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Transform Sensor

Sensor that measures the spatial relationship between two frames

Library

Frames and Transforms

Description

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.

Dialog Box and Parameters

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.

Rotation

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 (Vx, Vy, Vz) quaternion coefficients. The vector provides the coefficients in the order [S Vx Vy Vz]. Selecting 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.

Angular Velocity

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 (Vx, Vy, Vz) quaternion coefficients. The vector provides the coefficients in the order [S Vx Vy Vz]. Selecting 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.

Angular Acceleration

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 (Vx, Vy, Vz) quaternion coefficients. The vector provides the coefficients in the order [S Vx Vy Vz]. Selecting 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.

Translation

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.

Velocity

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.

Acceleration

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.

Ports

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

See Also

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