# Shoulder Kinematics Assessment towards Exoskeleton Development
## 6 Exoskeleton Alignment and Its Effect on the Shoulder Muscles: Case Study
### Methodology  
Research discussed in this section is aimed at obtaining motion capture data, simulation of shoulder movement for a healthy case, as well several other cases where an exoskeleton has imposed unintended pressure to the shoulder joint as the arm performing a certain task. Ten markers are placed at different sites of the fore arm and upper arm in such a way to appropriately capture the motion path of the arm [54; 55] as the weight is picked up, moved to right, placed down, and sequence repeats once more to have the weight back to its original location. In addition to necessary sites, additional markers are used to accurately track the upper arm motion during the course of action. OpenSIM musculoskeletal modeling software is utilized to replicate the arm motion by solving inverse kinematics (IK) equations using designated markers. OpenSIM provides two approaches for calculating the muscle activation levels. The first, Static Optimization (SO), distributes overall joint moments into forces generated by each muscle at any time frame [56]. Basically the movement of  
Figure 1: Anatomy of shoulder joint and shoulder girdle. the model is equipped to solve the equations of motion for the forces under the following conditions (Equation (1)):  
\[ \begin{split}\sum_{i=1}^{n_{i}}(a_{i}F_{i}^{0})r_{i,k}=\tau_{ki}\\ \sum_{i=1}^{n_{i}}[a_{i}f(F_{i}^{0},l_{i},v_{i})]r_{i,k}=\tau_{kc} \end{split}  \tag{1}\]  
while minimizing the cost function (Equation (2)). \[J=\sum_{i=1}^{n_{i}}(a_{i})^{p} \tag{2}\]  
where \(n_{i}\) represents the number of muscles consisted in the model, \(a_{i}\) denotes the activation level of muscle \(i\), \(l_{i}\) denotes the muscle fiber length, \(r_{i,k}\) denotes the moment arm of the muscle force about \(k\)-th joint axis, \(v_{i}\) denotes shortening speed of the muscle, \(p\) denotes a constant defined by the muscle properties and \(f(F_{i}^{0},l_{i},v_{i})\) represents force-length-velocity criteria, \(\tau_{ki}\) denote the torque for ideal force generators, and \(\tau_{kc}\) denotes the torque constrained by force-length parameters [57; 58]. The second approach to calculate the level of muscle excitation is known as Computed Muscle Control (CMC) [59]. This method calculates muscle activations to drive the system, so that the desired trajectory of the task is best met. First, the desired accelerations are calculated using Equation (3). \[ \begin{split}\ddot{q}^{\ast}(t+\Delta t)=\ddot{q}^{exp}(t+\Delta t )+k_{p}[\dot{q}^{exp}(t)-\dot{q}(t)]\\ +k_{p}[q^{exp}(t)-q(t)]\end{split}  \tag{3}\]  
where \(q\) denotes the model coordinates, \(\ddot{q}^{\ast}\) denotes the desired acceleration, \(q^{exp}\) denotes the position derived from the experiment, and \(k_{v}\) and \(k_{p}\) are proportional constants for velocity and positions set for the simulation. With this CMC process, actuator controls that lead to the desired accelerations are computed and, subsequently, a forward dynamics analysis is performed. This cycle iterates until the time reaches the end of the task interval. For this study, Stanford VA upper limb model comprised of 50 muscles crossing through shoulder, elbow, forearm, and wrist introducing 15 degrees of freedom is used to establish the simulation [60]. Markers pertaining to shoulder were placed at superior, anterior, lateral, and posterior side of that; biceps, medial and lateral elbow, forearm, medial, and lateral wrist are other locations that are selected for marker placement Figure 2. Same protocol has been followed to establish marker registration in OpenSIM and replicate the motion of interest Figure 3. Shoulder joint motion limit is assured by removing all muscles from the model to make sure arm posture is realistic. In addition, muscle wraps (green compartments) are another set of properties the software uses to ascertain muscles are not passing through bones. All of these considerations are embedded in the selected model Figure 4a; however, figures also indicate that all measures are taken into account.