Sensor that measures the spatial relationship between two frames

Frames and Transforms

This block represents a sensor that measures the spatial relationship between two frames. Parameters that this sensor measures include rotational and translational position, velocity, and acceleration. The sensor can measure these parameters between any two frames in a model. This block provides the broadest motion sensing capability in SimMechanics™.

Each measurement provides the value of a parameter for the follower
frame with respect to the base frame, resolved in the **Measurement
Frame** that you choose. Measurement frames include World
as well as rotating and non-rotating base and follower frames.

To output a parameter, the block provides a set of optional
physical signal ports. Ports remain hidden until you select the corresponding
parameters in the dialog box. Each port outputs a parameter as a time-varying
physical signal. By default, measurements are in SI units. If connecting
to Simulink^{®} blocks, you can use the PS-Simulink
Converter block to select a different physical unit.

The dialog box contains a **Properties** area
with expandable angular and linear measurement sections:

**Measurement Frame**Select a frame in which to resolve the selected spatial measurements. The choice of measurement frame affects the expression of a vector quantity in terms of its X, Y, and Z components. Some quantities, such as

**Angle**, are not affected by the choice of measurement frame. For more information, see Measurement Frames. The default is`World`

.

Select the rotation parameters to sense. These parameters encode the rotation operation required to bring the base frame into coincidence with the follower frame. Rotation observes the right-hand rule: with the rotation axis pointing out of the screen, counterclockwise motion defines positive rotation, while clockwise motion defines negative rotation.

Non-vector quantities require no measurement frame for resolution;
these quantities are unaffected by measurement frame choice. Vector
quantities, such as **Axis**, are *always* resolved
in either base or follower measurement frames; the `World`

measurement
frame does not apply.

**Angle**3–D rotation angle of the follower frame with respect to the base frame. Selecting

**Angle**exposes physical signal port**q**.**Axis**Vector components of the normalized rotation axis. The output is a three-element vector with the X, Y, and Z axis components resolved in the measurement frame. Selecting

**Axis**exposes physical signal port**axs**.**Quaternion**Unit quaternion that describes the pure rotation of the follower frame with respect to the base frame. The output is a four-element vector with the scalar (

*S*) and vector (*V*,_{x}*V*,_{y}*V*) quaternion coefficients. The vector provides the coefficients in the order [_{z}*S**V*_{x}*V*_{y}*V*]. Selecting_{z}**Quaternion**exposes physical signal port**Q**.**Transform**Transform matrix that describes the pure rotation of the follower frame with respect to the base frame. The output is a nine-element, 3×3 matrix. Selecting

**Transform**exposes physical signal port**R**.

Select the angular velocity parameters to sense. The parameters encode the angular velocity of the follower frame with respect to the base frame, resolved in the measurement frame. Rotation observes the right-hand rule: with the rotation axis pointing out of the screen, counterclockwise motion defines positive rotation, while clockwise motion defines negative rotation.

**Omega X/Omega Y/Omega Z**Relative angular velocities about the X, Y, and Z axes of the base frame. Selecting

**Omega X**,**Omega Y**, and**Omega Z**exposes physical signal ports**wx**,**wy**, and**wz**.**Quaternion**Unit quaternion that describes the angular velocity of the follower frame with respect to the base frame. The output is a four-element vector with the scalar (

*S*) and vector (*V*,_{x}*V*,_{y}*V*) quaternion coefficients. The vector provides the coefficients in the order [_{z}*S**V*_{x}*V*_{y}*V*]. Selecting_{z}**Quaternion**exposes physical signal port**Qd**.**Transform**Transform matrix that describes the angular velocity of the follower frame with respect to the base frame. The output is a nine-element, 3×3 matrix. Selecting

**Transform**exposes physical signal port**Rd**.

Select the angular acceleration parameters to sense. The parameters encode the angular acceleration of the follower frame with respect to the base frame, resolved in the measurement frame. Rotation observes the right-hand rule: with the rotation axis pointing out of the screen, counterclockwise motion defines positive rotation, while clockwise motion defines negative rotation.

