Developing the Model
The folding chair linkages are for the most part, simple. There are 6 in total, and one curved link that acts as a guide for the slider on the front leg. The configuration of the links is shown below. The arrows shown represent the vectors of the links. The links will be referred using the numbers shown in the picture.
Some of the vectors have a few quirks; they are not perfect straight lines However, they are still easy to analyze with the right assumptions First, Vector 0, or R0, only runs from the two pins, not the entire length of the folding mechanism. A similar approach is taken with R4 and R5. R4 and R5 will always be pointing in the opposite direction, because the arm rest they are attached to is rigid. R7 has a v