In the Winter of 2024, I was enrolled in a Machine Design class where the final project was to design a scissorjack according to a variety of requirements. This project relied on mechanical design principles, FEA, and failure analysis. An important aspect of the design was to identify all important parameters and optimize them within the bounds of the requirements. This was a group project, and I lead the design of the optimization algorithm which primarily relied on the 'fmincon' function in Matlab. The optimizer was the guiding tool in creating an effective design approach for the scissor jack. 

 The ultimate goal was to use an optimization algorithm to determine the best properties for the scissor-jack. As such, the methodology used for the design approach involved exploring different elements of the scissor-jack, selecting finalized parameter types based on computational results and engineering judgment, and then incorporating these into the model to be optimized. The outline of the workflow is provided here:

As seen from the diagram, the crossbar cross section, diagonal member cross section, and material selection were explicitly explored before the optimization algorithm was used. The findings for each exploration process are provided below:

Crossbar Cross Section Evaluation 

Multiple options for connection of the crossbar to the diagonal members were considered. First, a solid circular cross-section was considered because it could be turned into a lead screw that could extend and retract through the pin and diagonal members. This option seemed to be the most reasonable given the emphasis on buckling of the cross bar, which depends on the moment of area of the cross-section. A hollow circular cross-section may also have been a possibility, however the ability to manufacture a lead screw from the hollow rod becomes increasingly complex. 

Diagonal Member Cross-Section Evaluation 

Multiple cross-section shapes for the diagonal members were considered and a final shape was decided upon through the use of engineering judgment. Previously mentioned force calculations all depended on geometry as defined as in Figure 4. This means that circular, or other cross-sectional shapes with curvature are not able to be considered in the model. As a result, we considered 3 different shapes: a hollow square, a u-channel, and a set of parallel rectangles. 

Due to the nature of how the forces were calculated, the area of interest for each of these cross-sections remained the same. As such, the forces analysis would be equivalent between each shape. Because of this, the hollow square was ruled out due to the increased weight potential. However, the set of parallel rectangles was not considered due to an increased chance of out-of-plane buckling. For these reasons, a cross-sectional shape of the U-channel was selected for the diagonal members. 

Material Selection

Because of the fatigue requirement of 10^6 cycles, the scope of available materials able to be considered in the design is limited. In this model, only various aluminum alloys and steels were explored. Exploration options for steel included the following: 

• Low-Carbon Steels

• High-Carbon Steels

• Hot-Rolled Finish

• Cold-Drawn Finish

• 4000 Series Steels

Exploration options for aluminum just included high and low strength aluminum alloys. Each material and relevant properties used were obtained from matweb.com 

A matlab function requiring 17 inputs was created which produced 15 outputs to determine if requirements were met. Inputs include scissor-jack geometry, as well as material properties. Outputs include factors of safety, number of cycles until failure, as well as loading conditions, failure forces, and vertical distance range of motion. These variables are listed below:

In order to obtain the best possible solution, a built-in optimization function in matlab called fmincon was used. fmincon allows the user to pass in a function (the model), and select a single output to maximize or minimize. Nonlinear constraints can be applied to outputs to ensure resultant values are within a desired range. Linear constraints, as well as lower and upper bounds may be imposed on inputs to ensure that values are reasonable. A detailed outline of the geometric inputs and total outputs may be seen in the table above.

For this application, weight was the selected output for the optimization algorithm to minimize. Factor of safety ranges, vertical distance, and minimum forces until failure were all considered in the nonlinear constraint designation. Crossbar, diagonal member, and pin geometry relationships were designated in the linear constraints. This prevented the optimizer from creating impossible geometry (such as a pin diameter greater than the hole in the diagonal member). No constraints were able to be applied to the number of cycles required because when designated, the optimizer was unable to converge to a feasible point. In this case, feasible refers to a set of inputs that satisfy the constraints 

The inputs into the optimizer were divided into two groups, x-variables and auxiliaries. X-variables include inputs that are meant to be changed in the optimization algorithm. These include pin, cross bar, and the diagonal member geometry. Auxiliary inputs are not considered in the optimization algorithm, and remain constant. These include material properties and designations. 

Additionally, the optimizer requires an initial set of feasible guesses for x-variables to begin the optimization process. Hand-calculations were used to identify a starting point and were input into the model to ensure they produced a feasible result. 

Next, a table of material properties for various materials was created using data from the textbook and matweb. This table was loaded into Matlab, and a for-loop was used to execute the optimization algorithm, iterating through each set of material properties as auxiliaries. Outputs, and corresponding inputs were all saved to a .csv file that was analyzed to determine which material properties produced the best results. The best results for each tested material is seen in the table below.

Because fatigue was unable to be constrained in the optimizer, the number of cycles was the first identifiable output to narrow down possible material candidates. If both the diagonal member and crossbar had a life exceeding 10^6 cycles, then the factors of safety for each failure mode was evaluated to ensure that the most catastrophic failure modes occur last. 

The final report of these efforts, along with a more comprehensive analysis of failure modes and loading criteria, may be viewed below.