The first step taken to justify the position analysis. For this, the path of the front leg, which is just an extension of R6, is plotted. Based on experience, the path should move directly away from R0, then curve up towards the end of its path.
The graph does not have a constant curvature. However, this still works, because the curved rocker on the chair has a pin joint attaching it to R0, and a pin joint for attaching the slider. The rocker can trace out any path without restrictions. As for how this relates to real life, the path agrees with how the slider extends, relative to R0. The starting point is below the base of the vector R0 (negative y-axis), and has a slight offset away from the vector R2 (negative x-axis). The motion of the slider is not straight, however it is mostly in the x direction. This is not exact proof, however this was enough to show that the MATLAB model's motion does correspond to the rocking chair in real life.
The results of the analysis focus on the mechanical advantage if a force is applied to the seat of a chair, and if a force is applied to the backrest, with the output as the slider portion of the front leg of the chair. The picture shown depicts the curved slider as grounded, however the vector loop analysis assumes that R0 is the grounded link. For the analysis on mechanical advantage, the magnitude of the mechanical advantage will not change, regardless of which link is chosen as the ground. Theta 2, or the toggle linkage, is set as the dependent variable.
The Mechanical Advantage is found using the angular velocities from the Velocity analysis.
For the mechanical advantage, the force out is increased for theta 2 > 135°. Theta varies from 15° to 165°, with 165° corresponding to the closed position. For the extended position, where the chair is open, the mechanical advantage is much lower. This means that forces applied to the backrest and seat have less of an effect on the slider when the chair is open. This is good for stability, since less force when the chair is open means that it is less likely to have the slider move and cause the chair to collapse.
Despite the backrest having a longer lever arm, the mechanical advantage to the slider is always less than one. This is due to the mechanisms design, where the rotation velocity of the backrest is less than the rotational speed of the front leg. This was counter-intuitive for me, however this was proven true when I tried to prevent my family members from opening the chair by trying to hold the slider in place while they pulled on the backrest or the seat from the closed position. Keeping the chair closed was much easier when they pulled on the backrest portion.