\hypertarget{pageDirectkinematicsmodel_Overview}{}\subsection{Overview}\label{pageDirectkinematicsmodel_Overview}
The direct kinematics model (D\+K) provides the relative location of segments and their landmarks for specific joint angles defined by the user.\hypertarget{pageDirectkinematicsmodel_The}{}\subsection{The model}\label{pageDirectkinematicsmodel_The}
The D\+K model was developed consisting of a specific set of articulated segments. The D\+K model is described by an articulation chain of segments and the individual joints between them. For each joint a coordinate system (J\+C\+S) is defined that connects two adjacent segments and describes the joint rotation axes and their rotation sequence. Each segment is a rigid body that represents one or more bones (see following table). The D\+K model is positioned by changing the angles of these joints. Local coordinate systems (L\+C\+S) of the segments, were essentially constructed using anatomical landmarks, following the I\+S\+B recommendations \mbox{[}Wu 2002; Wu 2005\mbox{]}, and they are used to define the relative angles of the joints. The following tables summarize the segments and the joints defined into the D\+K model and the anatomical landmarks employed for the definition of the local coordinate systems.

\begin{center} \begin{table}[h]\begin{TabularC}{3}
\hline
\rowcolor{lightgray}{\bf Segment}&{\bf Alias}&{\bf Body parts }\\\cline{1-3}
Pelvis&Pelvis&Pelvic\+\_\+skeleton, Sacrum, Left\+\_\+hip\+\_\+bone, Right\+\_\+hip\+\_\+bone \\\cline{1-3}
Thigh$\ast$&Femur\+\_\+\+L&Left\+\_\+femur \\\cline{1-3}
Lower leg$\ast$&Tibia\+\_\+\+L&Left\+\_\+tibia, Left\+\_\+fibula \\\cline{1-3}
Foot$\ast$&Foot\+\_\+\+L&Left\+\_\+foot \\\cline{1-3}
Patella$\ast$&Patella\+\_\+\+L&Left\+\_\+patella \\\cline{1-3}
Lumbar vertebrae (L5-\/\+L1)$\ast$$\ast$&Lumbar\+\_\+\+L5,..., Lumbar\+\_\+\+L1&Fifth\+\_\+lumbar,...,First\+\_\+lumbar \\\cline{1-3}
Thoracic vertebrae (T12-\/\+T01)$\ast$$\ast$&Thoracic\+\_\+\+T12,..., Thoracic\+\_\+\+T01&Twelfth\+\_\+thoracic,..., First\+\_\+thoracic \\\cline{1-3}
Cervical vertebrae (C7-\/\+C1)$\ast$$\ast$&Cervical\+\_\+\+C7,..., Cervical\+\_\+\+C1&Seventh\+\_\+cervical,..., First\+\_\+cervical \\\cline{1-3}
Skull &Skull &Skull \\\cline{1-3}
Mandible &Mandible &Mandible \\\cline{1-3}
Clavicle$\ast$ &Clavicle\+\_\+\+L &Left\+\_\+clavicle \\\cline{1-3}
Scapula$\ast$ &Scapula\+\_\+\+L &Scapula\+\_\+\+L \\\cline{1-3}
Arm$\ast$ &Humerus\+\_\+\+L &Left\+\_\+humerus \\\cline{1-3}
Forearm$\ast$ &Ulna\+\_\+\+L &Left\+\_\+ulna, Left\+\_\+radius \\\cline{1-3}
Sternum &Sternum &Sternum \\\cline{1-3}
Rib cage&Rib\+Cage&Left\+\_\+first\+\_\+rib-\/\+Right\+\_\+twelfth\+\_\+rib \\\cline{1-3}
\end{TabularC}
\centering
\caption{Segments and the respective body parts included in the D\+K model}
\end{table}
\end{center} 

\begin{center}~\newline
{$\ast$} only the left side is presented ~\newline
{$\ast$} {$\ast$} each vertebral bone is represented by an individual entity ~\newline
\begin{table}[h]\begin{TabularC}{3}
\hline
\rowcolor{lightgray}{\bf Joint}&{\bf Segment 1}&{\bf Segment 2 }\\\cline{1-3}
Reference &Pelvis&Environment \\\cline{1-3}
L5-\/\+Sacrum&Pelvis&Fifth lumbar vertebra \\\cline{1-3}
L4-\/\+L5 vertebral arch&Fifth lumbar vertebra&Fourth lumbar vertebra \\\cline{1-3}
L3-\/\+L4 vertebral arch&Fourth lumbar vertebra&Third lumbar vertebra \\\cline{1-3}
L2-\/\+L3 vertebral arch&Third lumbar vertebra&Second lumbar vertebra \\\cline{1-3}
L1-\/\+L2 vertebral arch&Second lumbar vertebra&First lumbar vertebra \\\cline{1-3}
T12-\/\+L1 vertebral arch&First lumbar vertebra&Twelfth thoracic vertebra \\\cline{1-3}
T11-\/\+T12 vertebral arch&Twelfth thoracic vertebra&Eleventh thoracic vertebra \\\cline{1-3}
T10-\/\+T11 vertebral arch&Eleventh thoracic vertebra&Tenth thoracic vertebra \\\cline{1-3}
T9-\/\+T10 vertebral arch&Tenth thoracic vertebra&Ninth thoracic vertebra \\\cline{1-3}
