ESDU 10019 explores the effects of tolerances in the link lengths on the performance of four-bar linkages. This Item presents an analysis of the four-bar chain mechanism, which includes derivation of:

the coupler and rocker angles in terms of the link lengths,

errors in the link angles due to changes in the link lengths from their nominal values

and position errors of the offsets from the coupler and rocker.

Many applications require careful control of the magnitude of tolerance that is allowable in order that the performance of a linkage is not degraded. The four-bar chain is possibly the most commonly-used linkage because of the diversity of outputs that can be generated by suitable sizing of links.

An example of a simple four-bar crank-rocker linkage illustrates the analysis process, together with the error in the coupler and rocker angles resulting from small changes in the link lengths. The error in the position of the coupler point from small changes in the link lengths only is also shown. A second example illustrates the steering linkage of a vehicle, known as the Ackermann linkage, which is driven by the action of a four-bar linkage.

In an Appendix the equations of kinematic constraint are derived. This approach is an alternative to the approach used in the main body of the Item.