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In the constant condition, α2 = 0, but follows a sinusoidal curve in the variable condition (Figure 19).
Figure 19: The input angular acceleration α2 over time for the constant (left) and variable (right) conditions.
The handle acceleration (Figure 20) can be found by taking the time-derivative of its velocity:
Figure 1920: The input angular acceleration α2 over time for the magnitude and angle of the acceleration of the handle for the constant (left) and variable (right) input conditions as a function of input angle θ2.
Cam Acceleration
The horizontal linear acceleration of the cam (Figure 21) can be found by taking the time-derivative of its velocity:
Figure 21: Horizontal linear acceleration of the cam as a function of input angle θ2 for constant (left) and variable (right) conditions.
Gear Acceleration
Figure 20:
Cam Acceleration
Gear Acceleration
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The angular acceleration of the intermediate gear can be found by taking the time-derivative of its angular velocity (See Velocity, Figure 22):
Figure 22: Angular acceleration of the intermediate gear that spins the bicycle wheels as a function of time for the constant (left) and variable (right) conditions.
Four-bar Linkage Acceleration
For the leg links, an acceleration analysis can be performed by taking the derivative of the velocity vector loop equation and solving for αlleg and αuleg (Figure 23).
Figure 23: Angular acceleration of the upper and lower leg segments as a function of input angle θ2 for the constant (left) and variable (right) input conditions.
Then, the linear acceleration of the foot (Figure 24) and knee (Figure 25) can be found by taking the time-derivative of their velocity vectors.
and
Figure 24: Magnitude and angle of the acceleration of the foot as a function of input angle θ2 for the constant (left) and variable (right) conditions.
Figure 25: Magnitude and angle of the acceleration of the knee as a function of input angle θ2 for the constant (left) and variable (right) conditions.