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me351_lec04

# For example suppose p is a point xed in the coupler

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Unformatted text preview: cos θ3 r3 sin θ3 k3 k4 r4 cos θ4 r4 sin θ4 =− r2 cos θ2 r2 sin θ2 Now, let’s make sure we can ﬁnd the velocity of any point ﬁxed to any of the links. For example, suppose P is a point ﬁxed in the coupler bar, 3. Then RP = R2 + dei(θ3 +λ) , where d = |RP − R2 | ˙ ˙ ˙ and λ = (R3 , RP − R2 ) are constants. Thus, we ﬁnd that vP = RP = iθ2 R2 + iθ3 dei(θ3 +λ) . Of course, the vector RP/P2 = RP − R2 is ﬁxed in link 3 so we have directly dRP/P2 = VP − VP2 = iω3 RP/P2 , dt VP 2 = dR2 dt which gives the same result. At this point we can consider programming the combination of position and velocity analysis. A sample program of this sort is given below: function fourbar4(lnk, ang, omega2) % %function fourbar4(lnk, ang, omega2) % % Four bar linkage position/velocity analysis % links vectors z_j=r_jexp(th_j), j=1,..,4 % Inputs: % lnk= [r1,r2,r3,r4]= array of given link lengths % ang=[th1,th2,th3,th4]=array of input angles (degrees) % th1,th2=arg(z1), arg(z2) given input angles (th1 is usually 0 or 180) % th3=arg(z3), th4=arg(z4) approximations to link arguments % omega2= given angular velocity of link 2 % Four bar loop equation z2+z3+z4-z1=0: % r2cos...
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