A general graphical procedure for finding motion centers of planar mechanisms

For an infinitesimal motion of a given planar mechanisms we can consider a relative motion center for each pair of rigid components. The location of these relative centers is completely determined for mechanisms with only one internal degree of freedom. We give a graphical procedure to find all relative centers for such a mechanism in a given (non-singular) position, and give an inductive proof that it is general (by means of Henneberg sequences). Besides the known intersection techniques with Aronhold–Kennedy lines and center lines of 2-dof subframeworks, we make use of a classical geometric construction due to J. Baracs. We also show how a graphical procedure for relative centers can be used to find new geometric descriptions for the special positions of some isostatic frameworks.