Kinematics & Motion Analysis

Our Kinematic Analysis focused around the motion of the piston, sizing of the slider crank linkages, and the piston housing. To help the reader visualize the problem, reference figure 1 and its legend below:

Figure 1: Piston motion modeled as a slider-crank

B: Size of the bore (Effective diameter)

S: Stroke (Effective path of movement)

TDC: Top Dead Center

BDC: Bottom Dead Center

a: Length of the crankwebs (two linkages in parallel, spaced so the connecting rod can fit between them, allowing full revolution around the center crankshaft)

L: Length of the connecting rod (Secondary link)

Theta: Crankshaft angle

From analyzing the diagram, we decided to define the height of the piston relative to the BDC position to obtain a piston housing of correct dimensions. Through basic trigonometry, we obtain figure 2 below with the dimensions:

figure 2: Schematic of the Slider-Crank with relevant dimensions

We find that the height of the piston in relation to the crank origin is .

Then, to offset the distance between the BDC and origin, we subtract from the equation (L-a); we can image both rods projected straight upwards to image the piston at TDC. The resultant equation is:. 

Then, symbolically defining all the terms in MATLAB, we used the built in differential function to obtain both the velocity and acceleration terms respectively:

Plotting and analyzing these functions are in the MATLAB code portion, along with example graphs with explanations.