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 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

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

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

Classification of four-bar linkage

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

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

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 B b c O1 (2.1) a O2 A B (2.2) b A c a d O1 O2

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

Four-Bar slider-crank mechanism The output range:

Inverted slider-crank mechanism