WOLFRAM SYSTEMMODELER

RelativeSensor

Measure relative kinematic quantities between two frame connectors

Diagram

Wolfram Language

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Click for copyable input
SystemModel["Modelica.Mechanics.MultiBody.Sensors.RelativeSensor"]
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Information

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

Relative kinematic quantities between frame_a and frame_b are determined and provided at the conditional output signal connectors. For example, if parameter "get_r_rel = true", the connector "r_rel" is enabled and contains the relative vector from frame_a to frame_b. The following quantities can be provided as output signals:

  1. Relative position vector (= r_rel)
  2. Relative velocity vector (= v_rel)
  3. Relative acceleration vector (= a_rel)
  4. Three angles to rotate frame_a into frame_b (= angles)
  5. Relative angular velocity vector (= w_rel)
  6. Relative angular acceleration vector (= z_rel)

Via parameter resolveInFrame it is defined, in which frame a vector is resolved (before differentiation):

resolveInFrame =
Types.ResolveInFrameAB.
Meaning
world Resolve vectors in world frame
frame_a Resolve vectors in frame_a
frame_b Resolve vectors in frame_b
frame_resolve Resolve vectors in frame_resolve

If resolveInFrame = Types.ResolveInFrameAB.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 a RelativeSensor component is shown. The light blue coordinate system is frame_a, the dark blue coordinate system is frame_b, and the yellow arrow is the animated sensor.

Note, derivatives of relative kinematic quantities are always performed with respect to the frame, in which the vector to be differentiated is resolved. After differentiation, it is possible via parameter resolveInFrameAfterDifferentiation (in the "Advanced" menu) to resolve the differentiated vector in another frame.

For example, if resolveInFrame = Types.ResolveInFrameAB.frame_b, then

   r_rel = resolve2(frame_b.R, frame_b.r_0 - frame_a.r0);
   v_rel = der(r_rel);

is returned (r_rel = resolve2(frame_b.R, frame_b.r_0 - frame_a.r0)), i.e., the derivative of the relative distance from frame_a to frame_b, resolved in frame_b. If resolveInFrameAfterDifferentiation = Types.ResolveInFrameAB.world, then v_rel is additionally transformed to:

   v_rel = resolve1(frame_b.R, der(r_rel))

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 frame_a into frame_b along the axes defined by parameter sequence are returned. 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}

Connectors (9)

frame_a

Type: Frame_a

Description: Coordinate system a

frame_b

Type: Frame_b

Description: Coordinate system b

frame_resolve

Type: Frame_resolve

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

r_rel

Type: RealOutput[3]

Description: Relative position vector frame_b.r_0 - frame_a.r_0 resolved in frame defined by resolveInFrame

v_rel

Type: RealOutput[3]

Description: Relative velocity vector

a_rel

Type: RealOutput[3]

Description: Relative acceleration vector

angles

Type: RealOutput[3]

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

w_rel

Type: RealOutput[3]

Description: Relative angular velocity vector

z_rel

Type: RealOutput[3]

Description: Relative angular acceleration vector

Parameters (11)

animation

Value: true

Type: Boolean

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

resolveInFrame

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

Type: ResolveInFrameAB

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

get_r_rel

Value: false

Type: Boolean

Description: = true, to measure the relative position vector from the origin of frame_a to frame_b

get_v_rel

Value: false

Type: Boolean

Description: = true, to measure the relative velocity of the origin of frame_b with respect to frame_a

get_a_rel

Value: false

Type: Boolean

Description: = true, to measure the relative acceleration of the origin of frame_b with respect to frame_a

get_w_rel

Value: false

Type: Boolean

Description: = true, to measure the relative angular velocity of frame_b with respect to frame_a

get_z_rel

Value: false

Type: Boolean

Description: = true, to measure the relative angular acceleration of frame_b with respect to frame_a

get_angles

Value: false

Type: Boolean

Description: = true, to measure the 3 rotation angles

sequence

Value: {1, 2, 3}

Type: RotationSequence

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

resolveInFrameAfterDifferentiation

Value: resolveInFrame

Type: ResolveInFrameAB

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

Components (14)

relativePosition

Type: RelativePosition

Description:

der1

Type: Der[3]

Description:

der2

Type: Der[3]

Description:

relativeAngles

Type: RelativeAngles

Description:

relativeAngularVelocity

Type: RelativeAngularVelocity

Description:

der3

Type: Der[3]

Description:

zeroForce1

Type: ZeroForceAndTorque

Description:

zeroForce2

Type: ZeroForceAndTorque

Description:

zeroForce3

Type: ZeroForceAndTorque

Description:

transformVector_v_rel

Type: TransformRelativeVector

Description:

transformVector_a_rel

Type: TransformRelativeVector

Description:

transformVector_z_rel

Type: TransformRelativeVector

Description:

world

Type: World

Description:

arrow

Type: Arrow

Description:

Used in Examples (4)

PrismaticConstraint

Body attached by one spring and two prismatic joints or constrained to environment

RevoluteConstraint

Body attached by one spring and revolute joint or constrained to environment

SphericalConstraint

Body attached by one spring and spherical joint or constrained to environment

UniversalConstraint

Body attached by one spring and universal joint or constrained to environment