Modelica.Mechanics.MultiBody.Sensors

Sensors to measure variables

Information

Package Sensors contains ideal measurement components to determine absolute and relative kinematic quantities, as well as cut-forces, cut-torques and power. All measured quantities can be provided in every desired coordinate system.

Extends from Modelica.Icons.SensorsPackage (Icon for packages containing sensors).

Package Content

Name	Description
AbsoluteSensor	Measure absolute kinematic quantities of frame connector
RelativeSensor	Measure relative kinematic quantities between two frame connectors
AbsolutePosition	Measure absolute position vector of the origin of a frame connector
AbsoluteVelocity	Measure absolute velocity vector of origin of frame connector
AbsoluteAngles	Measure absolute angles between frame connector and the world frame
AbsoluteAngularVelocity	Measure absolute angular velocity of frame connector
RelativePosition	Measure relative position vector between the origins of two frame connectors
RelativeVelocity	Measure relative velocity vector between the origins of two frame connectors
RelativeAngles	Measure relative angles between two frame connectors
RelativeAngularVelocity	Measure relative angular velocity between two frame connectors
Distance	Measure the distance between the origins of two frame connectors
CutForce	Measure cut force vector
CutTorque	Measure cut torque vector
CutForceAndTorque	Measure cut force and cut torque vector
Power	Measure power flowing from frame_a to frame_b
TransformAbsoluteVector	Transform absolute vector in to another frame
TransformRelativeVector	Transform relative vector in to another frame
Internal	Internal package, should not be used by user

Modelica.Mechanics.MultiBody.Sensors.AbsoluteSensor

Measure absolute kinematic quantities of frame connector

Information

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:

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

-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 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}

Extends from Modelica.Mechanics.MultiBody.Sensors.Internal.PartialAbsoluteSensor (Base class for absolute sensor models).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.RelativeSensor

Measure relative kinematic quantities between two frame connectors

Information

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):

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}

Extends from Modelica.Mechanics.MultiBody.Sensors.Internal.PartialRelativeSensor (Base class for relative sensor models).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.AbsolutePosition

Measure absolute position vector of the origin of a frame connector

Information

The absolute position vector of the origin of frame_a is determined and provided at the output signal connector r.

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

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

Example

If resolveInFrame = Types.ResolveInFrameA.frame_a, the output vector is computed as:

r = MultiBody.Frames.resolve2(frame_a.R, frame_b.r_0);

Extends from Internal.PartialAbsoluteSensor (Base class for absolute sensor models).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.AbsoluteVelocity

Measure absolute velocity vector of origin of frame connector

Information

The absolute velocity vector of the origin of frame_a is determined and provided at the output signal connector v.

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

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

Example

If resolveInFrame = Types.ResolveInFrameA.frame_a, the output vector is computed as:

v0 = der(frame_a.r_0);
v  = MultiBody.Frames.resolve2(frame_a.R, v0);

Extends from Internal.PartialAbsoluteSensor (Base class for absolute sensor models).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.AbsoluteAngles

Measure absolute angles between frame connector and the world frame

Information

This model determines the 3 angles to rotate the world frame into frame_a along the axes defined by parameter sequence. 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

-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 transformation matrix between the world frame and 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 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}

Extends from Internal.PartialAbsoluteSensor (Base class for absolute sensor models).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.AbsoluteAngularVelocity

Measure absolute angular velocity of frame connector

Information

The absolute angular velocity of frame_a with respect to the world frame is determined and provided at the output signal connector w.

Via parameter resolveInFrame it is defined, in which frame the angular velocity is resolved:

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

Example

If resolveInFrame = Types.ResolveInFrameA.frame_a, the output vector is computed as:

w = MultiBody.Frames.angularVelocity2(frame_a.R);

Extends from Internal.PartialAbsoluteSensor (Base class for absolute sensor models).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.RelativePosition

Measure relative position vector between the origins of two frame connectors

Information

The relative position vector between the origins of frame_a and frame_b are determined and provided at the output signal connector r_rel.

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

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

Example

If resolveInFrame = Types.ResolveInFrameAB.frame_a, the output vector is computed as:

r_rel = MultiBody.Frames.resolve2(frame_a.R, frame_b.r_0 - frame_a.r_0);

Extends from Internal.PartialRelativeSensor (Base class for relative sensor models).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.RelativeVelocity

Measure relative velocity vector between the origins of two frame connectors

Information

The relative velocity vector between the origins of frame_a and of frame_b are determined and provided at the output signal connector v_rel. This vector is defined as:

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

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

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

Example

If resolveInFrame = Types.ResolveInFrameAB.frame_b, the output vector is computed as:

r_rel   = MultiBody.Frames.resolve2(frame_a.R, frame_b.r_0 - frame_a.r_0);
v_rel_a = der(r_rel);
v_rel   = MultiBody.Frames.resolveRelative(frame_a.R, frame_b.R, v_rel_a);

Extends from Internal.PartialRelativeSensor (Base class for relative sensor models).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.RelativeAngles

Measure relative angles between two frame connectors

Information

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

-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}

Extends from Internal.PartialRelativeSensor (Base class for relative sensor models), Modelica.Icons.RoundSensor (Icon representing a round measurement device).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.RelativeAngularVelocity

Measure relative angular velocity between two frame connectors

Information

The relative angular velocity between frame_a and frame_b is determined and provided at the output signal connector w_rel.

