Does there exist a tool to construct a perfect sine wave?

Question

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)?

Answer 1

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.

Answer 2

Here's an ideal mechanical device to draw a sine curve: When a disk $D$ of radius $r$ (shaded below) rolls without slipping inside a circle $C$ of radius $2r$, each point on the perimeter of $D$ traces a diameter of $C$. Place such an apparatus over a roll of paper whose lateral speed (here, left to right) is constant (possibly geared to the angular speed with which $D$ rolls inside $C$, in order to control the wavelength). The boundary point of $D$ lying on the diameter of $C$ perpendicular to the lateral motion of the paper traces a sine curve on the paper.