## 2 Upper Limb Modeling  
### Upper Limb Kinematic Model  
Anatomically, the upper limb consists of the pectoral girdle, the upper arm, the forearm and the hand [31]. The three joints of the upper limb are: the glenohumeral joint, the elbow, and the wrist joint. Hence, the upper limb could be modeled as a kinematic chain consisting of these three joints along with the corresponding DoFs, which account for the feasible rotations for each joint. Related configuration of upper limb for motion tracking, based on the DH parameters can be found in the literature. In [32], the authors studied the movement of the shoulder and the elbow, and they designed a 4 DoF kinematic chain to express only the shoulder glenohumeral rotations and the elbow flexion. In [17], the human upper limb is also represented by rigid links connected with joints, where the upper limb kinematics are described with a 7 DoF model. This model has the shoulder as the origin of the kinematic chain and represents the shoulder joint mobility by 3 DoFs, the elbow joint by only 1 DoF, and the wrist joint by 3 DoFs. The latter correspond to wrist flexion-extension and deviation and the third one, is the forearm pronation-supination motion. In our work, the forearm pronation-supination has been defined as a wrist joint rotational DoF. In [33], the authors assume a 7 DoF model of the left upper limb. The motions of the scapula and clavicle are also modeled by means of the humerus head ability to elevate and retract. This concludes to two extra DoFs that represent the clavicle elevation-depression and profusion-retraction, respectively. In this model, 3 rotational DoFs account for the shoulder abduction-adduction, internal rotation, and flexion-extension, followed by the 2 elbow DoFs performing the elbow flexion-extension and the forearm pronation-supination. The wrist joint DoFs is omitted in this model. Hence, this work is focused on the clavicle range of motion and on the shoulder joint DoFs. In [34], the authors proposed a more complex kinematic model, based on the DH parameters, as well. This refers to the total upper body of a rower along with the seat rail for the case of an indoor rowing performance assessment. Each upper limb is represented as a 7 DoF kinematic chain with 3 revolute joints for the shoulder abduction-adduction, rotation and flexion-extension, 2 DoFs for the elbow representing flexion-extension and rotation and, 2 DoFs for the wrist abduction-adduction and flexion-extension. Moreover, this model accounts for the clavicle DoF, representing it as a revolute one. In the present paper the forward kinematics were extracted for the human upper limb, which was designed as a kinematic chain consisting of three joints, namely, the shoulder, the elbow and the wrist and 7 DoFs. The shoulder/glenohumeral joint formed by the humeral head of the scapula and the glenoid cavity [35], performs three rotational DoFs: the flexion-extension one, abduction-adduction, and at last the internal-external rotation. The elbow can be represented as a hinge joint permitting elbow flexion-extension. The bones, muscles and ligaments structure in the elbow joint close area restricts its mobility. Nevertheless, a second DoF that originates a bit distal from the elbow is responsible for the pronation-supination of the forearm. Regarding the wrist joint, two DoFs are present, performing flexion-extension and deviation, respectively. The described kinematic chain used to model the human upper limb, is illustrated in Figure 1.  
The coordinate frames were defined for each DoF, with respect to a set of rules from robotics theory and the DH configuration convention. These are presented in Figure 1 and summarized in Table 1. The origin point of the kinematic chain is located at the human's chest. The corresponding coordinate frame is noted as [C] and is also regarded as the origin one. The shoulder joint's 3 DoFs follow with the frames [S1], [S2] and [S3] assigned on them denoting the flexion-extension, abduction-adduction and internal-external rotation, accordingly.