First time I tried my hands on routing a line art using a rotary tool with router attachment. Learning routing process on an acrylic sheet is easier than on wood. So, I selected a piece of left-over acrylic sheet from one of my earlier projects and a simple line art I downloaded from the internet. What you see here is the end result of my experiment.

Step 1: Materials Required

A piece of acrylic sheet. Here I have used 2 mm thick acrylic sheet of size 13 inches by 10 inches. Please see the information printed on the sheet, which shows that this sheet can be routed.
Plain A 4 printing paper
Adhesive taps of different colors. I will mostly use two colors only.
A packet of Playdough.

Step 2: Tools Required

Dremel 4000 Rotary tool or any such equipment
A Router Bit. I have selected an arrow head shaped bit for this project.
Plunge Router attachment for Dremel rotary tool. This attachment will allow you to convert your rotary tool into a router.
A small bench vice to hold the acrylic sheet with the work table.

Step 3: Transfer Image to Acrylic Sheet

First time I wanted to try a simple line drawing. I have searched the net and found this simple sketch showing the three wise men visiting Baby Jesus and Mother Mary. This picture does not have many intricate details and will be easy to work with.

Take a printout of the sketch on a A 4 printing paper.
Remove the protective covering from the Acrylic sheet on both sides
Attach the printed sketch on one side of the acrylic sheet with adhesive tap
Trace the sketch on the acrylic sheet with permanent marker pen.
Remove the printed sketch from below the acrylic sheet and attach a plain white paper in its place.

Step 4: Getting Ready to Route

Fix the Acrylic sheet to a working table with the mini vice.
Attach the Dremel rotary tool to the plunge router
Attach the Router bit to the rotary tool
Now adjust and fix the plunge router so that the router bit cuts just about one mm deep on the acrylic sheet

Step 5: Routing on the Acrylic Sheet

Place the plunge router with the rotary tool on the acrylic sheet
Lift the cutting bit just above the acrylic sheet and switch on the tool
Now place the router pit tip on the traced sketch and start routing along the line.
Go slow. If in doubt stop the rotary tool and check your work piece.
From time to time brush out the bits routed from the acrylic sheet. This will give you clear view of the trace lines.

Please see the video showing routing on acrylic sheet.

Step 6: Routing Progress

Here you can see in these pictures, that I have started from bottom right. After completing the right side, I have shifted the tool towards left and completed the lower portion of the sketch.
For upper portion, I have turned over the acrylic sheet on the work table and completed routing.
Using a brush remove all bits and pieces from the completed acrylic sheet

Step 7: Border and Edges

Mark the border along the routed sketch.
Now we need to trim the excess portion of acrylic sheet on all sides.
Mark another line all around leaving about half an inch from the border line.
Using a spacer adjustment tool, route on these lines as we did earlier.
Trim away the excess using a cutting tool. Remove and clean the acrylic sheet from the work table

The last picture shows the completed piece

Step 8: Border With Adhesive Tap

Using violet colored adhesive tap, I have added border all along the outer edges of the acrylic sheet

Step 9: Cover Backside

Now we can cover the back side with a different colored adhesive tap. Here I have used green color to cover the back.

Step 10: Fill the Routed Portion With Playdough

If you keep the routed piece as it is, the plain routed lines may not be visible from a distance. So we will use Playdough to fill the routed lines. I have selected orange colored Playdough which will highlight the picture from the green background.
Remove small quantities of playdough and fill the routed lines. This will help in the playdough getting spoiled due to exposure to air.
Scrap out excess playdough before it hardens.

Our routed picture on acrylic sheet is ready