# Use of Wearable Sensor Technology in Gait, Balance, and Range of Motion Analysis
## 5 A Taxonomy for Gait, Balance, RoM Analysis
### Analysis of Joint Range of Motion  
Range of motion (RoM) is the distance a subject's joints can be moved in a certain direction and is measured in degrees. The goniometer is an instrument used widely by physical therapists to measure RoM angles [136]. RoM testing is an integral part of any physical therapy examination, and generally RoM is examined before physical therapy treatment begins. RoM testing can be performed on specific joints, and if limited motion is found, the physical therapist determines if the cause is muscle tightness, pain, or tightness of ligaments or tendons [137]. Common RoM angles measured by physical therapists are at the shoulder, elbow, hip, knee, and ankle joints and spine angle/inclication (Figure 7). RoM is divided into three main types [137]:  
* passive RoM: physical therapist is moving the subject's joint and no active movement is performed by the subject,
* active assistive RoM: the subject can perform movements but cannot complete it because of pain or muscle weakness; assistance of the physical therapist is needed, and
* active RoM: the subject can perform the movement without manual assistance from the therapist. One common way to get RoM measurements is to calculated pitch, roll, and yaw angles. Pitch and roll angles can be computed using an accelerometer. A simple way to compute pitch and roll angles is using Equations (14) and (15), where \(Acc_{x}\), \(Acc_{y}\), and \(Acc_{z}\) are the normalized accelerometer values in the X, Y, and Z axis respectively and \(\frac{180}{\pi}\) is used to convert the angles from radians to degrees [138]. \[Roll=atan(\frac{Acc_{y}}{Acc_{z}})*\frac{180}{\pi} \tag{14}\]  
\[Pitch=atan(\frac{-Acc_{x}}{\sqrt{Acc_{y}^{2}+Acc_{z}^{2}}})*\frac{180}{\pi} \tag{15}\]  
However, there is a constraint using this method to extract the angles. These equations, besides being simple, are known to only work for the unrealistic assumption of zero or constant velocity. Additionally, there is no way to calculate the yaw angle (heading). Yaw angle can be measured by rate of gyroscope and magnetometer and not only with accelerometer values [138]. Additionally, roll, pitch, and yaw angles are not widely used in joint analysis in the recent years. Figure 7: RoM Angles Measured While Squatting. Some studies measure RoM by using unit quaternions and/or Euler angles [22; 40; 65]. A quaternion is a 4-tuple whose primary application is in a quaternion rotation operator that can offer fundamental computational, operational, and/or implementation and data handling over conventional rotation matrices [139]. The problem with unit quaternions is that the four quaternion parameters do not have intuitive meaning, a quaternion must have a unity norm to be a pure rotation, and it is harder to understand [140]. Euler angles are popular since they are easy to understand and use. Certain important functions of Euler angles have singularities and they are less accurate than unit quaternions when measuring incremental changes over time [140]. However, according to the International Society of Biomechanics (ISB) recommendations, Euler angles are preferred for joint coordinate systems of various upper body and lower body joints for the reporting of human joint motion [141; 142]. Joint coordinate system has been established by the ISB in order to report joint motion. There are two main reasons of why the joint coordinate system has been established: (1) lack of standard reporting for joint motion in biomechanics for human movements, making comparisons among studies more difficult, (2) and the advantage of reporting joint motion in clinically relevant terms, making interpretations easier for clinicians and researchers [141]. The joint coordinate system recommend by the ISB established a Cartesian coordinate system for each of the two adjacent body segments that are defined based on bony landmarks [141]. The system is established for both two cases: fixed body and \"floating\" or moving body and includes three rotational and three translational components.