How can a pantograph enlarge or reduce a drawing accurately?

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Figure 1: Two techniques of representing an object. (A) Perspective drawing, suggesting that the object is cubical. (B) Orthographic top and front views, revealing that the object is not cubical. — drafting Figure 1: *Two techniques of representing an object.* (A) Perspective drawing, suggesting that the object is cubical. (B) Orthographic top and front views, revealing that the object is not cubical.

A pantograph is a mechanical instrument designed to duplicate, enlarge, or reduce geometric shapes and drawings with precision. It functions through an assemblage of rigid bars connected by pin joints, which are configured to form a parallelogram.1

The device operates based on the relative movement of specific points on these bars:

Enlarging a drawing: When a guided point (P) is moved along the outline of the original drawing, a second point (Q) on a connected bar traces the same path on an enlarged scale.1
Reducing a drawing: Conversely, if the point (Q) is guided along the original outline, the point (P) will trace a reduced version of that path.1

Because the bars are adjustably joined, the scale of the reproduction can be predetermined by the configuration of the linkages. This makes the pantograph a reliable tool for drafting, as it ensures the copy maintains the exact geometric proportions of the original drawing or map.1