Some bases for an argument

01. For the reader already familiar with other discussions about the cylindroid (chapters 6, 15, 16 and elsewhere) it will be clear that a cylindroid is always lurking wherever there is a situation of two degrees of freedom – or wherever there are two forces or wrenches acting (§ 10.14). For the reader unaware as yet of the relevant generalities, the present chapter may be taken as a piece of purposely confusing, preliminary reading. It must be said in the kinematics (and the statics) of mechanism that the simpler a situation appears to be, the more baffling its deeper aspects often are. The science of the relative motion of rigid contacting bodies is bedevilled by degeneracies of its general geometry; these degeneracies, when taken in isolation, have a tendency to render the science a miscellany of unrelated facts and alleged separate theorems for which there appears to be no integrative binding. This chapter deals with some of that miscellany but with almost none of its binding; I shall be dealing here with the kinematics of only a few special cases of two degrees of freedom and I offer no conclusive results at the end of it.

02. However with no more than a primitive understanding of the relationship c + f= 6, where c is the number of constraints upon a body and/is its number of freedoms (§ 1.52), we can begin a useful argument here about the matter of two degrees of freedom.