
A
O1
B
O2
AO1
B
O2
(3.1)
(3.2)
bcadcb
trans 2)(cos222
Two limited status:
trans
trans
a
b
b
a
c
d
Four-Bar slider-crank mechanismThe output range:
Inverted slider-crank mechanism
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