**Alpha X/Alpha Y/Alpha Z**Relative angular accelerations about the X, Y, and Z axes of the base frame. Selecting

**Alpha X**,**Alpha Y**, and**Alpha Z**exposes physical signal ports**bx**,**by**, and**bz**.**Quaternion**Unit quaternion that describes the angular acceleration of the follower frame with respect to the base frame. The output is a four-element vector with the scalar (

*S*) and vector (*V*,_{x}*V*,_{y}*V*) quaternion coefficients. The vector provides the coefficients in the order [_{z}*S**V*_{x}*V*_{y}*V*]. Selecting_{z}**Quaternion**exposes physical signal port**Qdd**.**Transform**Transform matrix that describes the angular acceleration of the follower frame with respect to the base frame. The output is a nine-element, 3×3 matrix. Selecting

**Transform**exposes physical signal port**Rdd**.

Select the translation parameters to sense. The parameters encode the translation of the follower frame with respect to the base frame, resolved in the measurement frame.

**X/Y/Z**Offset vector from the base frame origin to the follower frame origin along the X, Y, and Z axes. Selecting

**X**,**Y**, and**Z**exposes physical signal ports**x**,**y**, and**z**.**Radius**Standard radius coordinate found in cylindrical coordinate systems. This radius is the shortest distance from the base frame Z axis to the follower frame origin. The value of the radius is always greater than or equal to zero. Selecting

**Radius**exposes physical signal port**rad**.The figure shows the cylindrical translation parameters

**Z**,**Radius**, and**Azimuth**.**Azimuth**Standard azimuth coordinate found in cylindrical and spherical coordinate systems. The azimuth is the angle from the base frame +X axis to the projection of the ray connecting base to follower frame origins onto the base frame XY plane. The angle measurement observes the right-hand rule. The azimuth falls in the range [-180°, +180°]. If base and follower frame origins coincide with each other, the azimuth is undefined. Selecting

**Azimuth**exposes sensing port**azm**.**Distance**Standard radius found in spherical coordinate systems. This is the distance from the origin of the base frame to the origin of the follower frame. This distance is always equal to or greater than zero. Selecting

**Distance**exposes sensing port**dst**.The figure shows the spherical translation parameters

**Azimuth**,**Distance**, and**Inclination**.**Inclination**Standard inclination found in spherical coordinate systems. The inclination is the angle of the ray connecting base to follower frame origins with respect to the projection of this ray onto the base frame XY plane. The angle measurement observes the right-hand rule. The inclination falls in the range [-90°, +90°]. If base and follower frame origins coincide with each other, the inclination is undefined. Selecting

**Inclination**exposes sensing port**inc**.

Select the linear velocity parameters to sense. The parameters encode the linear velocity of the follower frame with respect to the base frame, resolved in the measurement frame. Differentiation of a translation parameter occurs in measurement coordinates, after that parameter is resolved in the chosen measurement frame.

**X/Y/Z**Relative linear velocities along the X, Y, and Z axes. Selecting

**X**,**Y**, and**Z**exposes physical signal ports**vx**,**vy**, and**vz**.**Radius**Time rate of change of the

**Radius**coordinate defined under**Translation**. Selecting**Radius**exposes physical signal port**vrad**.**Azimuth**Time rate of change of the

**Azimuth**coordinate defined under**Translation**. Selecting**Azimuth**exposes physical signal port**vazm**.**Distance**Time rate of change of the

**Distance**coordinate defined under**Translation**. Selecting**Distance**exposes physical signal port**vdst**.**Inclination**Time rate of change of the

**Inclination**coordinate defined under**Translation**. Selecting**Inclination**exposes physical signal port**vinc**.

Select the linear acceleration parameters to sense. The parameters encode the linear acceleration of the follower frame with respect to the base frame, resolved in the measurement frame. Differentiation of a translation parameter occurs in measurement coordinates, after that parameter is resolved in the chosen measurement frame.

**X/Y/Z**Relative linear accelerations along the X, Y, and Z axes. Selecting

**X**,**Y**, and**Z**exposes physical signal ports**ax**,**ay**, and**az**.**Radius**Second time-derivative of the

**Radius**coordinate defined under**Translation**. Selecting**Radius**exposes physical signal port**arad**.**Azimuth**Second time-derivative of the

**Azimuth**coordinate defined under**Translation**. Selecting**Azimuth**exposes physical signal port**aazm**.**Distance**Second time-derivative of the

**Distance**coordinate defined under**Translation**. Selecting**Distance**exposes physical signal port**adst**.**Inclination**Second time-derivative of the

**Inclination**coordinate defined under**Translation**. Selecting**Inclination**exposes physical signal port**ainc**.

The block contains frame ports B and F, representing base and follower frames, respectively.

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