Biological evolution has not produced wheel-like organs that exhibit a continuously looping movement while remaining in contact with the ground. However, an organism can move continuously even if it's not on wheels and even if its foot—the part of its body in contact with the ground—consists of units that take turns moving sequentially. This type of movement has evolved in gastropods.
Part 1 of this series introduced the observation that during the locomotion of a snail (or a slug) the movement of a given point on the sole of the snail is not continuous, but intermittent, even though the overall movement of the snail is continuous. Here is another demonstration of the same phenomenon, this time using data from my files. Because these data are not published yet, I will not reveal the species; it will suffice to note that it's one of those snails that has a snout anatomically separate from its foot.
Notice how the horizontal movement of a selected point on the sole is intermittent, while that of the snout is more or less continuous*.
Here is a diagram to explain how a snail accomplishes this (that thing actually looks like slug, but it doesn't matter).
For simplicity, assume that the sole of the snail consists of only 3 units (A, B and C) that move sequentially. First, A moves forward, while B and C are at rest. Then, B moves forward, while A and C are at rest and so on. The trick is that the upper body is attached to the foot in such a way that it must move forward every time one of the units making up the sole moves forward. The results is that the progression of the body, for example, the front of it (thin blue line) is continuous, even though the progression of any one unit in the sole, for example, A (thin red line) is intermittent.
In a real gastropod, there is a wave-like motion within the sole that usually starts at the tip of the tail and moves forward to the head. Only that portion of the sole where the wave happens to be at a given instance moves forward, while the rest of the sole remains stationary on the substrate. However, the overall results is that the snail continuously moves forward.
That this is the general mechanism of gastropod locomotion was deduced a long time ago. For example, Parker wrote in 1911:
At first thought it might seem that such a wave movement could not produce so uniform a motion as snails show, but it must be remembered that the uniformity of this movement is seen only in parts of the animal some distance from the foot. On the foot itself the operation is alternate movement and rest, which becomes more and more continuous motion as points on the body more and more distant from the foot are reached. The locomotion is in many fundamental respects like that of the human being. In our locomotion each foot is alternately at rest and in motion and yet distant parts of our body, like the head, show a motion which in comparison with that of our feet is almost continuously uniform.Of course, there are many details and variations among different gastropod taxa that still need to be worked out.
I will return to this subject.
*The raw data consist of sequential photographs taken over several seconds. The horizontal axis of the graph is simply the image number. The horizontal displacement (vertical axis) is in arbitrary units, because no scale was included in the photographs.
G. H. Parker. 1911. The mechanism of locomotion in gastropods. Journal of Morphology, 22:155-170. pdf available at Biodiversity Heritage Library