Kinematic Analysis Overview

A position, velocity, and acceleration analysis were performed for the cam mechanism, gear mechanism, and four-bar linkage mechanism. Two conditions were used for kinematic analyses: a constant angular velocity condition and a variable angular velocity condition. For the constant condition, ω₂ is roughly 1 revolution per second. In the variable condition, ω₂ follows a sinusoidal curve, which is more realistic of the assembly's motion.

Constant Condition: ω₂ = 0.628 rad/s

Variable Condition: ω₂ = 0.628cos(2.2t) + 0.628

Measurements of the assembly were recorded and used in the code to solve for analyses. The following are the dimensions used for the analysis. All lengths are in centimeters and angles in degrees:

R₂ = 2.5        : length of the center of the axle to the actual handle
R₃₁ = 3.4       : longest radius of the cam disk
R₃₂ = 2.4       : the radius of the cam disk perpendicular to the longest and shortest radii
R₃₃ = 1.5       : shortest radius of the cam disk
x_cam = 5        : width of the cam component that has the ellipse inside of it
y_cam = 7.5     : the length of the cam component that has the ellipse inside of it
Grass = 10.8  : the length of the base of the "grass"
R₄ = 1.6         : "Radius" of the small gear that spins with main shaft
N₄ = 6           : Number of teeth on the small input gear
R₅ = 2.5         : "Radius" of the intermediate gear and gears that make the bicycle wheels
N₅ = 12         : Number of teeth on the intermediate gear
offset = 36.9 : The angle at which the bicycle wheels are offset from the center gear that's driving them
R₆ = 2           : distance between the foot and the center of the wheel
L_lleg = 4.5     : Length of lower leg segment
L_uleg = 4       : Length of upper leg segment
L_o = 6.25      : Distance between center of wheel and grounded hip
θ₀ = 40.9      : Angle between center of wheel and grounded hip from the horizontal