T8-\/\+T9 vertebral arch&Ninth thoracic vertebra&Eighth thoracic vertebra \\\cline{1-3}
T7-\/\+T8 vertebral arch&Eighth thoracic vertebra&Seventh thoracic vertebra \\\cline{1-3}
T6-\/\+T7 vertebral arch&Seventh thoracic vertebra&Sixth thoracic vertebra \\\cline{1-3}
T5-\/\+T6 vertebral arch&Sixth thoracic vertebra&Fifth thoracic vertebra \\\cline{1-3}
T4-\/\+T5 vertebral arch&Fifth thoracic vertebra&Fourth thoracic vertebra \\\cline{1-3}
T3-\/\+T4 vertebral arch&Fourth thoracic vertebra&Third thoracic vertebra \\\cline{1-3}
T2-\/\+T3 vertebral arch&Third thoracic vertebra&Second thoracic vertebra \\\cline{1-3}
T1-\/\+T2 vertebral arch&Second thoracic vertebra&First thoracic vertebra \\\cline{1-3}
C7-\/\+T1 vertebral arch&First thoracic vertebra&Seventh cervical vertebra \\\cline{1-3}
C6-\/\+C7 vertebral arch&Seventh cervical vertebra&Sixth cervical vertebra \\\cline{1-3}
C5-\/\+C6 vertebral arch&Sixth cervical vertebra&Fifth cervical vertebra \\\cline{1-3}
C4-\/\+C5 vertebral arch&Fifth cervical vertebra&Fourth cervical vertebra \\\cline{1-3}
C3-\/\+C4 vertebral arch&Fourth cervical vertebra&Third cervical vertebra \\\cline{1-3}
C2-\/\+C3 vertebral arch&Third cervical vertebra&Second cervical vertebra (Axis) \\\cline{1-3}
C1-\/\+C2 vertebral arch&Second cervical vertebra (Axis)&First cervical vertebra (Atlas) \\\cline{1-3}
C1-\/\+Skull&First cervical vertebra (Atlas)&Skull \\\cline{1-3}
Skull-\/\+Mandible&Skull&Mandible \\\cline{1-3}
Left hip&Pelvis &Left femur \\\cline{1-3}
Left tibiofemoral&Left femur &Left lower leg \\\cline{1-3}
Left ankle&Left lower leg&Left foot \\\cline{1-3}
Left patellofemoral&Left femur&Left patella \\\cline{1-3}
Left sternoclavicular&T1&Left clavicle \\\cline{1-3}
Scapula-\/\+Clavicle&Left clavicle&Left scapula \\\cline{1-3}
Left glenohumeral&Left clavicle&Left arm \\\cline{1-3}
Left elbow&Left arm&Left forearm \\\cline{1-3}
Left clavicle-\/sternum&Left cleavicle&Sternum \\\cline{1-3}
T4-\/rib cage&T4&Rib cage \\\cline{1-3}
\end{TabularC}
\centering
\caption{List of joints and articulated segments defined in the D\+K model}
\end{table}
\end{center} 

\begin{center}~\newline
~\newline
 \begin{table}[h]\begin{TabularC}{5}
\hline
\rowcolor{lightgray}{\bf Segment}&{\bf L\+M 1}&{\bf L\+M 2}&{\bf L\+M 3}&{\bf L\+M 4 }\\\cline{1-5}
Pelvis&Right\+\_\+acetabular\+\_\+center&Left\+\_\+acetabular\+\_\+center&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+L5&\\\cline{1-5}
Lumbar L5&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+L5&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+L5&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+L5&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+L5 \\\cline{1-5}
Lumbar L4&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+L4&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+L4&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+L4&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+L4 \\\cline{1-5}
Lumbar L3&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+L3&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+L3&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+L3&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+L3 \\\cline{1-5}
Lumbar L2&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+L2&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+L2&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+L2&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+L2 \\\cline{1-5}
Lumbar L1&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+L1&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+L1&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+L1&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+L1 \\\cline{1-5}
Thoracic T12&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T12&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T12&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T12&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T12 \\\cline{1-5}
