## 3 Methods and Materials
### Kinematic Model of Human Skeleton  
Formally, the human skeleton kinematic model can be defined using Denavit-Hartenberg (DH) parameters [79] by \(\eta(L^{H},J^{H})\), where \(L^{H}\) and \(J^{H}\) correspond to the sets of skeleton links and joints. The kinematic model corresponds to the skeletal pose data obtained from test subjects using a set of reference systems with a simple connection, limiting the degrees of freedom (DOF) of a 3-D space to four fundamental transformations. A direct kinematic model for a discrete series of joints may be found using this technique. The approach establishes various reference systems, one for the skeleton's basis and one for each of the joint linkages. The geometric transform between consecutive reference systems is achieved by combining four movements: translation \(a\) along the \(x\)-axis, translation \(d\) along the \(z\)-axis, rotation \(a\) around the \(x\)-axis, and rotation \(\theta\) around the \(z\)-axis. In the case of a rotational joint, the variable influenced by the joint would be \(\theta\) or \(d\) in the case of a translational joint. For each skeleton joint, a transformation matrix can be defined as follows:\[= \begin{bmatrix}\cos\theta_{k}&-\cos\alpha_{k}\sin\theta_{k}&\sin( \alpha_{k})\sin\theta_{k}&\alpha_{k}\cos\theta_{k}\\ \sin\theta_{k}&\cos\alpha_{k}\cos\theta_{k}&-\sin\alpha_{k}\cos\theta_{k}&a_{k }\sin\theta_{k}\\ 0&\sin\alpha_{k}&\cos\alpha_{k}&d_{k}\\ 0&0&0&1\end{bmatrix} \]  
By multiplying the matrices for each skeleton joint successively, the coordinates of the endpoints can be achieved as follows. \[{}^{B}A_{0}=T(0,0,l/2)Rot_{y}(-\pi/2)\]  
\[{}^{0}A_{1}=Rot_{z}(q_{1})T(0,0,0)T(0,0,0)Rot_{x}(-\pi/2)\]  
\[{}^{1}A_{2}=Rot_{z}(q_{2})T(0,0,l)T(0,0,0)Rot_{x}(\pi/2)\]  
\[{}^{2}A_{3}=Rot_{z}(q_{3})T(0,0,0)T(0,0,0)Rot_{x}(-\pi/2)\]  
\[{}^{3}A_{4}=Rot_{z}(q_{4})T(0,0,l)T(0,0,0)Rot_{x}(0)\]  
\[{}^{B}A_{4}=^{B}A_{0}\cdot^{0}A_{1}\cdot^{1}A_{2}\cdot^{2}A_{3}\cdot^{3}A_{4}\]  
The human body is divided into 13 rigid segments: head, forearms, upper arms, torso, pelvic segment, thighs, shanks, and feet. In addition, 1-DOF hinge joints depict the ankles, knees, and elbows. The 3-DOF spherical joints depict the hips, shoulders, and joints that connect the pelvic segment to the torso and the torso to the head, respectively. The pelvic section, which can move freely in space and, hence, has six DOF, serves as the mechanism's foundation. The kinematic model comprises a total of 24 articulated rotational DOF, including the 3 rotational DOF and 3 translational DOF of the pelvic segment, which determine the body's location and orientation in relation to the reference coordinate system. The human arm may be described as a rigid kinematic chain with three joints (shoulder, elbow, and wrist) and seven joints (\(q_{1},q_{2},q_{3},q_{4},q_{5},q_{6},q_{7}\)). The positions \((d_{1},d_{3},d_{5},d_{7})\) represent the lengths of the links that connect the torso, shoulder, elbow, wrist, and hand. The mobility of the upper arm is determined by the structure of the shoulder, which consists of three joints \((q_{1},q_{2},q_{3})\), where \(q_{1}\) controls its forward and backward motion, \(q_{2}\) controls its downward and upward motion, and \(q_{3}\) controls its rotation. The extension and flexion of the forearm are determined by the anatomy of the elbow, which has one joint \(q_{4}\). The structure of the wrist with three joints \((q_{5},q_{6},q_{7})\) regulates the mobility of the hand, where \(q_{5}\) represents the rotation of the forearm, \(q_{6}\) represents the extension and flexion of the hand, and \(q_{7}\) represents the rotation of the hand. The geometric structure of the arm is used to determine the joint angles and swived angles of the human arm according to [80]. Suppose that \(S_{L}\) and \(S_{R}\) are the left and right shoulders, \(M\) is the midline of the shoulders, \(T\) is the torso position, \(E\) is the elbow, \(W\) is the right wrist, and \(H\) is the right hand. \(\theta_{j}\) is the angle of joint \(q_{j},j=1,2,\ldots,7\).