Measure absolute kinematic quantities of frame connector



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

Absolute kinematic quantities of frame_a are determined and provided at the conditional output signal connectors. For example, if parameter "get_r = true", the connector "r" is enabled and contains the absolute vector from the world frame to the origin of frame_a. The following quantities can be provided as output signals:

  1. Absolute position vector (= r)
  2. Absolute velocity vector (= v)
  3. Absolute acceleration vector (= a)
  4. Three angles to rotate world frame into frame_a (= angles)
  5. Absolute angular velocity vector (= w)
  6. Absolute angular acceleration vector (= z)

Via parameter resolveInFrame it is defined, in which frame a vector is resolved:

resolveInFrame =
world Resolve vectors in world frame
frame_a Resolve vectors in frame_a
frame_resolve Resolve vectors in frame_resolve

If resolveInFrame = Types.ResolveInFrameA.frame_resolve, the conditional connector "frame_resolve" is enabled and the vectors are resolved in the frame, to which frame_resolve is connected. Note, if this connector is enabled, it must be connected.

In the following figure the animation of an AbsoluteSensor component is shown. The light blue coordinate system is frame_a and the yellow arrow is the animated sensor.

Velocity, acceleration, angular velocity and angular acceleration are determined by differentiating them in the world frame and then transforming them in to the frame defined by resolveInFrame.

For example, if resolveInFrame = Types.ResolveInFrameA.frame_a, then

   v0 = der(frame_a.r0);
   v  = resolve2(frame_a.R, v0);

is returned, i.e., the derivative of the absolute distance from the world frame to the origin of frame_a, resolved in frame_a.

The cut-force and the cut-torque in frame_resolve are always zero, whether frame_resolve is connected or not.

If get_angles = true, the 3 angles to rotate the world frame into frame_a along the axes defined by parameter sequence are returned. For example, if sequence = {3,1,2} then the world frame 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_a. 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 absolute transformation matrix of frame_a may be in a singular configuration with respect to "sequence", i.e., there is an infinite number of angle values leading to the same absolute 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 (10)


Value: true

Type: Boolean

Description: = true, if animation shall be enabled (show arrow)


Value: Modelica.Mechanics.MultiBody.Types.ResolveInFrameA.frame_a

Type: ResolveInFrameA

Description: Frame in which vectors are resolved (world, frame_a, or frame_resolve)


Value: false

Type: Boolean

Description: = true, to measure the absolute position vector of the origin of frame_a


Value: false

Type: Boolean

Description: = true, to measure the absolute velocity of the origin of frame_a


Value: false

Type: Boolean

Description: = true, to measure the absolute acceleration of the origin of frame_a


Value: false

Type: Boolean

Description: = true, to measure the absolute angular velocity of frame_a


Value: false

Type: Boolean

Description: = true, to measure the absolute angular acceleration of frame_a


Value: false

Type: Boolean

Description: = true, to measure the 3 rotation angles


Value: {1, 2, 3}

Type: RotationSequence

Description: If get_angles=true: Angles are returned to rotate world frame around axes sequence[1], sequence[2] and finally sequence[3] into frame_a


Value: 0

Type: Angle (rad)

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

Inputs (3)


Default Value: world.defaultArrowDiameter

Type: Diameter (m)

Description: Diameter of absolute arrow from world frame to frame_a


Default Value: Modelica.Mechanics.MultiBody.Types.Defaults.SensorColor

Type: Color

Description: Color of absolute arrow from world frame to frame_b


Default Value: world.defaultSpecularCoefficient

Type: SpecularCoefficient

Description: Reflection of ambient light (= 0: light is completely absorbed)

Connectors (8)


Type: Frame_a

Description: Coordinate system a of which the absolute kinematic quantities are measured


Type: RealOutput[3]

Description: Absolute position vector frame_a.r_0 resolved in frame defined by resolveInFrame


Type: RealOutput[3]

Description: Absolute velocity vector


Type: RealOutput[3]

Description: Absolute acceleration vector


Type: RealOutput[3]

Description: Angles to rotate world frame into frame_a via 'sequence'


Type: RealOutput[3]

Description: Absolute angular velocity vector


Type: RealOutput[3]

Description: Absolute angular acceleration vector


Type: Frame_resolve

Description: If resolveInFrame = Types.ResolveInFrameA.frame_resolve, the output signals are resolved in this frame

Components (14)


Type: AbsolutePosition


Type: AbsoluteVelocity


Type: AbsoluteAngles


Type: AbsoluteAngularVelocity


Type: Der[3]


Type: Der[3]


Type: TransformAbsoluteVector


Type: TransformAbsoluteVector


Type: World


Type: Arrow


Type: AbsoluteVelocity


Type: AbsoluteAngularVelocity


Type: ZeroForceAndTorque


Type: ZeroForceAndTorque