# A Kinematic Model of the Shoulder Complex Obtained from a Wearable Detection System
## 4 Discussion
### Comparison of Collected Data with Result of Klopcar Kinematic Model
#### 4.1.2 Comparison of Collected Data in the Sagittal and Coronal Planes  
According to Equation (7), \(x(\phi)\), \(y(\phi)\), and \(z(\phi)\) are zero when the elevation angle is equal to zero. For the unity of the results, the constant terms of \(x^{fl}\), \(y^{fl}\), \(z^{fl}\), \(x^{hd}\), \(y^{hd}\), and \(z^{hd}\) of the GH joint center displacement variable quantity are ignored, which are named \(x^{fli}\), \(y^{fli}\), \(z^{fli}\), \(x^{hdi}\), \(y^{hdi}\), and \(z^{hdi}\). Thus, the results are presented in Figures 11a-c and 12a-c, respectively. For further comparison, the displacement variable quantities \(d(\phi)\), \(x(\phi)\), \(y(\phi)\), and \(z(\phi)\) of the Klopcar kinematic model are also added to Figures 11 and 12, which are obtained based on Equation (7). Figure 10: (**a**) Reference points on the shoulder complex and the center of the GH joint in global coordinate frame. (**b**) four anatomical planes. (**c**) calculated position of the GH joint center in the global coordinate system. Figure 11: Comparison of the magnification ratio of the GH joint center displacement variable quantity relative to the thorax coordinate system during humeral elevation in the sagittal plane and the Klopčar kinematic model: (**a**) translational displacement variable quantities \(x^{\text{fli}}\) and x(\(\Phi\)), (**b**) translational displacement variable quantities \(y^{\text{fli}}\) and y(\(\Phi\)), and (**c**) translational displacement variable quantities \(z^{\text{fli}}\) and z(\(\Phi\)). Figure 12: Comparison of the magnification ratio of the GH joint center displacement variable quantity relative to the thorax coordinate system during humeral elevation in the coronal plane and the Klopčar kinematic model: (**a**) translational displacement variable quantity \(x^{\text{fli}}\) and x(\(\Phi\)), (**b**) translational displacement variable quantity \(y^{\text{fli}}\) and y(\(\Phi\)), and (**c**) translational displacement variable quantity \(z^{\text{fli}}\) and z(\(\Phi\)). In Figure 11a, the displacement variable quantity \(x^{\prime\!li}\) changes slightly with the angle \(\phi\), from \(0^{\circ}\) to \(60^{\circ}\). Then, the curve assumes a convex shape between \(60^{\circ}\) and \(120^{\circ}\). The GH joint center displacement variable quantity \(x(\phi)\) along the \(x\)-axis moves slightly with an angle \(\phi\), from \(0^{\circ}\) to \(40^{\circ}\). Then, the curve also assumes a convex shape between \(40^{\circ}\) and \(120^{\circ}\). Observing the two curves, the trend is basically the same except for the magnitude. In Figure 11b, the displacement variable quantity \(y^{\prime\!li}\) changes slightly with the angle \(\phi\) from \(0^{\circ}\) to \(55^{\circ}\), and the gradient of the curve decreases from \(55^{\circ}\) to \(110^{\circ}\), the change in which is large. Then, the gradient of the curve rises slightly with the angle \(\phi\), from \(110^{\circ}\) to \(120^{\circ}\). The GH center displacement variable quantity \(y(\phi)\) along the \(y\)-axis stays in the same position as the angle \(\phi\) changes from \(0^{\circ}\) to \(70^{\circ}\). The gradient of the curve decreases from \(70^{\circ}\) to \(110^{\circ}\), the change in which is very evident. From \(110^{\circ}\) to \(120^{\circ}\), the gradient of the curve does not change significantly. The curve \(y^{\prime\!li}\) is smoother than that of \(y(\phi)\). The motion pattern in the middle position and at the end position is slightly different. Given that \(y(\phi)\) is the sum of the four elevation planes, the reasonable analysis results of \(y^{\prime\!li}\) are acceptable. In Figure 11c, the displacement variable quantity \(z^{\prime\!li}\) changes steadily with the angle \(\phi\), from \(0^{\circ}\) to \(30^{\circ}\). However, the change is very small. The increases in displacement variable quantity \(z^{\prime\!li}\) are first large and then small as the angle \(\phi\) changes from \(30^{\circ}\) to \(120^{\circ}\).