Some Non-Linear Effects in the Vibration of a Four-Bar Linkage

The non-linear effects which are examined are those arising from the changes of linkage geometry during the course of the motion. The fundamental frequency of a linkage with rigid members controlled by discrete, linear torsion springs is analysed and solutions offered in terms of phase plane and energy methods, together with an approximate closed solution in the form of a harmonic series with terms in sin (2n + 1)ωt and cos 2nωt. Experimental results are presented for free and forced motions which, with one exception, agree well with the theoretical predictions of the energy and series solutions.

In Appendix 1 a (velocity)² term appearing in the series solution is shown to be a conservative, soft spring effect arising from apparently variable inertia.