Current swingarms are an extension of the technology of the aluminum perimeter frames in use: in short they are stressed skin structures welded to the billet machined (or forged) rear axle mounts and the front pivot tube / attachment points. They are extremely complex in engineering, but relatively simple to understand. For example, look at the video starting at 2:25 -- notice the three welded tubular structures more or less aligned with the pivot and axle mounts on both sides and in the radiused cross structure just behind the shock pass tube: those serve the same function as a square section tube linking the two ends / sides together without all the weight by tying the inner and outer skins together, thus creating an inherently stiffer structure in this critical area. The overall height of the assembly is necessary to provide torsional stiffness, but also allow some flex to self damp at the same rate as the chassis: necessary for a balanced package. I could give you a brief overview of the mathematics of the design, but it would be of little use unless you have a supercomputer necessary to complete the calculations within your lifetime! Suffice it to say some of the most talented engineers in the industry are not working on the engine designs -- instead they are designing the chassis / swingarms: considerably more complex as they have to tread a very fine line between weight, stiffness, and "tuned flex" to get the entire package to work at the speeds and loads of MotoGP racing.
Additionally, a process called superplastic forming is used to fabricate the sheets of the swingarm in order to vary the thickness of the sections: the individual sheet sections are heated to roughly 450 to 550 C depending on the alloy used and pressed into matching dies to make the sections thicker where necessary, and thinner where extra weight is unnecessary / undesirable. In short, while it is possible to make a swingarm like this without the vast amount of knowledge and resources necessary to calculate the load vectors and stresses, it would be a very hit or miss situation to make a structure to handle the loads applied.
Then, of course, you have to set up the shock and linkages for a nearly linear progression for racing, or a rising rate for the street, and tie it all to the frame. Again, more math. here is a pretty good article on that subject: http://www.promecha.com.au/leverage_linkages.htm#
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