A unified treatment is presented of certain portions of Burmester theory by including finite as well as infinitesimal displacements. Theorems of R. Mueller concerning collinearity, order of contact, symmetry, and location of the Burmester points associated with infinitesimal, coplanar displacements of a plane, are extended to the more general case of arbitrary, coplanar displacements. Additional extensions relate to a recent study of infinitesimal displacements by G. R. Veldkamp [27] and, in some instances, are not related to earlier studies. The results of the present investigation are summarized in Table 2.

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