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Drafting U.S. Patent Applications in LyX and LaTeX
The LaTeX package and LyX layout can be found here: http://ctan.org/pkg/uspatent
All of the files can be found here: http://ctan.org/tex-archive/macros/latex/contrib/uspatent
The instructions can be found here: http://mirrors.ctan.org/macros/latex/contrib/uspatent/doc/PatentApplicationGuide.pdf
These instructions provide all of the necessary instructions for both LaTeX and LyX (mixed together).
For LyX, you'll basically want to copy all of these files to a working directory named 'MyInvention'. Then you'll want to rename the PatentApplication.lyx file to MyInvention.lyx or whatever you want. You will then edit this file, replacing the information in the predefined sections (you can change the names of these sections, delete them, or add new ones).
Here's what the final document produced looks like: http://mirror.ctan.org/macros/latex/contrib/uspatent/doc/PatentApplication.pdf
You'll want to follow make sure in the document settings that you are using the uspatent layout. You'll need to select it locally until it gets included in the LyX distribution. This means you'll need a copy of the uspatent.layout file provided in your directory along with your patent application file.
All of the customizations can be found in the LyX environments and the custom insets where all of this has been customized to restrict your formatting capability, enter arguments for LaTeX macros, and cross-reference claims, figures, and drawing element annotations.
There is a sample Drawings.lyx file provided (that gets included in your document). In this file you will want to reference all of the patent drawings and the drawing elements for referencing within your application.
You can use many of the common drawing tools, but the LaTeX friendly ones are the best because here you can provide macros that automatically number your drawing elements. The best I know of and use extensively for this purpose is TpX found at: http://tpx.sourceforge.net. I provide instructions on how to operate TpX to work with the patent application file.