Handle Position
The position of the handle is a function only of the angle of the handle from the horizontal, θ2, and the radius, R2, which is the distance from the center of the rotating disk to the handle itself (Figure 7). Because the angular velocity could either be constant or variable depending on the condition, θ2 was determined over the course of 20 seconds (about 2 revolutions) using the following equation:
This angle was then used as the "input" for the position analysis.
Figure 7: Sketch of the handle input.
The following animations show the position of the handle for constant (left) and variable (right) inputs over a simulated 20 seconds.
Cam Position
Cam position was found by modeling the input disk as an ellipse with three different radii: the longest along the major axis, R31, the radius along the minor axis, R32, and the shortest along the major axis, R33. At the start when θ2 is 0º, the angle of the cam disk, θ3, is 90º, with the longest radius pointing upward (Figure 8). Since the cam disk is on the same shaft that the handle rotates, θ3 = θ2 + 90º.
Figure 8: Sketch of the cam disk in its starting position at θ3 = 90º.
As the cam disk rotates, if the distance between the center and the effective radius (at 0º and 180º) is greater than xCam (Figure 8), then the rod is moved side to side by the difference between that radius and xCam. The following animations show the position of the cam assembly for constant (left) and variable (right) inputs over a simulated 20 seconds.
Gear Position
Since the input gear is also on the same shaft that the handle turns, the angle of the input gear, θ4, is the same as θ2, but rotated 90º. The "arc length" traveled by the input gear has to be the same as that traveled by the output gear. Therefore, when the gears are modeled as two disks, their positions (Figure 9) are:
θ4 = θ2 + 90º
θ5 = R4/R5*θ4 = R4/R5*(θ2 + 90º)
Figure 9: Sketch of the gear mechanism. R4 and θ4 belong to the input gear, R5 and θ5 belong to the intermediate gear that turns the wheels. R6 and θ6 are the distance and angle of the vector from the center of the front wheel to the "foot".
The following animations show the position of the gear assembly for constant (left) and variable (right) inputs over a simulated 20 seconds.
Four-bar Linkage Position
The input link for the four-bar linkage is the "link" from the center of the front wheel to the foot, R6 (Figure 9). θ6 is known, because it is the same gear as Gear 5, and therefore θ6 = θ5 + 90º (because it has an offset start position). Since R6 and θ6 are known, and Llleg, Luleg, L0, and θ1 are measured, θlleg and θuleg can be found using the vector loop equation (Figure 10).
Figure 10: Sketch of the four-bar linkage that makes up the leg segments.
The following animations show the position of the gear assembly for constant (left) and variable (right) inputs over a simulated 20 seconds.
Additional plots from the position analysis can be found in the Appendix.