A small driving link (red link) with rotational motion connects three larger links. In this mechanism, rotational motion is converted into linear, straight-line motion. The second link, highlighted in red, has 360 degrees of motionBelow is the animation of our linkage, with arrows conveying the velocities of each joint and the dotted curve showing the path of the end effector.
Figure 1. Linkage Animation
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After obtaining a basic understanding of the dimensions and angles through Grashof calculations conducted in the initial proposal, we proceeded with position, velocity, and acceleration analysis.
Position
By solving the 4-bar linkage mechanism, we determined the values of theta 3 and theta 4, which could be used to find the position for every input angle from 0 to 360 degreesFigs. 2 and 3 show our position graph as well as the position profile displayed in the linkage animation. The "pulling" of the noodles will occur between approximately 50 degrees and 300 degrees, on the lower "flat" portion of the profile, while the rest of the rotation will be used to bring back and (ideally) re-fold the noodles.
Figure 2. Position Analysis vs. Angle
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Figure 3. Position Profile (y vs. x)
Velocity
Taking the derivative of the position equations and calculating omega 3 and omega 4 values using the theta values found, we were able to conduct velocity analysisAs demonstrated in Fig. 4, the velocity between ~50 and 300 degrees is near constant in both magnitude and direction. This is ideal for pulling the noodles, as the action must be slow and consistent to avoid tearing the dough. Conversely, the magnitude between 0/50 and 300/360 degrees is much higher, which will allow the mechanism to re-fold the noodles quickly.
Figure 4. Velocity Analysis
Acceleration
Similarly, for acceleration, we took the derivative of velocity and plotted the speed of the mechanism's movement at different positionsThe acceleration analysis in Fig. 5 once again shows that our velocity is near close in the noodle-pulling phase, as the magnitude is near zero from 50 to 300 degrees.
Figure 5. Acceleration Analysis
Force Analysis
Charting We can see the mechanical advantage solutions for each input angle revealed peaks, indicating our greatest mechanical advantage occurs between 75 to 100 degrees and 300 to 350 degreesfor our mechanism in Fig. 6, which is low and near-constant apart from two peaks at ~90 and 325 degrees. If the dough provides too much resistance, we can add gears to increase the overall mechanical advantage.
Figure 6. Mechanical Advantage
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