# Photogrammetric Measurement and Analysis of the Shape Profile of Pneumatic Artificial Muscles
## 4 Results
### Shape Profile Characterization  
The analysis methods described above are applied to get measurements of the shape profile for every image acquired during the characterization testing of the force-contraction response. As a first step, the timing of the photogrammetric data must be synced with that of the force-contraction response data recorded by the MTS machine. This was done in this research by comparing the contraction of the PAM, as directed by the MTS machine, to the contraction as found through the shape profile data. To do this, the recorded time of the MTS data was shifted to produce a minimum error between the MTS and photogrammetric contraction data. With measurements of the MTS machine recorded every 0.02 s, fine adjustment of the time shift can be made to sync the time between the two measurement systems accurately. The comparison of the photogrammetric and MTS contraction data also provides a method of ensuring the fidelity of the photogrammetric results. The photogrammetric measurements can be checked through comparison to manually acquired measurements taken during testing. However, manually acquiring measurements would be time consuming and difficult to perform accurately. The MTS machine controls and records the contraction of the PAM length during testing to the ten-thousandth of an inch. Therefore, if we consider these contraction values as the true contraction of the PAM, a simpler and more accurate method of checking the photogrammetric measurements would be to compare the contraction as found through the photogrammetric data to that of the MTS machine. This comparison of the time synced data is shown in Figure 12b. Figure 12: Test results of the 236 mm long, 22.2 mm diameter test PAM: (**a**) Actuation diagram. (**b**) Comparison between contraction values found from the image data using photogrammetry, and the displacement values recorded by the MTS machine. Results are shown for a single contraction cycle at all tested pressures. Figure 12b shows that the photogrammetric data tracks that of the MTS machine very well, with a maximum differential between the two of 0.60 mm (0.02 in) occurring at the PAM's resting length, which results in an error of the length measurement of 0.25%. With a measurement resolution of 0.112 mm/pixel (0.004 in/pixel), a portion of this error is a limitation of the resolution of the image. A portion of this measurement error can also be attributed to the slightest amount of distortion along the length of the PAM. The diameter measurements of the shape profile, with an even narrower angle-of-view, would be subject to even less perspective distortion which would result in even less measurement error. Therefore, the 0.25% error of the photogrammetric measurements can be treated as an absolute maximum. With this comparison, the photogrammetric measurements of this research can be received as a high-fidelity representation of the true dimensions of the PAM's braid. The shape profile of the PAM is now analyzed with confidence in the accuracy of the photogrammetric measurements. With the maximum contraction achieved at the highest test pressure, the 689 kPa (100 psi) test serves as a good starting point for analysis of the PAM's shape profile. Figure 13 provides snapshots of the PAM's shape profile in 2.5% contraction increments up to the maximum contraction of about 35% at 689 kPa. There are a few observations to be made from the shape profiles in Figure 13. The distinct shape, with a maximum diameter at each end of the midsection, resembles the shape of a peanut. The profile near each end-fitting is also of interest, with a slope of the braid that dramatically changes as the PAM contracts. The slope is close to zero at low levels of contraction, but rapidly increases with increased contraction. This distinct change in the shape of the braid makes it difficult to have a single assumed shape for the profile near each end-fitting, as has been assumed by other authors (e.g., circular arc, toroid, etc.