I've been thinking about rolling motion, helped by @kuruman's excellent Insights article on the topic. A crucial insight from that article is that, when a wheel rolls along a flat surface, its axis of rotation is through the instantaneous point of contact with the ground, not through its axle. Thinking about this, I reached a tentative conclusion that a necessary condition for the commencement of rolling to be possible is that either the wheel not be a perfect circle as it sits on the floor OR the ground deforms under the weight of the wheel. Otherwise the wheel could not rotate around the point of contact without part of the wheel going below the floor. The problem is easily solved by replacing the circular wheel by a regular polygon of n sides. No matter how large n is, there will always be one or two vertices in contact with the floor and, on application of a suitable force to the wheel, it can always pivot around the grounded vertex closest to the forward direction of the applied force. It pivots around that until the next vertex hits the ground, then it starts to rotate around that vertex instead. A more realistic depiction that makes the commencement of rolling possible is to consider the wheel's shape as a circle with a portion of the bottom part chopped off, along a chord so that the contact with the ground is a line segment (the chord at which the excision takes place) rather than just a point. This allows the wheel to rotate around the foremost part of the chord without 'running into the ground'. So in practice, the commencement of rolling is possible because the wheel will deform under its own weight (plus that of any load on the axle) to create a flat contact region that allows rolling. With a pneumatic tyre, this is easy to imagine. But even with a metal railway or tram wheel there will be some deformation of the wheel to create a small flat contact patch. My theory (speculation, rather) is that, without that deformation, the commencement of rolling motion would be impossible. This would all be much clearer and make much more sense with some diagrams, and I am proposing to make some, and maybe write a short note about this idea if it turns out not to be misconceived. But before I do that, I'd be interested to hear from anybody that has thought deeply about the commencement of rolling motion, if they think the idea is daft because I've missed some important feature, or alternatively if they think it is correct. Perhaps somebody has already written about this. If so it would be good to get a link to that. Thank you EDIT 6 Nov 2017: I realised after some of the discussion below that the real difficulty was not in explaining rolling motion, but in explaining the commencement of rolling motion by application of a force to the wheel. That is corrected in later posts below. But in order to avoid wasting the time of newcomers to the thread, who don't have time to read the whole thing, and who otherwise might spend the time to help by writing explanations of the constant-speed motion of a translating, rotating circle - which is already clearly understood, I have added words in this green font above to make clear that it is only the commencement of motion that is under investigation. EDIT 2: 18 Nov 2017: There are now diagrams of what this is talking about, in this post.