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Rigid Transform

Fixed spatial relationship between frames

• Library:
• 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.

Ports

Frame

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Frame with respect to which you specify the transforms.

Frame to which you apply the transforms.

Parameters

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

MethodDescription
`None`Constrain the base and follower frames to share the same orientation.
`Aligned Axes`Set frame rotation by aligning two follower frame axes with two base frame axes.
`Standard Axis`Specify frame rotation as an angle about a standard axis (x, y, or z).
`Arbitrary Axis`Specify frame rotation as an angle about a general [x, y, z] axis.
`Rotation Sequence`Specify frame rotation as a sequence of three elementary rotations.
`Rotation Matrix`Specify frame rotation as a right-handed orthogonal rotation matrix.

`Aligned Axes`

Select two pairs of base-follower frame axes.

ParameterDescription
Pair 1First pair of base-follower frame axes to align.
Pair 2Second pair of base-follower frame axes to align. Axis choices depend on Pair 1 axis selections.
`Standard Axis`

Select a standard rotation axis, resolved in the base frame, and specify the follower frame rotation angle.

ParameterDescription
AxisStandard rotation axis (X, Y, or Z) resolved in the base frame.
AngleFollower frame rotation angle about the rotation axis with respect to the base frame.
`Arbitrary Axis`

Select a general 3-D rotation axis, resolved in the base frame, and specify the follower frame rotation angle.

ParameterDescription
AxisGeneral rotation axis [X Y Z] resolved in the base frame.
AngleFollower frame rotation angle about the rotation axis with respect to the base frame.
`Rotation Sequence`

Specify a sequence of three elementary rotations about the selected permutation of x, y, and z axes. These rotation sequences are also known as Euler and Tait-Bryan sequences. The rotations are those of the follower frame relative to the frame selected in the Rotate About parameter.

If you set the Rotate About parameter to `Follower Frame`, the follower frame rotates about its own axes. These axes change orientation with each successive rotation. If you set the Rotate About parameter to `Base Frame`, the follower frame rotates about the fixed base frame axes.

ParameterDescription
Rotation AboutFrame whose axes to rotate the follower frame about.
SequenceSequence of axes about which to apply the elementary rotations.
AnglesThree-element vector with elementary rotation angles about the axes specified in the Sequence parameter.
`Rotation Matrix`

Specify the 3×3 transformation matrix of a proper rotation between the base and follower frames. The matrix must be orthogonal and have determinant +1. The default matrix is `[1 0 0; 0 1 0; 0 0 1]`.

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

MethodDescription
`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.

ParameterDescription
AxisAxis the follower frame translates along
OffsetTranslation 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.

ParameterDescription
RadiusDistance between the origin of the follower frame and the Z axis of the base frame. This is the cylindrical radius coordinate.
ThetaRotation 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 OffsetDistance between base and follower frame origins along the base frame Z axis. This is the cylindrical length coordinate.

Extended Capabilities

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

Introduced in R2012a

Simscape Multibody Documentation

Modeling Flexible Bodies with Simscape Multibody Software

Download technical paper