Does there exist a tool to construct a perfect sine wave? For example, a perfect circle can be constructed using a compass and a perfect ellipse can be constructed using two pins and a piece of string, because a circle can be defined as the locus of points equidistant from a circle point and an ellipse can be defined as the locus of all points such that the sum of the distances from that point to the two foci is constant. 

I know that the sine function can be represented by the y-coordinate of an object in uniform circular motion, but does there exist a tool which allows you to draw a perfect sine wave (i.e. drawn by a human on paper)?

Take a circular cylinder and cut it by a plane not orthogonal to the axis.
As you roll the cylinder (without slipping) along the paper, the cut edge traces out a sine wave.

