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 vertical offset perpendicular to the metal bar because of the plastic bracket used to attach to the backrest. For this reason, R7 is represented as a ternary link, originating from tip of R6 and ending at the joint with R3 and R2.

The links R2, R3, and R7 all are joined at the same pin, and all are free to rotate. The Degree of Freedom of the mechanism is 1.

The curved guide on the bottom of the chair can be ignored for the analysis. The path will be verified using MATLAB.