Model Element

Description

A Reference_Marker defines an orthonormal, right-handed coordinate system and reference frame in MotionSolve.  A Reference_Marker must belong to a body.  The body can be any type: rigid, flexible, or point.  The Newtonian reference frame (Ground) is considered to be a special case of a rigid body.

The image below illustrates how a Reference_Marker is defined.

Defining a Reference_Marker on Ground

In the image above, N represents the Newtonian reference frame and coordinate system.  It consists of a global origin O and three right-handed, mutually perpendicular directions denoted as OX, OY, and OZ.

M represents another coordinate system of interest.  The origin of M is denoted by oM, and the axes of M are denoted as xM, yM, and zM.  For this example, assume M is fixed with respect to N.

To define M, the measure numbers of the vector O-oM in the coordinate system N are needed.  This is denoted as r in the image.

The rotation  matrix that converts from the xM-yM-zM basis to the x-y-z basis is needed.  This is denoted as NAM in the image.

A Reference_Marker is defined by specifying the following:

Common uses for Reference_Markers in MotionSolve include:

The Reference_Marker with id = 0 has special significance.  In all MotionSolve expressions, it is used to denote the global coordinate system.

The attribute node_id is optional.  It is used only for flexible bodies.

Format

<Reference_Marker

      id                    = "integer"

    [ label                 = "string" ]

    body_id               = "integer"

    [ body_type             = {"RIGIDBODY" | "FLEXBODY" | "POINTBODY"} ]

    [ rm_id                 = "integer" ]

    [ node_id               = "integer" ]

{    

      pos_x                 = "real"

      pos_y                 = "real"

      pos_z                 = "real"

[{  

      a00                   = "real"

      a10                   = "real"

      a20                   = "real"

      a01                   = "real"

      a11                   = "real"

      a21                   = "real"

      a02                   = "real"

      a12                   = "real"

      a22                   = "real"

  |

     psi                    = "real"

     theta                  = "real"

     phi                    = "real"

  |

     yaw                    = "real"

     pitch                  = "real"

     roll                   = "real"

  |

     e0                     = "real"

     e1                     = "real"

     e2                     = "real"

     e3                     = "real"

}]

}

|

{

     usrsub_param_string    = "USER(..,..)"

     usrsub_fnc_name        = "valid fnc name"

     usr_dll_name           = "valid dll name"

|

     usrsub_param_string    = "USER(..,..)"

     usrsub_fnc_name        = "valid fnc name"

     interpreter            = "PYTHON | MATLAB"

     script_name            = "valid script name"

}

/>  

Attributes

id

Element identification number (integer>0).  This number is unique to all Reference_Marker elements.

label

The name of the Reference_Marker element.

body_id

ID of the body to which marker belongs.  The body may be Ground, a rigid body, a point mass, or a flexible body.

body_type

Specifies whether the body is of type RIGIDBODY, FLEXBODY or POINTBODY

This parameter is optional.  The default type is RIGIDBODY.

rm_id

An optional attribute that specifies the Reference_Marker ID.  If specified,  the position and orientation of the marker is assumed to be with respect to the reference marker.

The default ID is 0 which refers to the global reference frame.

node_id

An optional attribute used only for flexible bodies.

pos_x, pos_y, pos_z

The x, y, z coordinates of the marker origin specified in terms of the global frame. pos_x defines the x-coordinate of the origin, pos_y defines the y-coordinate of the origin, and pos_z defines the z-coordinate of the origin.

a00 a01 a02

a10 a11 a12

a20 a21 a22

Elements of the transformation matrix defining the orientation of the Reference_Marker with respect to the global frame.

{a00 a10 a20} defines directions cosines of the x-axis

{a01 a11 a21} defines directions cosines of the y-axis

{a02 a12 a22} defines directions cosines of the z-axis.  The nine elements define a 3x3, orthonormal matrix.

This means that the nine numbers must satisfy the following conditions:

psi

In radians, the rotation around the original z-axis.

theta

In radians, the rotation around the new x-axis after Psi has been applied.

phi

In radians, the rotation around the new z-axis after Theta has been applied.

yaw

In radians, the rotation around the original z-axis of the marker.

pitch

In radians, the rotation about the new location of the y-axis of the marker after yaw has been applied.

roll

In radians, the rotation about the new location of the x-axis after pitch has been applied.

e0, e1, e2, e3

Euler parameters that describe the rotation.

usrsub_param_string

The list of parameters that are passed from the data file to the user defined subroutine.

usrsub_fnc_name

Specifies an alternative name for the user subroutine MARKER_READ.

usrsub_dll_name

Specifies the path and name of the DLL or shared library containing the user subroutine.  MotionSolve uses this information to load the user subroutine in the DLL at run time.

script_name

Specifies the path and name of the user written script that contains the routine specified by usrsub_fnc_name.

interpreter

Specifies the interpreted language that the user script is written in.  Valid choices are MATLAB or PYTHON.

Comments

Example

The following example defines a Reference_Marker on a rigid body.

<Reference_Marker

     id                  = "1012"

     body_id             = "1000"

     body_type           = "RIGIDBODY"

     pos_x               = "1.414"

     pos_y               = "3.14159"

     pos_z               = "1.61804"

     a00                 = "0."

     a10                 = "1."

     a20                 = "0."

     a01                 = "0.041630503"

     a11                 = "0."

     a21                 = "0.99913307"

     a02                 = "0.99913307"

     a12                 = "0."

     a22                 = "-0.04163050">

 </Reference_Marker>

In the following example, only two of the columns of the DC matrix have been specified, namely those corresponding to the X and Z axes.  The third column, corresponding to the Y axis, is computed using the vector cross product between the Z and X vectors.

<Reference_Marker

    id                  = "90000072"

    body_id             = "30303"

    body_type           = "RigidBody"

    pos_x               = "-130."

    pos_y               = "0."

    pos_z               = "-50."

    a00                 = "0."

    a10                 = "1."

    a20                 = "0."

    a02                 = "0.447214"

    a12                 = "0."

    a22                 = "0.89442699"

 />

In the following example, the DC matrix is omitted, implying that it is an identity matrix.  Note that pos_x, pos_y and pos_z have also been omitted, which implies that they are all zero by default.

<Reference_Marker

    id                  = "90000072"

    body_id             = "30303"

    body_type           = "RigidBody"

 />

In the following example, the Reference_Marker is specified using a Python script.

<Reference_Marker

    id                  = "30102040"

    label               = "Joint 3-Marker I"

    body_id             = "30102"

    body_type           = "RigidBody"

    usrsub_param_string = "USER(1,-0.5,0.3,0.,1.57079633,1.57079633,-1.57079633)"

    interpreter         = "Python"

    script_name         = "script/marker_read.py"

    usrsub_fnc_name     = "MARKER_READ"

 />

The script marker_read.py is defined below:
 

def MARKER_READ(id, par, npar):

    eflg = 0

    errflg = 0

    r = 3*[0.0]

    angle = 6*[0.0]

    angle_type = int(par[0])

    r[0] = par[1]

    r[1] = par[2]

    r[2] = par[3]

    if angle_type==0: # DCMTX

        angle[0] = par[4]

        angle[1] = par[5]

        angle[2] = par[6]

        angle[3] = par[7]

        angle[4] = par[8]

        angle[5] = par[9]

    elif (angle_type == 1) | (angle_type == 2): # Euler angles (313 or YPR)

        angle[0] = par[4]

        angle[1] = par[5]

        angle[2] = par[6]

    elif angle_type == 3: # Euler parameters

        angle[0] = par[4]

        angle[1] = par[5]

        angle[2] = par[6]

        angle[3] = par[7]

    else:

        errflg = 1;

        return errflg

    eflg = py_put_marker(id, r, angle_type, angle)

    return errflg

Model Element

Description

MARKER defines an orthonormal, right-handed coordinate system and reference frame in MotionSolve.  A MARKER must belong to a part.  The body can be any type: rigid, flexible, or point.  The Newtonian reference frame (Ground) is considered to be a special case of a rigid PART.

Declaration

def MARKER(id, LABEL="", PART=0, POINT_MASS=0, FLEX_BODY=0, QP=[], ZP=[], XP=[], REULER=[],FLOATING=False, RM=0, NODE=0, USEXP=False, FUNCTION="", ROUTINE="", INTERPRETER="", SCRIPT=""):

Attributes

id

Element identification number (integer>0).  This number is unique among all the MARKER elements.

LABEL

The name of the MARKER element.

PART

Specifies the ID of the part to which MARKER belongs.

POINT_MASS

Specifies the ID of the point mass to which the MARKER belongs.

FLEX_BODY

Specifies the ID of the flexible part to which the MARKER belongs.

QP

Specifies the coordinates of MARKER with respect to RM.

ZP

Specifies a point with respect to RM, denoting the direction of Z axis from QP.

XP

Specifies a point with respect to RM, denoting the direction of X axis from QP.

REULER

Specifies the Euler angles of MARKER with respect to RM.

FLOATING

Specifies whether the MARKER is a floating marker or not.  By default it is set to "FALSE".

RM

An optional attribute that specifies the Reference Marker ID.  If unspecified, the position and orientation of the MARKER is assumed to be with respect to the LPRF of the hosting body.  If specified, the position and orientation of the MARKER is assumed to be with respect to the reference marker.  For example, if you want to specify the position and orientation of the MARKER in the global reference frame, use RM=0.

NODE

Specifies the node on the flexible body to which the MARKER is associated.

USEXP

This attribute when set to TRUE uses the x-point-z-point method of orientation.  It causes the marker to be oriented such that x-axis lies on XP, and z-axis lies in the positive xz-plane(ignoring ZP), in a situation when XP and ZP are not mutually orthogonal (as they are supposed to be).

FUNCTION

The list of parameters that are passed from the data file to the user defined subroutine.  This attribute is common to all types of user subroutines and scripts.  The name of the user subroutine depends on the type of the element.

ROUTINE
 

Specifies an alternative name for the user subroutine.

When ROUTINE is specified, the position and orientation calculated in MARKER_READ and defined in py_put_marker should be with respect to the global reference frame. In other words, the position and orientation you passed to MotionSolve via py_put_marker in MARKER_READ are assumed to be defined in the global reference frame in all cases.

INTERPRETER

Specifies the interpreted language that the user script is written in.  Valid choices are MATLAB or PYTHON.

SCRIPT

Specifies the path and name of the user written script that contains the routine.

Comments

See Reference_Marker

Example

The following example defines a marker on a rigid part.

MARKER(1012,LABEL="Marker 2",PART=1000,QP=[1.414,3.142,1.618],ZP=[101.327,3.142,-2.545],XP=[1.414, 3.142, 101.618])

In the following example, both QP and ZP have been omitted, which implies that they are all zero by default.

MARKER(90000072,LABEL="Joint 3-Marker I",PART=30303)

In the following example, the Reference_Marker is specified using a Python script.

MARKER(30102040,LABEL="Marker 2",PART=30102,QP=[1.414,3.142,1.618],ZP=[101.327, 3.142, -2.545],XP=[5.577, 3.142, 101.531],FUNCTION="USER(1,-0.5,0.3,0.,1.57079633,1.57079633,-1.57079633)",ROUTINE="MARKER_READ",INTERPRETER="Python",SCRIPT="MARKER_READ.py")

The script marker_read.py is defined below:

def MARKER_READ(id, par, npar):
   eflg = 0
   errflg = 0
   r = 3*[0.0]
   angle = 6*[0.0]
   angle_type = int(par[0])
   r[0] = par[1]
   r[1] = par[2]
 
   r[2] = par[3]
   if angle_type==0: # DCMTX
       angle[0] = par[4]
       angle[1] = par[5]
       angle[2] = par[6]
       angle[3] = par[7]
       angle[4] = par[8]
       angle[5] = par[9]
   elif (angle_type == 1) | (angle_type == 2): # Euler angles (313 or YPR)
       angle[0] = par[4]
       angle[1] = par[5]
       angle[2] = par[6]
   elif angle_type == 3: # Euler parameters
       angle[0] = par[4]
       angle[1] = par[5]
       angle[2] = par[6]
       angle[3] = par[7]
   else:
       errflg = 1;
       return errflg
   eflg = py_put_marker(id, r, angle_type, angle)
   return errflg