The cone parts of cheiroballistra arms are made from hardwood. This article describes a method for planing the cones without violating the grain of the wood on the back, i.e. the side where the groove for the metal bar will be cut. After the cones are finished, you need to cut the grooves for the bars as described here.
The process step-by-step Edit
Take a straight piece of hardwood - elm is a good choice - with unviolated outside surface and cut it to correct length. Mark the forward and butt-ends of the cone to the ends of the piece. Also mark the location of the groove:
Use a spokeshave to make the cone roughly the correct shape:
Place the roughly formed cone into a planing board and carefully plane the cone to correct dimensions with a smoothing plane. Take special care to leave the back of the wood intact:
The finished cone should look like this: