Many thanks to Alistair of Histon Junior School, who sent in this solution:
Set compass to 3 cm.
Mark a point in pencil and draw a circle around that
point with the compass.
Draw a vertical line with a ruler through the middle of the circle.
Measure and mark each 1.5 cm along it.
Set compass to 1.5 cm.
Draw semicircle to the left around the lowest 1.5cm
Draw another semicircle to the right around the topmost 1.5cm mark.
Set compass to a very small size, and draw circles around both 1.5cm
Rub out vertical line and centre marks.