That is only an approximation to a true cycloidal form. A true cycloidal form cannot be made using arc segments alone. For clocks, any approximation will probably give good service since gear motion is start-stop. My company uses a form called PRESCOTT for some molded gears (no, we don't make clocks), and it is made with circular arc segments.

True cycloidal teeth are formed by "generating circles" -- one above the pitch circle (addenda circle) and one below (dedenda circle). The curves for add and ded are traced out as a point on the generating circles roll without slipping along the pitch circle (in opposite directions). For gears in mesh, the size of the addenda circle of the pinion is equal to the size of the gear's dedenda circle, and vice versa. For pinions of few teeth, the diameter of the addenda circle of the gear is made equal to half the pinion pitch circle diameter. This has an interesting property of making the pinion dedenda straight radial lines. The do "taper" to the center of the pinion.

The parallel flanks for wooden gears is probably just a strength consideration.

I'll try to scan a sketch to clarify.