In physics and mechanical engineering, it’s often useful to reduce a system of forces and couples to a single force and a single couple, in order to simplify the problem. The net forces and couples are easier to think about than several forces and couples would be.
We can take this simplification to the extreme by reducing a system into a single force, applied at a single point P, and a single couple which is parallel to that force. This is called a “wrench,” and any system of forces and couples may be reduced into a wrench. There aren’t a lot of references about “wrenches” online, but you can read about them here on Wikipedia, or in Chapter 4 or Bedford and Fowler’s Statics.
As a fun exercise in 3D programming, I made a tool which allows you to input any system of couples and forces, and which shows you, step-by-step, how to reduce it into a wrench. Hopefully this is actually interesting and not as hopelessly nerdy as it seems to me right now.
The tool is here: Wrench generator
(This tool requires WebGL, an in-browser 3D framework which can be a bit tough to get running on certain browsers and certain computers. If after some Googling you still can’t figure out how to get it running, leave a comment here and I’ll try to help you get going.)