WOLFRAM SYSTEM MODELER

RelativeSensor

Measure relative kinematic quantities between two frame connectors

Diagram

Wolfram Language

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

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

-π <= angles[i] <= π

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 (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)

Inputs (2)

arrowColor

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

Type: Color

Description: Color of relative arrow from frame_a to frame_b

specularCoefficient

Default Value: world.defaultSpecularCoefficient

Type: SpecularCoefficient

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

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

Components (14)

relativePosition

Type: RelativePosition

Description: Measure relative position vector between the origins of two frame connectors

der1

Type: Der[3]

Description: Derivative of input (= analytic differentiations)

der2

Type: Der[3]

Description: Derivative of input (= analytic differentiations)

relativeAngles

Type: RelativeAngles

Description: Measure relative angles between two frame connectors

relativeAngularVelocity

Type: RelativeAngularVelocity

Description: Measure relative angular velocity between two frame connectors

der3

Type: Der[3]

Description: Derivative of input (= analytic differentiations)

zeroForce1

Type: ZeroForceAndTorque

Description: Set force and torque to zero

zeroForce2

Type: ZeroForceAndTorque

Description: Set force and torque to zero

zeroForce3

Type: ZeroForceAndTorque

Description: Set force and torque to zero

transformVector_v_rel

Type: TransformRelativeVector

Description: Transform relative vector in to another frame

transformVector_a_rel

Type: TransformRelativeVector

Description: Transform relative vector in to another frame

transformVector_z_rel

Type: TransformRelativeVector

Description: Transform relative vector in to another frame

world

Type: World

Description: World coordinate system + gravity field + default animation definition

arrow

Type: Arrow

Description: Visualizing an arrow with variable size

Used in Examples (5)

PlanarFourbar

Modelica.Mechanics.MultiBody.Examples.Loops

Planar four bars mechanism with one kinematic loop (with RevolutePlanarLoopConstraint joint)

PrismaticConstraint

Modelica.Mechanics.MultiBody.Examples.Constraints

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

RevoluteConstraint

Modelica.Mechanics.MultiBody.Examples.Constraints

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

SphericalConstraint

Modelica.Mechanics.MultiBody.Examples.Constraints

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

UniversalConstraint

Modelica.Mechanics.MultiBody.Examples.Constraints

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