Rigid Transform

Time-invariant rotation and translation transforms between two frames

Library

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.

Dialog Box and Parameters

Rotation:Method

Select the method to use to specify rotation. The default is None.

MethodDescription
NoneApply no rotation between the base and follower frames. The two frames share the same orientation throughout simulation.
Aligned AxesAlign two follower-frame axes with two base-frame axes.
Standard AxisRotate the follower frame with respect to the base frame about one of the base-frame axes—i.e., ±X, ±Y, or ±Z.
Arbitrary AxisRotate the follower frame with respect to the base frame about a general axis [X, Y, Z] resolved in the base frame.
Rotation MatrixRotate the follower frame with respect to the base frame according to a 3×3 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 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 value is [1 0 0; 0 1 0; 0 0 1].

Translation: Method

Select the method to use to specify translation. The default is None.

MethodDescription
NoneMake base and follower frames coincident. This method requires no parameters.
CartesianSpecify a 3-D translation in terms of Cartesian coordinates
Standard AxisSpecify a 1-D translation along the X, Y, or Z axis
CylindricalSpecify 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.

Ports

Frame ports B and F represent the base and follower frames.

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