Thoracic T11&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T11&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T11&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T11&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T11 \\\cline{1-5}
Thoracic T10&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T10&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T10&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T10&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T10 \\\cline{1-5}
Thoracic T09&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T9&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T9&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T9&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T9 \\\cline{1-5}
Thoracic T08&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T8&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T8&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T8&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T8 \\\cline{1-5}
Thoracic T07&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T7&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T7&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T7&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T7 \\\cline{1-5}
Thoracic T06&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T6&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T6&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T6&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T6 \\\cline{1-5}
Thoracic T05&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T5&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T5&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T5&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T5 \\\cline{1-5}
Thoracic T04&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T4&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T4&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T4&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T4 \\\cline{1-5}
Thoracic T03&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T3&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T3&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T3&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T3 \\\cline{1-5}
Thoracic T02&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T2&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T2&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T2&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T2 \\\cline{1-5}
Thoracic T01&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T1&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T1&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+T1&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+T1 \\\cline{1-5}
Cervical C7&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C7&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C7&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+C7&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+C7 \\\cline{1-5}
Cervical C6&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C6&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C6&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+C6&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+C6 \\\cline{1-5}
Cervical C5&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C5&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C5&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+C5&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+C5 \\\cline{1-5}
Cervical C4&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C4&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C4&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+C4&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+C4 \\\cline{1-5}
