# Photogrammetric Measurement and Analysis of the Shape Profile of Pneumatic Artificial Muscles
## 5 Analysis
### Testing of Different PAMs  
A few other PAMs have been characterized thus far using the photogrammetric methods as described above. Three 22.2 mm (7/8 in) diameter PAMs and one 57.2 mm (2 1/4 in) diameter PAM have been characterized using photogrammetry. The three 22.2 mm diameter PAMs have identical material construction. The 236 mm (9 9/32 in) long PAM has been used to demonstrate the photogrammetric methods up to this point, and PAMs with 305 mm (12.0 in) and 508 mm (20.0 in) lengths have also been tested (Figure 17). These PAMs were tested to compare their shape profiles while also demonstrating the ability of the photogrammetric test setup to characterize PAMs of varying length scales. Analysis of the 57.2 mm diameter by 351 mm (13 13/16 in) long PAM (Figure 18) further demonstrates the capability of the test method to characterize PAMs of a wide range of diameters. The shape profiles of the 22.2 mm diameter PAMs are compared in Figure 17d for the same five states of percent contraction. Despite their slight differences in shape, their resulting diameters are very similar. The three PAMs were all able to achieve nearly identical free contraction values at 689 kPa (100 psi) of 35.43%, 35.55%, and 35.36% for the 236 mm, 305 mm, and 508 mm PAMs, respectively. Each of their profiles has an undulation at each end of the PAM that resembles the previously noted peanut-like shape which seems to be a characteristic of many PAMs. The shape profile of the 508 mm (longest) PAM has an additional small undulation at its mid-length that is barely visible. A Fourier series fit was conducted on the three PAMs resulting in an accurate representation of their profiles. A three-term Fourier series provides an accurate fit for the 236 mm and 305 mm long PAMs, while the additional undulation of the 508 mm long PAM profile requires a four-term Fourier series to achieve a good fit. The largest discrepancy between the profiles comes in the zero-percent contraction state, where the 236 mm PAM has the largest amplitude of the PAMs. The 236 mm PAMs were also observed in the 236 mm and 305 mm long PAMs. The 236 mm PAMs were observed in the 236 mm and 305 mm long PAMs. largest average diameter of the three. The difference in initial diameters is reflected by the difference in their estimated initial braid angles. The three PAMs had estimated initial braid angles of 69.4, 71.1, and 71.9 degreesl for the 236 mm, 305 mm, and 508 mm PAMs, respectively. With all three PAMs using the same braid, the differences in initial braid angle and diameter indicates slight differences in their fabrication or identification of their resting length. As previously noted from observation of Figure 15a, the diameter of the PAM is much more sensitive to changes in length at lower states of contraction, so a small deviation in length or braid angle near the resting length state results in a relatively large change in the expected diameter. The shape profiles of the 57.2 mm diameter PAM, as shown in Figure 18b, are also accurately captured using the described photogrammetric methods. The simpler rounded shape of its profile allows for an accurate Fourier series fit of the profiles to be achieved with the use of only two terms. Testing of both the 22.2 mm diameter by 508 mm long PAM, and the 57.2 mm diameter by 351 mm long PAM, represents the maximum extent of what has been produced with regard to sizing of PAM lengths and diameters, respectively. Although the photogrammetric measurement of PAMs of different sizes might seem trivial, many previous test setups for PAM volume testing have required modifications or redesigns in order to administer tests for PAMs of different sizes. Photogrammetric characterization is capable of testing PAMs with a large range of sizes by just repositioning the camera to capture and fill each image with the entire PAM. As mentioned earlier, the positioning of the camera will effect the accuracy of the photogrammetric measurements.