So guess you never heard of a "Family Crest" ? like a Coat of Arms but is called the Family Crest is usually found on a shield or shield design.
I have heard that widely-misused term, but it doesn't mean what most people think it does.
A coat of arms will generally include a shield (the design on which is often referred to as the coat of arms, or just arms) and a crest (which is displayed on a helmet).
In the above image (the arms of the Canadian Heraldic Authority), the crest is the lion standing on the helmet. People may often call the shield (or the whole thing) a crest, but it isn't one.
you obviously are not aware of the entymology of the term coat of arms here is the Dictionary definition of Coat-of-arms:
coat of arms noun 1.a surcoat or tabard embroidered with heraldic devices, worn by medieval knights over their armor.
2.a heraldic achievement of arms.
now nowhere does it mention it was on the shield, now while helmets did have crests, that is not where the family crest would be displayed, since the family crest was more then just a symbol, which a crest is, it was a gathering of symbols to represent events and such of the family and was usually presented on a shield in a 2-4 field design, while the formal family crest was presented on a banner, now I don't know who you are, but i'm gonna believe the people with doctorates and such in this field over you.