I've seen a few of these interesting contraptions over the past few years, and really had no idea what they did. All I understood was that it created a copy of something at a smaller or larger ratio. Today I came on a plan to build a trim-router based pantograph that looks simple enough to tackle.
Mattias over at Woodgears came up with a great design and walks through the steps of construction really cleanly and even offers a set of downloadable plans for an exact copy (for a price). His plan also allows for 1/3 and 1/2 ratio copies and a depth dimension for 3D copies.
Take a look as the plan here and if you're interested enough make it a weekend project!