Most moped companies were short lived enough that the evolution of their logo was slight or never happened. One exception is Motobecane, who changed their mark numerous times. Starting off as a low powered motorcycle manufacturer in 1923, the company quickly expanded into pedal bicycles. In 1949 they fused these two interests into a third product, the moped.
The initial Motobecane trademark contained the company name in a custom typeface on top of two heads, facing each other, with elongated helmets. Behind the heads is a shield form, typical of logos for that time period. The negative space created by the heads and shield creates an anchor shape. Both the imagery and the symmetry of the logo imply stability and strength.
In Image 2 you can see the name has been shortened to the initials MB, and the helmets are much shorter to accommodate this change. This might have been used simultaneously with the logo shown in Image 1, but in areas where width was a concern. This points to a problem in the original logo in that it's hard to read at small sizes. The background of the new mark extends upward to form a diamond shape, which ties the three elements together into a whole.
The changes found in Image 3 show a further refinement using the same principles. The initials are now shorted to a single "M". The faces are abstracted and have lower helmet markings, giving them the appearance of wings. The outside shape is now circular, which continues the cohesion between the elements that was started in the last logo. This new design works better at smaller sizes, gives the mark a more open and modern feeling. This logo also signifies the entrance of the lone "M" as a hint at future changes.
The differences between Image 3 and Image 4 are slight, but important. In this variation the company name can be used within the logo when desired, but left out if size dictates. Also, the outer ring contains the abstracted heads, which completes the move toward enclosing all elements within a single shape.
The trademark shown in Image 5 is quite a departure from the one before it. The heads are all but gone, reduced to mere platforms for the legs of the M to stand upon. The M itself is stretched out, most likely to reduce its height. This version is often found on the backs of moped seats, where vertical space is limited.
The final example, Image 6, is the marking that Motobecane used to brand all of its products throughout the moped's heyday in the 70's and early 80's. The heads below the M are gone, as is the outer ring. They're replaced instead by an outline of the M itself, emphasizing the letter while creating a third M its negative space. This pattern of three is continued to the coloring of the internal M, which is striped horizontally with blue, white and red. The choice of colors no doubt came as a symbol of France as Motobecane stepped up the exportation of its products. Additionally, the colors resonated with one of its new subsidiaries, Motobecane of America.
The evolution of the Motobecane mark is subtle, never alienating or confusing customers with too large of a change. Compare Image 1 with Image 6 and it becomes clear that the change couldn't of happened directly without the intermediary steps. As Motobecane refined their business they updated their logo, keeping with the times without rejecting their heritage. The logo was retired in 1983 when the company was sold to Yamaha and marketed under the name MBK. Although manufacturing the same products, often with the same materials, MBK chose not to base their logo off of the existing Motobecane mark.