# Photogrammetric Measurement and Analysis of the Shape Profile of Pneumatic Artificial Muscles
## 6 Conclusions  
This research presents an approach for characterizing the shape profile of PAMs through photogrammetric measurement. The method of measuring the PAM's shape profile is described including a basic test setup, method of image acquisition, and a process of abstracting measurements from the image data. A 22.2 mm diameter PAM served as an example for describing the presented test method and analysis. The photogrammetric testing was performed in parallel with the isobaric force-contraction characterization that is typically performed to define the actuation of PAMs. The photogrammetric test setup requires the addition of only a camera, backdrop, lighting,and masking to acquire measurement data. The complete method of acquiring measurements from the image data, including a background on the methods used, was provided in detail to ease the adoption of this characterization method for future research efforts. Some preliminary analysis of the shape profile data was then performed. The average diameter and volume of the PAM were found to be primarily a function of the contraction state. However, there was an indication of strain in the braid fibers from the small but appreciable increase in PAM diameter with increased pressure. This strain in the braid fibers had not been quantifiable prior to the characterization performed in this testing. The measured shape profiles were redefined from a set of data points to a cylindrical approximation or fit equation. The average of each measured profile was used to define each profile as a single value. This assumes a cylindrical shape profile that can be readily applied to previously existing models. If the assumption of a cylindrical shape profile is not sufficient for a high-fidelity modeling effort, the complex curvature of the shape profiles can be defined to a high-degree of accuracy using Fourier series fit equations. Working with equations instead of the raw shape profile data greatly simplifies usage of the shape profile information garnered from the photogrammetric testing. The estimated diameters found using the cylindrical approximation and initial geometry have long served as the basis for most PAM modeling. These estimates were tested by comparing them to the measured average diameters of the tested PAM. The comparisons resulted in discrepancies between the estimated and measured diameters, with the first comparison finding an inaccuracy in the initial estimated diameter. After this initial offset in diameter was corrected, the estimated diameters still did not match the measured diameters, warranting further future investigation of the effect of the cylindrical approximation on these estimates. A new method of characterizing the internal volume of PAMs using the acquired shape profile data was also presented. This new non-contact method of calculating the internal volume is desirable compared to current methods which often require specialized test equipment that must be altered in order to test PAMs of different sizes. Finally, the accuracy and adaptability of the presented test method is demonstrated through the shape profile characterization of multiple PAMs of different sizes. A comparison of three 22.2 mm diameter PAMs was performed, demonstrating some of the similarities in their contraction-diameter characteristics, and also the slight differences in the undulations and curvature of their profiles. A wide 57.2 mm PAM was also accurately characterized with the same test setup without the need for any modifications. The Fourier series fit was able to accurately replicate the profile data for all tested PAMs with an observed correlation between the number of undulations of the profile's curvature, and the number of terms required to provide an accurate fit. The presented method was developed out of a need to be able to quantify modeling unknowns and long-used estimations of diameter, but also out of the necessity to define the dimensions of PAMs for implementation into mechanism designs, and define system requirements for the PAM's supporting hardware.