When building a covered walkway, patio cover, or pergola, an ogee on the end of the beams adds a nice finishing touch. An ogee is a curve the is roughly S shaped that consists of two arcs, one concave and one convex. This shape is sometimes called Cyma Recta but most people know it as an ogee. (Cyma Recta sounds like something the Proctologist does at you annual check up.)
There are two problems with using them; laying then out and cutting them out. This Instructable with cover the steps required to lay out your own.
Step 1: Select Type
Again an ogee is an S curve in which some embellishments that can be added. I recommend that you do not carried away. The ogee on the bottom is the basic S curve with a bit on the beam left on the top. Lets call it the simple ogee. I find proportions of equal thirds to be pleasing to my eye. You may want to vary you proportions.
The ogee on the top is same as the bottom ogee with a definition step added to the bottom. Let's called it the stepped ogee. This gives a more formal appearance. I measure this type of ogee using proportions of sevenths. Again you are free to lay out with whatever proportion you find pleasing.
The following steps will show how to lay out these two examples. If you care to use different proportions you will have to figure those out yourself.
Step 2: Draw Proportion Lines
If making a simple ogee then draw a line on the top right of the beam. 1/3rd the width on the beam.
If making a stepped ogee then draw a line on the top right of the bean, 2/7ths the width of the beam and on the line on the left, 1/7th of the width.
The lines need not be much longer than the width of the beam.
Step 3: Draw First Arc
You will need a compass to draw the arcs. Here are links to some decent, inexpensive compasses, one large and one small.
For the simple ogee place the compass center at the top left corner of the beam. Set the width so it draws an arc the touches the reference line on the right. Draw a quarter circle.
For the step ogee place to compass center at the top of the left reference lines, Set the width it draws an arc the touches the reference line on the right. Draw a quarter circle.
Step 4: Draw Second Arc
Adjust the compass so it draws an arc exactly twice the length as the first arc. (This is easily done by using the compass set to it original length to mark two lengths and use this length to set the compass.)
Place the center of the compass in the same place the used for the first arc. Draw the arc and mark the place where intersects the right reference line. Mark this point!
Step 5: Draw Third Arc
Set the compass back to the original length, center the compass in new reference point and draw a arc the touches s the first arc and the left reference line. (Left side for simple ogee.) For the stepped ogee, mark a perpendicular line from the new reference point to the left side.)
The are only three arcs to draw and the first and last have the same length. If I am laying out many ogees I will use two compasses. It will save time. (Imagine having 10 beams, each with an ogee on each side, all the same width.)
Step 6: Clearly Mark the Ogee
You have many lines drawn on your beam and I guarantee you will make a wrong cut on at least one if you do not clearly mark the curve to cut. Darken the curve to be cut.
Step 7: Cut Your Ogee
There are many options to cut the beam. If they are 2 by material than a saber saw works well. For really thick beams, it is fun to hack into shape with an hand ax and finish up with a rasp.