Grades 3–5 · Mathematics
How can linked rods make a larger drawing?
Before a copier could enlarge a drawing, joined rods could do the job. A pantograph connects a tracing point to a pencil. Moving the tracer along a small outline makes the pencil follow a larger matching outline.
In the diagramLinked rods keep a two-times scaleA fixed anchor, a tracer and an extended pencilAnchorTracerPencilPencil distance =2 × tracer distanceDistances are measured from the anchor.
The illustrated linkage has four sides that keep a parallelogram shape as the joints turn. One corner is anchored to the table. The tracer sits halfway along the opposite side. Another rod continues beyond its corner to carry the pencil.
These positions make the anchor, tracer and pencil stay on one straight line. The pencil is always twice as far from the anchor as the tracer. If the tracer moves one centimeter sideways, the pencil moves two centimeters sideways. Vertical changes double too.
Every traced point follows the same scale rule, so a whole outline becomes a two-times copy. The rods cannot reach every point on the table. Within their range, their geometry keeps the enlargement consistent without a motor or computer.
About this explanation
Starting knowledge: Recognize parallel sides and understand doubling a distance.
Sources
- Wolfram MathWorld — Pantograph