Cervical C3&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C3&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C3&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+C3&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+C3 \\\cline{1-5}
Cervical C2&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C2&Posterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C2&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+C2&Center\+\_\+upper\+\_\+plate\+\_\+of\+\_\+\+C2 \\\cline{1-5}
Cervical C1&V\+C1&D\+C1&Center\+\_\+lower\+\_\+plate\+\_\+of\+\_\+\+C1&Center\+\_\+atlanto\+\_\+occipital\+\_\+joint \\\cline{1-5}
Scull&Center\+\_\+atlanto\+\_\+occipital\+\_\+joint&Left\+\_\+porion&Right\+\_\+porion&Nasion \\\cline{1-5}
Mandible&Left\+\_\+jaw\+\_\+angle&Right\+\_\+jaw\+\_\+angle&Inferior\+\_\+crest\+\_\+of\+\_\+the\+\_\+jaw&\\\cline{1-5}
Thigh L&Medial\+\_\+epicondyle\+\_\+of\+\_\+left\+\_\+femur&Lateral\+\_\+epicondyle\+\_\+of\+\_\+left\+\_\+femur&Left\+\_\+acetabular\+\_\+center&\\\cline{1-5}
Lower leg L&Lateral\+\_\+point\+\_\+lateral\+\_\+condyle\+\_\+of\+\_\+left\+\_\+tibia&Medial\+\_\+point\+\_\+medial\+\_\+condyle\+\_\+of\+\_\+left\+\_\+tibia&Tip\+\_\+lateral\+\_\+malleolus\+\_\+of\+\_\+left\+\_\+fibula&Tip\+\_\+medial\+\_\+malleolus\+\_\+of\+\_\+left\+\_\+tibia \\\cline{1-5}
Foot L&Lateral\+\_\+point\+\_\+lateral\+\_\+condyle\+\_\+of\+\_\+left\+\_\+tibia&Medial\+\_\+point\+\_\+medial\+\_\+condyle\+\_\+of\+\_\+left\+\_\+tibia&Tip\+\_\+lateral\+\_\+malleolus\+\_\+of\+\_\+left\+\_\+fibula&Tip\+\_\+medial\+\_\+malleolus\+\_\+of\+\_\+left\+\_\+tibia \\\cline{1-5}
Patella L&Patella\+L\+\_\+anterior\+\_\+center&Patella\+L\+\_\+lateral&Patella\+L\+\_\+medial&Patella\+L\+\_\+distal \\\cline{1-5}
Clavicle L&Dorsal\+\_\+point\+\_\+of\+\_\+left\+\_\+acromioclavicular\+\_\+joint&Ventral\+\_\+point\+\_\+of\+\_\+left\+\_\+sternoclavicular\+\_\+joint&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T8&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+C7 \\\cline{1-5}
Scapula L&Dorsal\+\_\+point\+\_\+of\+\_\+left\+\_\+acromioclavicular\+\_\+joint&Angulus\+\_\+acromialis\+\_\+of\+\_\+left\+\_\+scapula&Angulus\+\_\+inferior\+\_\+of\+\_\+left\+\_\+scapula&Trigonum\+\_\+spinae\+\_\+of\+\_\+left\+\_\+scapula \\\cline{1-5}
Arm L&Lateral\+\_\+epicondyle\+\_\+of\+\_\+left\+\_\+humerus&Medial\+\_\+epicondyle\+\_\+of\+\_\+left\+\_\+humerus&Head\+\_\+center\+\_\+of\+\_\+left\+\_\+humerus&\\\cline{1-5}
Forearm L&Lateral\+\_\+epicondyle\+\_\+of\+\_\+left\+\_\+humerus&Medial\+\_\+epicondyle\+\_\+of\+\_\+left\+\_\+humerus&Styloid\+\_\+process\+\_\+of\+\_\+left\+\_\+radius&Styloid\+\_\+process\+\_\+of\+\_\+left\+\_\+ulna \\\cline{1-5}
Sternum&Left\+\_\+sternum\+\_\+sternoclavicular\+\_\+joint&Right\+\_\+sternum\+\_\+sternoclavicular\+\_\+joint&Substernale\+\_\+(xyphoid\+\_\+process)&Jugular\+\_\+notch \\\cline{1-5}
Rib cage&Ventral\+\_\+point\+\_\+of\+\_\+left\+\_\+sternoclavicular\+\_\+joint&Right\+\_\+sternum\+\_\+sternoclavicular\+\_\+joint&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T4&Anterior\+\_\+midpoint\+\_\+of\+\_\+the\+\_\+body\+\_\+of\+\_\+\+T10 \\\cline{1-5}
\end{TabularC}
\centering
\caption{Anatomical landmarks used for the definition of the local coordinate systems}
\end{table}
\end{center} \hypertarget{pageDirectkinematicsmodel_Structure}{}\subsection{Structure}\label{pageDirectkinematicsmodel_Structure}
The segments are articulated to each other following a tree structure, with the pelvis being the root of this structure (see following figure). Three rotational degrees of freedom (D\+O\+F) are allowed for each joint, with the exception of the joint connecting the pelvis with the environment that three additional translational D\+O\+F are allowed. The orientation of each segment is computed relative to its predecessor in the tree structure, taking into account the rotational angles of the joint connecting the segments.

