# Wheelchair Lift Motion Study

This project included the study and optimization of an existing wheelchair lift design, to be installed in wheelchair accessible vans. A series of equations were derived and analyzed in MATLAB for the determination of mechanical advantage, forces on linkage members, and positions of mechanism components under several initial conditions.

The ultimate objective of this project was to improve the mechanical advantage of the lift by exploring and comparing multiple installation positions of the hydraulic actuator.

## Process

### Step 1  Calculate the Range of Motion of the Actuator

Vector Loop Analysis on Loop 1   The rotation angles for links 4 and 5 were determined for each input rotation angle.

Point Path Analysis 1   Equations to determine the position of the platform for any input rotation angle were calculated.

Point Path Analysis 2   Equations to determine the position of the hydraulic actuator connection for any input rotation angle were calculated.

Conclusions   Link 3 rotates between 4.6° and 50.74°, which corresponds to an initial actuator length of 17.72" and final length of 23.54".

### Step 2  Determine the Hydraulic Force of the Actuator

Kinematic Coefficients   Equations for the kinematic coefficients of all links were derived and solved using the Newton Raphson iteration process.

Center of Mass Coefficients   Point Path equations corresponding to the center of mass of each link were derived and solved to obtain each respective center of mass coefficient.  The vector loops were iterated and solved for a variable input using MATLAB. Each color represents an individual vector loop.

Conclusions   Using a simplified version of the Power Equation, the output force of the hydraulic actuator was determined for a variable input. A graph of the output force for a variable actuator length may be found in the next step.

### Step 3  Determine the Mechanical Advantage of the Actuator

Calculations   The mechanical advantage of the mechanism is defined as the sum of the weight of each link in the system, divided by the force of the hydraulic actuator. If the force of the hydraulics is low then the mechanical advantage must be high, indicating that the system relies less on the input and uses less energy.

Conclusions   The graphs below display the mechanical advantage and hydraulic force versus the input length of the hydraulic cylinder for the initial configuration. The mechanical advantage begins at 0.231 at the initial actuator length, decreases to a minimum value, and then finishes at 0.236 at the final length. Based on  these results, I concluded that the mechanism would be more efficient if the mechanical advantage was more consistent and only increased instead of fluctuating between low and high. This strategy would produce a consistent load on the actuator, resulting in a longer and healthier part life.

### Step 4  Optimize the Actuator Attachment Locations

To achieve a mechanical advantage with a consistent  trend as discussed previously, the connection points of the hydraulic actuator were altered and the process for determining the mechanical advantage was repeated. A computer program was created in MATLAB to iterate both actuator connection points and calculate the mechanical advantage of that configuration for a variable actuator length. Plots of the results were output for each iteration. During this optimization process I was searching for a mechanical advantage graph that increased continuously with increasing actuator length without sacrificing a large maximum advantage.

Conclusions   The figures below show the final actuator connection points that provide optimal advantage and the numerical results. The mechanical advantage at the initial length is 0.376, already much higher than the maximum in the given configuration, and 0.604 at the final length. The overall trend is consistent with the desired result and was thus chosen as the optimal configuration. The initial and final actuator lengths exceed the operating range of the current actuator, so a new part with a larger travel will need to be selected.