上海文通大学 NUMBER SYNTHESIS NUMBER SYNTHESIS:the determination of the number and order of links and joints necessary to produce motion of a particular DOF; ④ Order refers to the number of nodes perlink,i.e.,binary, ternary,quaternary etc; ©Conclusions: >For one DOF,the simplest linkage is four Binary links-the 4-bar linkage. >The addition or subtraction of Ternary links in pairs will not affect the DOF of the mechanism. How to prove? )上海充通大￥ NUMBER SYNTHESIS 1-2-0-生 3 (rewriting Gruebler's equation) Try:M=2m L=2n-1 (even-odd,vice versa) J=3n-m-3 CL=B+T+0+P+H nodes 2B+3T +40+5P+6H 2 2 M=B-Q-2P-3H-3 (1) L-3-M=T+2Q+3P+4H (2) 22 NUMBER SYNTHESIS: the determination of the number and order of links and joints necessary to produce motion of a particular DOF; Order refers to the number of nodes perlink, i.e., binary, ternary, quaternary etc; Conclusions:  For one DOF, the simplest linkage is four Binary links- the 4-bar linkage.  The addition or subtraction of Ternary links in pairs will not affect the DOF of the mechanism. NUMBER SYNTHESIS How to prove? (rewriting Gruebler's equation) (even-odd, vice versa) (1) (2) NUMBER SYNTHESIS