# Photogrammetric Measurement and Analysis of the Shape Profile of Pneumatic Artificial Muscles
## 5 Analysis
### Shape Profile Analysis
#### 5.1.3 Comparison to Previous Cylindrical Profile Estimates
It should be noted that the value of \(\theta_{0}\) found through this method is a function of the estimated value of \(D_{0}\). The average diameter of the measured profile data will be compared to the estimated cylindrical profile. The assumed cylindrical profiles for both the estimated and average of the measured data provide a basis of direct comparison. An accurate estimated profile diameter should match the average of the measured profiles. The value of \(D_{0}\) for the tested PAM is equal to the outer diameter of the bladder at 22.2 mm (7/8 in). An estimated value of \(\theta_{0}\) was found using the blocked force with respect to pressure data to be 72.27 degreesl. The resulting estimated diameter values, labeled as \(D_{est,1}\), are compared to the results of the measured data in Figure 16a for a single stroke of the PAM. There is an observed error in the estimated value of \(D_{0}\) which is about 3.8 mm (0.15 in) below the initial measured average diameter of about 26.0 mm (1.025 in). This initial increase in diameter was not due to any noticeable slack in the braid prior to pressurization, with the braid being taut in the resting length state. The resulting discrepancy between the estimated and measured diameters is especially large at low levels of contraction. With knowledge of the actual value of \(D_{0}\), using the measured data we can attempt to estimate the shape profile again with corrected values of \(D_{0}\) and \(\theta_{0}\). Since there is a slight range of the measured initial diameter values with respect to pressure, the average of these measured values of 26.0 mm (1.025 in) can be used for this comparison. This value of \(D_{0}\) results in a value of 69.04 degreesl, a significant difference from the previous value of 72.27 degreesl. Estimated diameter values, \(D_{est,2}\), are calculated using the new initial geometry conditions (Figure 16b). With proper alignment of the curves at low levels of contraction, there is now a sizeable error in the maximum contraction state. The resulting error between curves could be the result of the estimated value of \(\theta_{0}\) being too high. A lower value of \(\theta_{0}\) would result in lower values of estimated maximum contraction. If the value of \(\theta_{0}\) is reduced to 68-68.5 degreesl with \(D_{0}\) still equal to 26.0 mm, the estimated and measured diameter curves match very well. However, an accurate physical measurement of the value of \(N\) for the tested PAM found that the braid angle should be around 68.9-69.7 degreesl which coincides well with the value of \(\theta_{0}\) used to define \(D_{est,2}\). It is therefore likely that the discrepancy between the values of \(D_{avg}\) and \(D_{est,2}\) are a result of error from using the cylindrical approximation for the estimated diameter values. The cylindrical approximation, in estimating a diameter from the initial geometry state, neglects the length of the braid that is effectively lost to the curvature of the PAM's braid resulting in overestimates of the estimated diameter. This research serves as an initial comparison of these estimated and measured diameter values, with the resulting discrepancy between these values deserving of further investigation.