Via parameter resolveInFrame it is defined, in which frame the angular velocity is resolved:

In this basic sensor model, the connector frame_resolve is always enabled. If resolveInFrame = Types.ResolveInFrameAB.frame_resolve, the vector w_rel is resolved in the frame to which frame_resolve is connected.

Example

If resolveInFrame = Types.ResolveInFrameAB.frame_a, the output vector is computed as:

// Relative orientation object from frame_a to frame_b
R_rel = MultiBody.Frames.relativeRotation(frame_a.R, frame_b.R);

// Angular velocity resolved in frame_a
w_rel = MultiBody.Frames.angularVelocity1(R_rel);

Extends from Internal.PartialRelativeSensor (Base class for relative sensor models).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.Distance

Measure the distance between the origins of two frame connectors

Information

The distance between the origins of frame_a and of frame_b are determined and provided at the output signal connector distance. This distance is always positive. Derivatives of this signal can be easily obtained by connecting the block Modelica.Blocks.Continuous.Der to "distance" (this block performs analytic differentiation of the input signal using the der(…) operator).

In the following figure the animation of a Distance sensor 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.

If the distance is smaller as parameter s_small (in the "advanced" menu), it is approximated such that its derivative is finite for zero distance. Without such an approximation, the derivative would be infinite and a division by zero would occur. The approximation is performed in the following way: If distance > s_small, it is computed as sqrt(r*r) where r is the position vector from the origin of frame_a to the origin of frame_b. If the distance becomes smaller as s_small, the "sqrt()" function is approximated by a second order polynomial, such that the function value and its first derivative are identical for sqrt() and the polynomial at s_small. Furthermore, the polynomial passes through zero. The effect is, that the distance function is continuous and differentiable everywhere. The derivative at zero distance is 3/(2*s_small).

Extends from Interfaces.PartialTwoFrames (Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected), Modelica.Icons.RectangularSensor (Icon representing a linear measurement device).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.CutForce

Measure cut force vector

Information

The cut-force acting between the two frames to which this model is connected, is determined and provided at the output signal connector force (= frame_a.f). If parameter positiveSign = false, the negative cut-force is provided (= frame_b.f).

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

If resolveInFrame = Types.ResolveInFrameAB.frame_resolve, the conditional connector "frame_resolve" is enabled and output force is 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 CutForce sensor is shown. The dark blue coordinate system is frame_b, and the green arrow is the cut force acting at frame_b and with negative sign at frame_a.

Extends from Modelica.Mechanics.MultiBody.Sensors.Internal.PartialCutForceSensor (Base class to measure cut force and/or torque between two frames, defined by components).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.CutTorque

Measure cut torque vector

Information

The cut-torque acting between the two frames to which this model is connected, is determined and provided at the output signal connector torque (= frame_a.t). If parameter positiveSign = false, the negative cut-torque is provided (= frame_b.t).

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

If resolveInFrame = Types.ResolveInFrameAB.frame_resolve, the conditional connector "frame_resolve" is enabled and output torque is 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 CutTorque sensor is shown. The dark blue coordinate system is frame_b, and the green arrow is the cut torque acting at frame_b and with negative sign at frame_a.

Extends from Modelica.Mechanics.MultiBody.Sensors.Internal.PartialCutForceSensor (Base class to measure cut force and/or torque between two frames, defined by components).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.CutForceAndTorque

Measure cut force and cut torque vector

Information

The cut-force and cut-torque acting between the two frames to which this model is connected, are determined and provided at the output signal connectors force (= frame_a.f) and torque (= frame_a.t). If parameter positiveSign = false, the negative cut-force and cut-torque is provided (= frame_b.f, frame_b.t).

Via parameter resolveInFrame it is defined, in which frame the two vectors are resolved:

If resolveInFrame = Types.ResolveInFrameAB.frame_resolve, the conditional connector "frame_resolve" is enabled and the output vectors force and torque 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 CutForceAndTorque sensor is shown. The dark blue coordinate system is frame_b, and the green arrows are the cut force and the cut torque, respectively, acting at frame_b and with negative sign at frame_a.

Extends from Modelica.Mechanics.MultiBody.Sensors.Internal.PartialCutForceSensor (Base class to measure cut force and/or torque between two frames, defined by components).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.Power

Measure power flowing from frame_a to frame_b

Information

This component provides the power flowing from frame_a to frame_b as output signal power.

Extends from Modelica.Icons.RoundSensor (Icon representing a round measurement device), Modelica.Mechanics.MultiBody.Interfaces.PartialTwoFrames (Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected).

Connectors

Modelica.Mechanics.MultiBody.Sensors.TransformAbsoluteVector

Transform absolute vector in to another frame

Information

The input vector "Real r_in[3]" is assumed to be an absolute kinematic quantity of frame_a that is defined to be resolved in the frame defined with parameter "frame_r_in". This model resolves vector r_in in the coordinate system defined with parameter "frame_r_out" and returns the transformed output vector as "Real r_out[3]";

Extends from Modelica.Icons.RoundSensor (Icon representing a round measurement device).

Parameters

Connectors

Modelica.Mechanics.MultiBody.Sensors.TransformRelativeVector

Transform relative vector in to another frame

Information

The input vector "Real r_in[3]" is assumed to be a relative kinematic quantity between frame_a and frame_b that is defined to be resolved in the frame defined with parameter "frame_r_in". This model resolves vector r_in in the coordinate system defined with parameter "frame_r_out" and returns the transformed output vector as "Real r_out[3]";

Extends from Internal.PartialRelativeSensor (Base class for relative sensor models).

Parameters

Connectors