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

2. 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.

3. Analysis of the mobility (DOF)
2D 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
3D mechanism

4. Examples N=6 J1=7 J2=1 M=0 (b) N=3 J1=2 J2=1 M= 1 (c) N=4 J1=4 J2=0
(d) N=7
J1=7
J2= 1
M=3

5. Classification of four-bar linkage
Grashof condition
Where: L: length of shortest link
S: length of longest link
P: length of one remaining link
Q: the length of another remaining link

6. Classification of four-bar linkage

7. Position analysis of 4-bar linkage: graphical method
2=45° A 3 4 O4 O2 B2

8. Position analysis of 4-bar linkage: graphical method
2=45° A O2 4 3 B2

10. Position analysis for Crank-Rocker mechanism
The calculation of out-put angle

11. Transmission angle

13. Example Given L1=12 ,L2=4, L3=8, L4=9;
(1) Calculate range of output angle
(2) Calculate range of the transmission angle

14. (1) , S=4, L=11, Q=9, P=8; therefore S+L<Q+P
(2) a=4, b=9, c=8, d=11 B b c O1
(2.1) a O2 A B
(2.2) b A c a d O1 O2

15. Transmission angle (3.1) (3.2) Two limited status: B b A a O1 O2 B b c

17. Four-Bar slider-crank mechanism
The output range:

18. Inverted slider-crank mechanism