Our mechanism linkage went through several iterations. These different mechanisms included a quick return fourbar, a slider crank, and a curvilinear slider crank.

Quick Return Fourbar Mechanism

The initial Fourbar mechanism was designed to have a quick return in order to get out of the way of the curb. It's grounded points were placed on the axles of the major and minor wheels of the wheelchair. This was done for simplicity in mounting and ease of attachment. 

Kinematics

Initial variations of this mechanism were based off of quick return fourbar mechanisms and iterated to minimize the input displacement needed for the return to occur (ie, minimize the quick return time). A representation of this can be found on the prototyping page.

Problems

This version's major flaws included a lack of curb clearance and the resultant angle of the wheelchair through travel. The footprint of the pushbar for this mechanism was made large in order to time the contact with the ground and to provide more stability for the CG. However, this meant that during the quick return travel, the foot intersected with the curb. Re-timing the system to avoid this meant that the wheel would not be the proper distance behind the curb. This version also took the user through around 20 degrees of deviation from the horizontal, providing too much deflection than the 6-10 degrees sought after.

Curvilinear Crank Slider

This iteration of the mechanism was designed to solve 2 major problems introduced in the Quick Return Fourbar mechanism, while also resolving the angle of attack issues posed by the regular crank slider. 

Kinematics

The geometry of the device and timing of the mechanism meant that 4 different models of the mechanism had to be made. 

1. Regular Crank Slider - When traveling on the ground and the mechanism gets engaged. The device is on the straight portion of the rail.
2. Inverted Crank Slider - This mode is engaged when the pushbar is grounded and the wheelchair moves above. The mechanism is still on the straight portion of the rail.
3. Fourbar - The mechanism is now on the curved portion of the rail. This models as a fourbar as the center of rotation is fixed (relative to the wheelchair). This is because the curve is circular.
4. Fourbar (Inversion) - The wheelchair is now on the curb above and the mechanism retracts, still on the curved portion of the rail.

A demonstration of the mechanism's position analysis can be seen in the above video. 

The mechanical advantage of the system during lift (phase 3) can be seen in the following image. The mechanical advantage stays above 4 and peaks at approximately 17 at the beginning. The motion of the lift implies that as the person is being lifted (up to 80 degrees in theta 2) will only need to assert 33 pounds of force as the mechanical advantage stays above 6. The mechanical advantage tapers off only once the lift motion transitions to horizontal translation which requires much less input force.