Rigid Transform

Fixed spatial relationship between frames

• 

Libraries:
Simscape / Multibody / Frames and Transforms

Description

This block applies a time-invariant transformation between two frames. The transformation rotates and translates the follower port frame (F) with respect to the base port frame (B). Connecting the frame ports in reverse causes the transformation itself to reverse. The frames remain fixed with respect to each other during simulation, moving only as a single unit. Combine Rigid Transform and Solid blocks to model compound rigid bodies.

Examples

Creating Frames Using Rigid Transforms

The correspondence of coordinate frames to connection lines and frame ports. It highlights the Rigid Transform block as the fundamental method to rigidly relate nonidentical frames. The network reference frame is the world frame, located at the center of the bottom face of the cube. The other frames are the frames at the eight vertices of the cube, one at the center of the top face, and two on the upper curved section.

Open Model

Ports

Frame

B — Base frame

frame

Frame with respect to which you specify the transforms.

F — Follower frame

frame

Frame to which you apply the transforms.

Parameters

Rotation

Method — Method to specify rotation transform

None (default) | Aligned Axes | Standard Axis | Arbitrary Axis | Rotation Sequence | Rotation Matrix | Quaternion

Method to use to specify the rotation transform between the base and follower frames. Set the parameter to None to constrain the base and follower frames to the same orientation.

Pair 1: Follower — Follower frame axis used to align with specified base frame axis

+X (default) | -X | +Y | -Y | +Z | -Z

Follower frame axis used to align with the base frame axis set by the Pair 1: Base parameter, specified as an orthogonal axis of the follower frame. The follower frame rotates with respect to the base frame to enable the alignment between the selected axes of the base and follower frames.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Aligned Axis.

Pair 1: Base — Base frame axis

+Y (default) | +X | -X | -Y | +Z | -Z

Base frame axis to align with the follower frame specified by the Pair 1: Follower, specified as an orthogonal axis of the base frame.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Aligned Axis.

Pair 2: Follower — Follower frame axis used to align with specified base frame axis

+Y | +X | -X | -Y | +Z | -Z

Base frame axis to align with the follower frame specified by the Pair 2: Follower, specified as an orthogonal axis of the follower frame. The follower frame rotates with respect to the base frame to enable the alignment between the selected axes of the base and follower frames.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Aligned Axis.

Pair2: Base — Base frame axis

+Z (default) | +X | -X | +Y | -Y | -Z

Base frame axis used to let the follower frame axis set in the Pair2: Follower parameter to align with, specified as an orthogonal axis of the base frame. The axis choices for Pair 2 depend on the Pair 1 axis selections.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Aligned Axis.

Axis — Standard axis of relative rotation

+Z (default) | +X | -X | +Y | -Y | -Z

Axis of the relative rotation, specified as an orthogonal axis of the base frame.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Standard Axis.

Angle — Angle of relative rotation

0.0 deg (default) | scalar

Angle of the relative rotation, specified as a scalar. The angle indicates the rotation of the follower frame with respect to the base frame about the specified axis.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Standard Axis.

Axis — Axis of relative rotation

[0 0 1] (default) | 3-by1 vector

Axis of the relative rotation, specified as a 3-by-1 unit vector. The vector is dimensionless and indicates the rotational axis resolved in the base frame.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Arbitrary Axis.

Angle — Angle of relative rotation

0.0 deg (default) | scalar

Angle of the relative rotation, specified as a scalar. The angle indicates the rotation of the follower frame with respect to the base frame about the axis specified by the Axis parameter.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Arbitrary Axis.

Rotation About — Frame whose axes to rotate follower frame about

Follower Axes (default) | Base Axes

Frame whose axes to rotate the follower frame about, specified as Follower Axes or Base Axes. If you set the parameter to Follower Axes, the follower frame rotates about its own axes, and the follower frame changes the orientation with each successive rotation. If you set the parameter to Base Axes, the follower frame rotates about the fixed base frame axes. See Rotational Measurements for more information.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Rotation Sequence.

Sequence — Sequence of rotation axis

X-Y-X (default) | X-Y-Z | X-Z-X | X-Z-Y | Y-X-Y | Y-X-Z | Y-Z-X | Y-Z-Y | Z-X-Y | Z-X-Z | Z-Y-X | Z-Y-Z

Sequence of the rotation axis for three successive elementary rotations. See Rotation Sequence Measurements for more information.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Rotation Sequence.

Angles — Angles for elementary rotations

[0 0 0] deg (default) | 3-by-1 vector

Angles for elementary rotations, specified as a 3-by-1 vector. See Rotation Sequence Measurements for more information.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Rotation Sequence.

Matrix — Rotation matrix

[1 0 0; 0 1 0; 0 0 1] (default) | 3-by-3 matrix

Relative rotation, specified as a 3-by-3 matrix. The matrix must be orthogonal and have determinant 1. See Rotational Measurements for more information.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Rotation Matrix.

Quaternion — Relative rotation using quaternion

[1 0 0 0] (default) | unit quaternion vector

Relative rotation, specified as a vector in quaternion parameterization. See Rotational Measurements for more information about the quaternion.

Dependencies

To enable this parameter, under Rotation, set Method parameter to Quaternion.

Translation

Method — Method for specifying the translation transform

None (default) | Cartesian | Standard Axis | Cylindrical

Method to use to specify the translation transform between the base and follower frames. The table summarizes the available options.

Method	Description
None	Make base and follower frames coincident. This method requires no parameters.
Cartesian	Specify a 3-D translation in terms of Cartesian coordinates
Standard Axis	Specify a 1-D translation along the X, Y, or Z axis
Cylindrical	Specify a 3-D translation in terms of cylindrical coordinates

Cartesian Axis

Specify the Offset of the follower frame with respect to the base frame. This is the 3-D translation vector that brings the base frame into coincidence with the follower frame. Select or enter a physical unit.

Standard Axis

Specify the offset of the follower frame with respect to the base frame along the base frame X, Y, or Z axis. Select or enter a physical unit.

Parameter	Description
Axis	Axis the follower frame translates along
Offset	Translation of the follower frame with respect to the base frame along the specified axis

Cylindrical

Specify in cylindrical coordinates the translation that brings the base frame into coincidence with the follower frame. Select or enter a physical unit.

Parameter	Description
Radius	Distance between the origin of the follower frame and the Z axis of the base frame. This is the cylindrical radius coordinate.
Theta	Rotation angle of the line connecting base and follower frame origins with respect to the base frame X axis. This is the cylindrical azimuth coordinate.
Z Offset	Distance between base and follower frame origins along the base frame Z axis. This is the cylindrical length coordinate.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2012a