Find the midpoint along one of the long edges of the 36" x 16" x 3/4" piece of MDO. Make a small pencil mark 3/4" from the edge at that midpoint. This will be the pivot point for the carriage. Using a pencil and ruler, draw a radius from the midpoint you marked across the front of the MDO. Measure from the back edge out 10", and draw a line parallel with the back edge. This gives you the basic outline for the table. Using a jigsaw, cut along the 10" line you just drew until you get to the radius, then cut around the radius line and back down the 10" line on the other side. This will create the shape of the table. Turn the table over onto its back side. Nail six strips of 1" by 2" lumber to all edges of the table except the circular edge. These will act as supports for the table.
At the midpoint marked along the long edge in the previous step, drill a 1/2" hole to accept the dowel. Along the same edge as the dowel hole, attach two more strips of 1" by 2", securing them with nails. These strips should be 10" long and will act as the fence for the saw guide. For the carriage, cut 45-degree angles off each end of two 8 1/2" by 1 1/2" by 3/4" MDO blocks. Place these blocks at either end of the 36" by 8 1/2" by 3/4" piece of MDO (Image 1). Screw the blocks in place so that their 45-degree angles face in (Image 2). The blocks will act as spacers to provide the necessary clearance for the carriage top.
The 36" by 4" by 3/4" piece of MDO and the 36" by 1 1/2" by 3/4" piece of MDO will act as the guide. Screw the 1 1/2"-wide piece to the edge of the 4"-wide piece at a right angle. This will create a lip along one edge of the 4" piece for the saw's base plate to ride against. Attach this guide to the top of the support blocks with screws. Screw the 36" by 2" by 3/4" piece of MDO into place, parallel to the guide but on the opposite side of the carriage. Note: Your saw's blade will ride in the gap that's created after these two pieces are in place. We used a Porter-Cable circular saw. You may need to change the width of the carriage's top plates to fit your saw.
Place your saw onto the carriage plate, with its blade protruding through the slot and the base plate flush against the lip. On the opposite end of the base plate, attach a strip of 36" by 1" by 3/4" MDO. This will serve as a guide to keep the saw straight and true.
Turn the carriage over to its back side. Measure down 7" from the top edge of the carriage, and find and mark the center point of the width (it should be 4 1/4"). Drill a 1/2" hole at that point. This will be the pivot point for the dowel and will match up with the 1/2" hole on the table.
To mount the carriage on the table, remove the jig's upper assembly (everything above the spacer blocks). Place the base of the carriage assembly under the table so that the two 1/2" holes are aligned. Place a 1/2" dowel into the two holes, through the tabletop and into the carriage so that it doesn't extend below the carriage. Reattach the upper assembly of the carriage.
The carriage arm should swing left and right from the pivot dowel (Image 1). Swing as far right as it will go. Place a speed square between the fence of the table and the carriage so that the carriage is at a 45-degree angle to the fence (Image 2). (Note: If the carriage will not swing all the way to 45 degrees; you need to trim the table supports on the bottom of the carriage.) At this 45-degree angle, drill a 1/4" hole through the carriage upper assembly next to the left base plate's guide strip. This hole should extend through the carriage's upper assembly and 1/2" into the tabletop. Place a 1/4" carriage bolt in the hole to secure the carriage assembly in the 45-degree position for making repetitive 45-degree cuts. You can repeat this procedure for a 90-degree stop and a 45-degree stop on the other side. To use the jig, place the work piece against the fence. Align the carriage to the desired angle. Place your circular saw onto the carriage between the guide strips. Be sure to set the saw blade depth so that you cut no more than 1/8" into the table.