\begin{center}\end{center} 

\begin{center}{$\ast$} the vertebral segments are connected to each other as described in the first table.\end{center} 

\begin{center}\end{center} \hypertarget{pageDirectkinematicsmodel_Examples}{}\subsection{Examples}\label{pageDirectkinematicsmodel_Examples}
The following figure demonstares two examples of positioning the reference model, by using joint angles defined by the user. Initially, the D\+K model is constructed by calling the function \char`\"{}\+Create\+Piper\+Model.\+m\char`\"{}. The model structure in .txt format and anatomical landmarks coordinates in .csv format serve as inputs for this function. This function computes L\+C\+S using the anatomical landmarks coordinates, articulates the segments using the model structure and computes the local coordinate systems (figure bellow, gray skeleton). The function provides the dimensions of the articulated model and the anatomical landmarks coordinates both in global coordinate system and in L\+C\+S. The function \char`\"{}\+Reposition\+Skeleton\+By\+D\+K.\+m\char`\"{} is used to re-\/position the skeleton. The dimensions and the structure of the articulated model and the joint angles corresponding the desired posture serve as input for this function. The function computes the new position of each segment using the position of its predecessor in the tree structure and the angles of the joint connecting the segments as defined by the user. The function provides the anatomical landmarks coordinates in the new posture, expressed in both the global coordinate system and in L\+C\+S (figure bellow, red skeleton). For the first example the flexion angles of the right hip, right knee, right glenohumeral and right elbow were increased 60, -\/80, 80 and -\/60\textdegree{} respectively. These flexion angles resulted in the posture represented with the red skeleton (figure bellow left, red skeleton). Although only flexion angles were defined, it can be noticed that the forearm is also internally rotated relative to the spine. This occurred because the computation of the position of the forearm segment is based on the position and orientation of the arm and the angles defined for the elbow joint. As the arm is inverted the elbow flexion causes the forearm to move internally relatively to the spine. For the second example, the joint angles of the driving posture were employed (figure bellow right).



~\newline
\hypertarget{pageDirectkinematicsmodel_the}{}\subsection{Description of the program scripts}\label{pageDirectkinematicsmodel_the}
~\newline
\begin{center} \begin{table}[h]\begin{TabularC}{3}
\hline
\rowcolor{lightgray}{\bf Step }&{\bf Action }&{\bf Script }\\\cline{1-3}
1 &Symmetrize skeleton &Sym\+L\+Ms \\\cline{1-3}
2 &Compute joint angles of the driving posture (target posture) &Create\+Personalized\+Piper\+Model \\\cline{1-3}
3 &Compute joint coordinate systems and express anatomical landmarks with repect to L\+C\+S for source skeletons &Create\+Personalized\+Piper\+Model \\\cline{1-3}
4 &Compute the coordinates of the anatomical landmarks on the target posture&Reposition\+Skeleton\+By\+D\+K \\\cline{1-3}
\end{TabularC}
\centering
\caption{Workflow and respective scripts}
\end{table}
~\newline
\begin{table}[h]\begin{TabularC}{4}
\hline
\rowcolor{lightgray}{\bf Script }&{\bf Input }&{\bf Output }&{\bf Description }\\\cline{1-4}
Create\+Personalized\+Piper\+Model(sbj) &Piper.\+Model.\+txt ~\newline
 (sbj)\+\_\+\+L\+Ms\+Import.\+csv ~\newline
 Zero\+Joint\+Angles.\+txt~\newline
 &(sbj).Scanned\+Posture.\+L\+Ms.\+csv ~\newline
