We can observe that at the Equinox the sun raises everywhere on earth exactly due east and sets everywhere exactly due west. The path of the sun between east and west depends only on Latitude. At the Equator the sun at noon is directly overhead. At other locations the path between east and west is slanted according to the Latitude of the location.
While it is obvious how the shadow behaves at the equator, it is not so easy to comprehend anywhere else. The sun is about 150,000,000 km away, so the sun rays come in essentially parallel everywhere on earth. We can transport a sundial from the equator to any location while maintaining its north-south axis parallel to earth axis and keep the surface of the sundial parallel to the surface at the equator at the same longitude. In my sundial model I can do this by tilting the top of the sundial to a degree corresponding to the latitude of the location. In this way the sundial shows everywhere on the same longitude exactly the same shadow. This observation only works on the globe.
The following animation visualizes this fact. If you move the Latitude slider, the top part of the sundial changes its tilt in such a way, that the red line of the sundial stays parallel to earth's axis.
Use the Time slider to change the local time at the location of the sundial and observe how the shadows progress. On the graphic in the top left corner the orange arrow shows the direction of the sunlight as it illuminates the sundial.
The Celestial sphere in the top left corner maintains the same orientation as the globe. You can see where the sun is with respect to earth and from which direction the light is cast onto the earth. The orange circle represents the Ecliptic, the apparent path the sun follows during the year. If you change the slider Earth Tilt, you change the month of the year accordingly, so that the sun is below or above the celectial equator. On the equinox the Earth Tilt is 0, so no pole of the earth is tilted towards the sun. The tilt is sideways.
Note: the animation uses an earth fixed coordinate system to keep the sundial in view. So the change in tilt, which corresponds to a change in earth's orbital position, is only visible on the celectial sphere, where the ecliptic rotates accordingly. But you can also see that the shadow of the earth changes as the sun moves on the ecliptic.
The sundial is constructed in such a way, that on Equinox the shadows bild exact parallel lines. On each other day the shadow diverts up or down and builds a corner.
I made my observations at the 20. Sept. 2018, 3 days before equinox. It shows a slight deviation of the shadow from exactly parallel as expected. The shadows are a little bit off to the bottom, because the sun's path is still a little bit higher than at the equinox.
Here are some pictures of my Equinox Sundial:
I created the blueprints with Inkscape out of my head after I had an idea of how the sundial sould look like. I designed the sundial as 3 parts: Base, Protractor and Top. All parts can simply be stacked together, although I glued the Protractor and the Top together.
You can download the Blueprints as PDF files below:
I used thicker than normal A4 paper and printed the Blueprints on them. Then I cut out the shapes and glued it together as shown in the images below: