WOLFRAM SYSTEMMODELER

RelativeAngles

Measure relative angles between two frame connectors

Wolfram Language

In[1]:=
SystemModel["Modelica.Mechanics.MultiBody.Sensors.RelativeAngles"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

This model determines the 3 angles to rotate frame_a into frame_b along the axes defined by parameter sequence. For example, if sequence = {3,1,2} then frame_a is rotated around angles[1] along the z-axis, afterwards it is rotated around angles[2] along the x-axis, and finally it is rotated around angles[3] along the y-axis and is then identical to frame_b. The 3 angles are returned in the range

    -p <= angles[i] <= p

There are two solutions for "angles[1]" in this range. Via parameter guessAngle1 (default = 0) the returned solution is selected such that |angles[1] - guessAngle1| is minimal. The relative transformation matrix between frame_a and frame_b may be in a singular configuration with respect to "sequence", i.e., there is an infinite number of angle values leading to the same relative transformation matrix. In this case, the returned solution is selected by setting angles[1] = guessAngle1. Then angles[2] and angles[3] can be uniquely determined in the above range.

The parameter sequence has the restriction that only values 1,2,3 can be used and that sequence[1] ≠ sequence[2] and sequence[2] ≠ sequence[3]. Often used values are:

  sequence = {1,2,3}  // Cardan or Tait-Bryan angle sequence
           = {3,1,3}  // Euler angle sequence
           = {3,2,1}

Parameters (2)

sequence

Value: {1, 2, 3}

Type: RotationSequence

Description: Angles are returned to rotate frame_a around axes sequence[1], sequence[2] and finally sequence[3] into frame_b

guessAngle1

Value: 0

Type: Angle (rad)

Description: Select angles[1] such that abs(angles[1] - guessAngle1) is a minimum

Connectors (3)

frame_a

Type: Frame_a

Description: Coordinate system a

frame_b

Type: Frame_b

Description: Coordinate system b

angles

Type: RealOutput[3]

Description: Angles to rotate frame_a into frame_b via 'sequence'

Components (1)

R_rel

Type: Orientation

Description: Relative orientation object from frame_a to frame_b

Used in Components (1)

RelativeSensor

Modelica.Mechanics.MultiBody.Sensors

Measure relative kinematic quantities between two frame connectors