 (sbj).Scanned\+Posture.\+Joint\+Angles.\+csv~\newline
 (sbj).Joint\+Centers.\+csv~\newline
 (sbj).Dimensions.\+mat~\newline
 (sbj).Body.\+mat &Computes local coordinate systems for each segment~\newline
 and computes the positions of the anatomical landmarks~\newline
 with respect to the G\+C\+S and L\+C\+S~\newline
 \\\cline{1-4}
Reposition\+Skeleton\+By\+D\+K(sbj) &Piper.\+Model.\+txt ~\newline
 (sbj).Dimensions.\+mat ~\newline
 (sbj).Body.\+mat ~\newline
 Driving\+Posture.\+Joint\+Angles.\+csv &(sbj).Driving\+Posture.\+L\+Ms.\+csv &Positions the articulated model based on joint angles~\newline
 defined by the user and computes the positions of the~\newline
 anatomical landmarks in the target posture with respect~\newline
 to the G\+C\+S and L\+C\+S \\\cline{1-4}
Sym\+L\+Ms &(sbj)\+\_\+lm.\+csv &(sbj)\+\_\+\+L\+Ms\+Sym.\+csv &i) Creates symmetrized to the left extremities anatomical landmarks on the respective right extrimities ~\newline
 ii) Modifies the input landmarks set such as the headers are~\newline
 capitalized and landmarks are registered to segments instead~\newline
 of body parts (Alias table 1)~\newline
 ex. Styloid\+\_\+process\+\_\+of\+\_\+left\+\_\+radius Left\+\_\+radius Ulna\+\_\+\+L~\newline
 Left\+\_\+ischial\+\_\+tuberosity Left\+\_\+hip\+\_\+bone Pelvis \\\cline{1-4}
Segment\+\_\+(segment name) &Previous segment in the~\newline
 kinematic chain, anatomical~\newline
 landmarks~\newline
 &L\+C\+S~\newline
 A structure variable including the~\newline
 the segment, body parts, L\+C\+S,~\newline
 axes rotation sequence,~\newline
 distal and proximal joints &Defines~\newline
 i) the L\+C\+S of the (segment name)~\newline
 ii) the proximal and the distal joints of the (segment name)

\\\cline{1-4}
\end{TabularC}
\centering
\caption{Description of the main scripts of the kinematic model}
\end{table}
~\newline
~\newline
\begin{table}[h]\begin{TabularC}{2}
\hline
\rowcolor{lightgray}{\bf Script }&{\bf Description }\\\cline{1-2}
Batch\+Process4\+Computing\+L\+Ms\+In\+Scanned\+And\+Driving\+Postures&Executes the Create\+Personalized\+Piper\+Model and Reposition\+Skeleton\+By\+D\+K scripts for all the selected sbj \\\cline{1-2}
Batch\+Process4\+Sym\+L\+Ms&Executes the Sym\+L\+Ms script for all the selected sbj \\\cline{1-2}
\end{TabularC}
\centering
\caption{Description of batch process scripts}
\end{table}
~\newline
~\newline
\begin{table}[h]\begin{TabularC}{2}
\hline
\rowcolor{lightgray}{\bf File}&{\bf Description }\\\cline{1-2}
Piper.\+Model.\+txt &Defines the structure of the model\+: Joints, segments and containing body parts, anatomical landmarks to be used for L\+C\+S \\\cline{1-2}
(sbj)\+\_\+lm.\+csv &Anatomical landmarks coordinates (name, body part, x, y, z) \\\cline{1-2}
(sbj)\+\_\+\+L\+Ms\+Sym.\+csv &Anatomical landmarks coordinates (name, segment, x, y, z) \\\cline{1-2}
Zero\+Joint\+Angles.\+txt &Zero values for all the joint angles \\\cline{1-2}
(sbj).Scanned\+Posture.\+L\+Ms.\+csv &Anatomical landmarks coordinates for the scan posture (name, segment, x, y, z, X, Y, Z) \\\cline{1-2}
(sbj).Driving\+Posture.\+L\+Ms.\+csv &Anatomical landmarks coordinates for the driving posture (name, segment, x, y, z, X, Y, Z) \\\cline{1-2}
(sbj).Scanned\+Posture.\+Joint\+Angles.\+csv &Joint angles for the articulated model \\\cline{1-2}
(sbj).Joint\+Centers.\+csv &Coordinates of the joint centers \\\cline{1-2}
\end{TabularC}
\centering
\caption{Description of input/output files}
\end{table}
~\newline
~\newline
\begin{table}[h]\begin{TabularC}{4}
\hline
\rowcolor{lightgray}{\bf Joint}&{\bf Definition }&{\bf Anterior view}&{\bf Lateral view }\\\cline{1-4}
Pelvis-\/\+Environment&\begin{TabularNC}{1}
\hline
O\+: midpoint of left and right acetabular centers \\\cline{1-1}
Z\+: the line crossing the right and left acetabular centers, pointing to the right \\\cline{1-1}
Y\+: the line crossing the center of the fifth lumbar vertebral lower plate and the origin, pointing cranially \\\cline{1-1}
X\+: the common line perpendicular to the Z and Y axes, pointing anteriorly \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Hip&\begin{TabularNC}{1}
\hline
O\+: the acetabular center \\\cline{1-1}
Y\+: the line connecting the acetabular with the knee center, pointing proximally \\\cline{1-1}
X\+: the common line perpendicular to the line connecting the lateral and medial femoral epicondyles and the Y axis, pointing anteriorly \\\cline{1-1}
Z\+: the common line perpendicular to the X and Y axes, pointing to the right \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Knee&\begin{TabularNC}{1}
\hline
O\+: the midpoint of the femoral epicondyles \\\cline{1-1}
Z\+: the line connecting the medial and lateral malleoli, pointing to the right \\\cline{1-1}
X\+: the common line perpendicular to the line connecting the lateral malleolus with the midpoint of the lateral and medial tibial condyles and the line connecting the medial malleolus with the midpoint of the tibial condyles, pointing anteriorly \\\cline{1-1}
Y\+: the common line perpendicular to the Z and X axes, pointing proximally \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
C2-\/\+C3&\begin{TabularNC}{1}
\hline
O\+: center of distal vertebral segment \\\cline{1-1}
Y\+: the line connecting the centers of the proximal and distal vertebral plates, pointing cranially \\\cline{1-1}
Z\+: the common perpendicular line to the line connecting the ventral and the dorsal points of the vertebral and the Y axis, pointing to the right \\\cline{1-1}
X\+: the common line perpendicular to the Y and Z axes, pointing anteriorly \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Sternoclavicular&\begin{TabularNC}{1}
\hline
O\+: the most ventral point of the clavicle \\\cline{1-1}
Z\+: the line connecting the origin with the most dorsal point of the clavicle, pointing laterally \\\cline{1-1}
X\+: the common line perpendicular to the Z axis and the line connecting the most anterior point of the superior plate of C7 and the most anterior point of the superior plate of T8, pointing anteriorly \\\cline{1-1}
Y\+: the common line perpendicular to the Z and X axes, pointing caudally \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Glenohumeral&\begin{TabularNC}{1}
\hline
O\+: the center of the humerus \\\cline{1-1}
Y\+: the line connecting the center of the humerus with the elbow center, pointing cranially \\\cline{1-1}
X\+: the common line perpendicular to the the Y axis and the line connecting the epicondyles of the humerus, pointing anteriorly \\\cline{1-1}
Z\+: the common line perpendicular to the Y and X axes, pointing laterally \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Skull&\begin{TabularNC}{1}
\hline
O\+: the center of the atlanto-\/occipital joint \\\cline{1-1}
Z\+: the line connecting the left with the right porion, pointing to the right \\\cline{1-1}
X\+: the line perpendicular to plane defined by the nasion, the left and the right porion, pointing caudally \\\cline{1-1}
Y\+: the common line perpendicular to the Z and X axes, pointing anteriorly \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Mandible&\begin{TabularNC}{1}
\hline
O\+: the midpoint of the right and the left jaw angles \\\cline{1-1}
Z\+: the line connecting the left and the right jaw angles,pointing right \\\cline{1-1}
X\+: the line perpendicular to plane defined by the incisive, the left and the right jaw angles, pointing caudally \\\cline{1-1}
Y\+: the common line perpendicular to the Z and X axes, pointing anteriorly \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Patella&\begin{TabularNC}{1}
\hline
O\+: the anterior center of the patella \\\cline{1-1}
Z\+: the line connecting the most medial with the most lateral points of the patella, pointing laterally \\\cline{1-1}
X\+: the common line perpendicular to the X axis and the line connecting the most proximal with most distal points on the anterior surface of the patella, pointing posteriorly \\\cline{1-1}
Y\+: the common line perpendicular to the Z and X axes, pointing distally \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Scapula&\begin{TabularNC}{1}
\hline
O\+: the most dorsal point of the left acromioclavicular joint \\\cline{1-1}
Z\+: the line connecting the angulus acromialis with the trigonum spinae, pointing laterally \\\cline{1-1}
X\+: the line perpenticular to plane defined by the angulus acromialis, trigonum spinae and the angulus inferior, pointing anteriorly \\\cline{1-1}
Y\+: the common line perpendicular to the Z and X axes, pointing caudally \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Sternum&\begin{TabularNC}{1}
\hline
O\+: the most ventral point of the left clavicle \\\cline{1-1}
Z\+: the line connecting the points of the left and right sternoclavicular joints, pointing laterally \\\cline{1-1}
X\+: the common line perpendicular to axis Z and the line connecting the xyphoid process and jugular notch, pointing anteriorly \\\cline{1-1}
Y\+: the common line perpendicular to the Z and X axes, pointing caudally \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Rib\+Cage&\begin{TabularNC}{1}
\hline
O\+: anterior midpoint of T4 \\\cline{1-1}
Z\+: the line connecting the most ventral point of the the left sternoclavicular joint with the right point of the right sternoclavicular joint, pointing right \\\cline{1-1}
X\+: the common line perpendicular to axis Z and the line connecting the anterior midpoints of T4 and T10, pointing posteriorly \\\cline{1-1}
Y\+: the common line perpendicular to the X and Z axes, pointing cranially \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
Elbow&\begin{TabularNC}{1}
\hline
O\+: the midpoint of the epicondyles of the humerus \\\cline{1-1}
Y\+: the line connecting the lateral epicondyle of the humerus with the most lateral point on the radial styloid, pointing proximally \\\cline{1-1}
X\+: the common line perpendicular to the line connecting the most lateral point of the radial styloid with the most medial point of the ulnar styloid and the Y axis \\\cline{1-1}
Z\+: the common line perpendicular to the X and Y axes \\\cline{1-1}
\end{TabularNC}
& & \\\cline{1-1}
\end{TabularC}
\centering
\caption{Definitions of the joint coordinate systems}
\end{table}
\end{center} 

~\newline
\hypertarget{pageDirectkinematicsmodel_References}{}\subsection{References}\label{pageDirectkinematicsmodel_References}
Wu G et al., 2002. I\+S\+B recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion -\/ Part I\+: ankle, hip, and spine. Journal of Biomechanics 35\+: 543 -\/ 548. ~\newline
Wu G et al., 2005. I\+S\+B recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion -\/ Part I\+I\+: shoulder, elbow, wrist and hand. Journal of Biomechanics 38\+: 981 -\/ 992. 