======DH======
Determines a list of Denavit Hartenberg parameters and the corresponding coordinate systems from a list of revolute joint axes.

If static calibration is used the determined joint axes origins and points are determined in local coordinates to the coordinate systems of its corresponding joint axes.

The x- and z-Axes of the base coordinate system (and its origin) are determined by the general attribute "coordinateSystem".
====Attributes====
^ Name ^ Type ^ Description ^ optional ^
^ name | String | name of the element | No |
^ method | String | Different variants of Denavit Hartenberg parameterisation exists. The most used one named "distal" and defines the coordinate systems at the distal end of the segments. The x-axes of the the corresponding coordinate systems are upright to both adjusting joint axes. An importend variant is named as "modified". Its x-axes are upright only to one of the two adjoining joint axes. The default method is "distal" and is used if to method is explicitly defined by usage this attribute. | Yes |
^ xAxesDirections | Comma separated list of Strings | List of x-axis direction names. Typically these axes are determined by calibration from a static trial, with all theata angles equal zero, the zero-pose of the robot. | No |
^ jointAxes | Comma seperated List of Strings | List of joint axes element names with an optional "-" as an prefix which indicates the the direction of the axis should be negated. Die position of the first axis is used as origin of the base coordinate system. | No |
^ calibrateIncludes | name of a switch | Name of a switch to define the static calibration trial with the normal pose of the robot arm | Yes |
^ nominalD | Comma seperated list of double values >=0, NaN included | Used for method="modified" only. List of nominal values useful to set to values >=0 for nearly parallel joint axes. There exist no d0-value but the TCP system is in line with the previous axis and in a fixed length distance. So set the last values in the list to that value explicitly. Set values to "NaN" if the corresponding axes are not nearly parallel which allows automated determination of the d-value. | Yes |
^ lastD | REAL| Used for classical Denavit Hartenberg method only. Defines the last d parameter in [mm]. This parameter can not be estimated. It is assumed that the last coordinate system (the CS of the TCP) has the same z-direction as the last joint axis (r==0, alpha==0). The parameter d is the translation of the origin of the last joint axis in direction of this axis. If the parameter is not set it is automatically set to (0d,0d,0d) which results in a TCP coordinate system identical to the wrist2 CS, but a warning is written into the log. | Yes |
^ signR | Comma seperated list of boolean values "true" or "false" | This allows to switch the sign of r-vector, default should be false. Especially in the case of DH-classical the calculation of the theta angles is based on a flipped r-vector/x-axis if the signR attribute is set to "true". | Yes |
^ Origin | VECTOR_3D | Mathematical expression of the origin of the base coordinate system. | No|
^ X0Axis| VECTOR_3D | Mathematical expression defining the x-axis of the base coordinate system, fixed on the base segment, rotating with the rotation of the base joint. This can be determined in a static calibration trial and fixed to the base cluster.| No |
====Methods====
^ Name ^ Description ^
^ classical | This is the default method. This defines coordinate systems at the distal end of the links and the x-axes are orthogonal to both adjacent joint-axes. | 
^ modified | The modified version of the Denavit Hartenberg parameterisation defines coordinate systems at the proximal side of the links. The x-axes are orthogonal only to its corresponding coordinate system (joint axis).| 
====Generated trajectories====
^ Name ^ Type ^ Description ^ 
^ <name>X0Axis | Vector3d | The direction of the X-axis of the base coordinate system, as defined by the attribute X0Axis (expression). |
^ <name>Origin | Vector3d | The Origin of the base coordinate system, as defined by the attribute Origin (expression)". |
^ <name>XAxis<Index> | Vector3d | X-axes directions, as defined by the attribute (expression) "xAxisDirections". |
^ <name>Alpha<Index> | Double| alpha (twist angle) in [deg] | 
^ <name>Theta<Index> | Double | theta (joint angle) in [deg] | 
^ <name>D<Index> | Double | d (displacement or link offset) in [mm] | 
^ <name>R<Index> | Double | r (link length) in [mm] |
^ <name>O<Index> | Vector3d | Origin of the Denavit Harteberg based coordinate system. |
^ <name>P<Index> | Vector3d | Endpoint of the previous x-axis on the z-axis.|

If the method is "modified" than the index starts for "R" and "Alpha" with one and for "Theta" and "D" with zero, else all of them start with one.
====Generated parameters====

If the attribute "calibrateIncludes" is used, the following parameters are determined as mean/std values over the complete trial, which is assumed to be a static trial.

^ Name ^ Type ^ Description ^ 
^ <name>P<Index>Mean | Vector3d | Position on the joint axis, where the x-axis of the previous joint ends,  in local coordinates of the CS to the correspoinding joint axis. | 
^ <name>O<Index>Mean | Vector3d | Origin of the DH-coordindate system in local coordinates of the CS to the corresponding joint axis. | 
^ <name>Alpha<Index>Mean | Double| alpha (twist angle) in [deg] | 
^ <name>Theta<Index>Mean | Double | theta (joint angle) in [deg] | 
^ <name>D<Index>Mean | Double | d (displacement or link offset) in [mm] | 
^ <name>R<Index>Mean | Double | r (link length) in [mm] |
^ <name>Alpha<Index>Std | Double| alpha (twist angle) std in [deg] | 
^ <name>Theta<Index>Std | Double | theta (joint angle) sd in [deg] | 
^ <name>D<Index>Std | Double | d (displacement or link offset) std in [mm] | 
^ <name>R<Index>Std | Double | r (link length) std in [mm] |

**Example**

<code xml>
<DH name="mDHSARA"
    method="modified"
    xAxesDirections="GlobeX,BaseX,ShoulderX,ElbowX,Wrist1X,Wrist2X,TCPX"                      
    jointAxes="GlobeZ,BaseAxisSARA,ShoulderAxisSARA,ElbowAxisSARA,WristAxis1SARA,WristAxis2SARA,TCPAxisSARA"
    calibrateIncludes="static_calibrate1"
    nominalD="NaN, 0.0, 0.0, NaN, NaN, 0.099381832"/> 
</code>

<code xml>
<DH name="DHSARA"
    method="classical"
    xAxesDirections="GlobeX,BaseX,ShoulderX,ElbowX,Wrist1X,Wrist2X,TCPX"                      
    jointAxes="GlobeZ,BaseAxisSARA,ShoulderAxisSARA,ElbowAxisSARA,WristAxis1SARA,WristAxis2SARA,TCPAxisSARA"
    Origin="UROrigin"
    X0Axis="URXAxis"
    calibrateIncludes="static_calibrate1"
    lastD="99.9"/>
</code>

====Generated parameters====

The mean/std values of the following table are calculated, if the attribute "phase" is set and also the attribute average="true" or meanStd="true". If the last attribute is set than also the corresponding std-values are calculated. All values are are based on mean-values for each phase. These mean-values are averaged and also the std for this mean is determined.

^ Name ^ Type ^ Description ^ 
^ <name>Alpha<Index>PhasesMean | REAL| alpha in [deg]; for each phase the mean is calculated; than the mean of all of these values is determined. | 
^ <name>Alpha<Index>PhasesStd | REAL| For each phase the mean is calculated; than the mean of all of these values is determined and the std of this mean is determined. | 
^ <name>Theta<Index>PhasesMean | REAL| theta in [deg]; for each phase the mean is calculated; than the mean of all of these values is determined. | 
^ <name>Theta<Index>PhasesStd | REAL| theta in [deg]; for each phase the mean is calculated; than the mean of all of these values is determined and the std of this mean is determined. | 
^ <name>D<Index>PhasesMean | REAL| D in [mm]; for each phase the mean is calculated; than the mean of all of these values is determined. | 
^ <name>D<Index>PhasesStd | REAL| std for each phase the std is calculated; than the mean of all of these values is determined and the std of this mean is determined. | 
^ <name>R<Index>PhasesMean | REAL| R in [mm]; for each phase the mean is calculated; than the mean of all of these values is determined. | 
^ <name>R<Index>PhasesStd | REAL| R in [mm]; for each phase the mean is calculated; than the mean of all of these values is determined and the std of this mean is determined. | 


======FKDH======
This element determines forward (direct) kinematics. A cartesian coordinate system based on a parent coordinate system and by a sequence of screw motions defined by Denavit-Hartenberg convention is determined.

==== Attributes ====

^ Attribute ^ Type ^ Description ^ Required ^
^ name | String | Name of the element | Yes | 
^ method | String | Name of the method: default="classical" or "distal", "modified" | No |
^ coordinateSystem | String | Defines the the reference coordinate system by its name. If it is not set than (0,0,0) ist used as the origin and e1, e2, e3 are used as its axes. | No|
^ alpha | Comma seperated list of REAL values in [rad]. | Denavit-Hartenberg parameter alpha between the joint axes. | Yes |
^ deltaTheta | Comma seperated list of REAL values in [rad]. | Angle in static neutral pose between Denavit Hartenberg x-axis (r) and the corresponding joint angle measurement by the robot.  | Yes |
^ theta | Comma seperated list of REAL value in [rad] variable names. | Denavit-Hartenberg parameter theta around the joint axes.| Yes |
^ d | Comma seperated list of REAL values in [mm] | Denavit-Hartenberg parameter d along the joint axes. | Yes |
^ r | Comma seperated list of REAL values in [mm] | Denavit-Hartenberg parameter r (equivalent to a) between the joint axes. | Yes |

====Generated trajectories ====
^ Name ^ Type ^ Description ^ 
^ <name> | MATRIX_3X3D| Representation of the three orthogonal orientation axes of the result coordinate system (columns of the matrix). This is the last in the DH sequence, often called TCP frame.| 
^ <name>Position | COLUMN_VECTOR_3D| Origin of the result coordinate system. | 
^ <name><index> | MATRIX_3X3D| Representation of the three orthogonal orientation axes of the determined local coordinate system (columns of the matrix). | 
^ <name>Position<index> | COLUMN_VECTOR_3D| Origin of the coordinate system. | 

The index starts with 1 because with the index 0 typically the reference system is called.

For the last coordinate system trajectories are created without the index as a suffix. This system can be accessed by further calcmodel elements.

**Example**

<code xml>
<FKDH name="DK"
      coordinateSystem="GLOBE"
      alpha="0.5,90,0.0,0.0"
      deltaTheta="1.0,3.4,2.0,0.5"
      d="0.145,7089234,0892734"
      r="0.234,5123,123,765"
      theta="Angle0,Angle1,Angle2,Angle3"/> 
</code>

An alternative is to use corresponding function

<code xml>
<CoordinateSystem name="BaseUR"
                  Pose="dhm(Angle0, DH_alpha0, DH_d0, DH_r0)"/> 
</code>

for each joint in the sequence. This makes the sequence of transformations more transparent but also needs to write more xml.