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

Solution 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.

Solution 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.