The cone parts of cheiroballistra arms are made from hardwood. This is an early method I've used to make the cones, and as long as you take care that grain of the wood is not violated at the back, i.e. the side where the groove will be, the arms made with this method should work well. An alternative method for making the cones is described here.
After the cones are finished, you need to cut the grooves for the bars as described here.
Tapering the cone Edit
Mark the outline of the cone to a piece of hardwood:
Cut and plane the piece of wood so that you get two straight sides that are in 90 degree angle:
Mark the outline of the cone onto one side:
Plane one side into tapering, conical form:
At this point the other side is still untapered:
Plane the other side into tapering form:
After planing the cone should look like this:
Any minor irregularities will get removed when the cone is rounded.
Rounding the tapered cone Edit
Use a rasp to make the bottom side of the cone round:
Do the same for the top side of the cone round, but leave the fairly narrow tips somewhat rectangular:
After rasping the entire cone it should look like this:
Finish the work with a file and some sandpaper: