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Figures 4,5,6.
Left to Right -  First iteration, Intermediate iteration, final MotionGEN iteration
(Click image to play gif showing mechanism motion)

Custom Simulation and Nitinol Input Integration

After producing a satisfactory design using MotionGEN, the geometry was copied to a custom python simulator and integrated with the finalized nitinol actuator input profile to further refine the output kinematics. Figure 87, below, shows the exact shape of the nitinol actuator input profile. The cusp points at the upper left and lower right corners are toggle points where the nitinol actuator reverses its motion. More information about the function of the nitinol actuator can be found in [LINK TO NITINOL ACTUATORManufacturing and Prototype Iterations]

Figure

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7.
Nitinol actuator input profile
Image Modified

As seen in figure 98, the first simulation of the mechanism with the nitinol actuator input changed the output significantly from the simplified ellipsoid input. This change, while expected, means further simulations needed to be performed to regain a flat profile.

Figure 98.
Initial nitinol input integration with undesirable result

For the simulation in figure 98, the nitinol input was rotated to match the rotation of the generic input ellipse used in the initial analysis in MotionGEN. To move forward we decided to simulate every possible orientation of the nitinol input profile. Figure 10 9 shows a gif with the profile of every joint including the foot output for every rotation angle theta of the nitinol input.

Figure 109.
Nitinol input rotation gif for theta = 0°-360° with 5° increments

From visual inspection of figure 9, the foot tip output profile has a long flat section for angles of theta from 45° to 70°. This reduced range was used to run another simulation with a finer angle increment. This is shown by the gif in figure 1110.

Figure 1110.
Nitinol input rotation gif for theta = 45°-70° with 0.5° increments

This narrowed search interval was then used to perform a linear regression on the flat section to compare R2 values and find the optimal angle. This method yielded an input rotation of 56.5° with R2=0.992. Even though the output was not horizontal, the mechanism can just be rotated until the flat is horizontal. Analysis of the data shows the entire mechanism should be rotated by 29.8 degrees. Figure 12 11 below shows the foot output profile for the optimal input rotation angle as well as the linear regression line for the ground contact section.

Figure 1211.
Optimal output profile with regression line

Next Section: Manufacturing and Prototype Iterations