Numerical evaluation of periodic transverse vibration of elastic connecting rods in a six-link mechanism

In the case of stationary motion, the generalized Ritz's method has been applied to obtain system of linear differential equations with periodic coefficients. We have written computer programs to check conditions of dynamic stability and to find periodic solutions of the obtained equations. Numerical examples are given and from which the effect of elastic factors on articulation reactions is evaluated. | T~p chi C OzOs = l1, 01A = lz, AB = ls, OzB = t., OzC = "l., CD= is, D03 =is. The kinematics relations between links are: lz cos ~ cos( ~ sin(z)], () - 'Ps + 2). () + •) J, () () F~r the rocker OaD (Fig. 4): Xo, = XD + Pa sin :3 , {) 0 t, YA = Ys- j [p,(gcos 'Ps 0 37 +a,.)+ c3yv3y]d:>:3, () 4 £~ { j Ys = ~ 3 0~3~~2 ) dxs + j [J.'s (g cos lOs + asy) ,, [Ps Js ( s'is + 0 0 + c3 yvsy]xsdxs- J () [J.'s(gsinl"s +as.)+ .]wsdxs. Q As for the connecting rod CD, it is seen that the model is completely similar to that of AB by changing the index 3 into 5 and the letters A, B into C, D respectively. So we have: J'• e. J £~ J ,, -J(~ts(gsinl"s Xa = Xv- ((gsinl"s +as.)+ ,]dxs,. () [(gcos\Os + asy) + csyvs.]dxs, () 0 Yo= Yv- 0 is Yv = { [psJs(s;, 3''""''"'''" ,,,,;.E;.;J;,~;o ,,· ,!iJ,-!f ; /.(t) ·· (3 4} B;J; • ~;''':;irJ~t)':''£f.~;f~siJi~i"-:-:t;;:;, sin t/1; -lj_ 12 = n, and .Pk,