Fixed spatial relationship between frames (2024)

Table of Contents
Description Examples Ports Frame B — Base frameframe F — Follower frame frame Parameters Rotation Method — Method to specify relative rotationNone (default) | Aligned Axes | Standard Axis | Arbitrary Axis | Rotation Sequence | Rotation Matrix | Quaternion Pair 1: Follower — Follower frame axis used to align with specified base frame axis+X (default) | -X | +Y | -Y | +Z | -Z Pair 1: Base — Base frame axis +Y (default) | +X | -X | -Y | +Z | -Z Pair 2: Follower — Follower frame axis used to align with specified base frame axis+Y | +X | -X | -Y | +Z | -Z Pair2: Base — Base frame axis +Z (default) | +X | -X | +Y | -Y | -Z Axis — Standard axis of relative rotation +Z (default) | +X | -X | +Y | -Y | -Z Angle — Angle of relative rotation 0.0 deg (default) | scalar Axis — Axis of relative rotation [0 0 1] (default) | 3-by1 vector Angle — Angle of relative rotation 0.0 deg (default) | scalar Rotation About — Frame whose axes to rotate follower frame about Follower Axes (default) | Base Axes 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 Angles — Angles for elementary rotations [0 0 0] deg (default) | 3-by-1 vector Matrix — Rotation matrix [1 0 0; 0 1 0; 0 0 1] (default) | 3-by-3 matrix Quaternion — Relative rotation using quaternion [1 0 0 0] (default) | unit quaternion vector Translation Method — Method for specifying the translationNone (default) | Cartesian | Standard Axis | Cylindrical Extended Capabilities C/C++ Code Generation Generate C and C++ code using Simulink® Coder™. Version History See Also Topics MATLAB Command Americas Europe Asia Pacific FAQs

Fixed spatial relationship between frames

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  • Fixed spatial relationship between frames (1)

Libraries:
Simscape / Multibody / Frames and Transforms

Description

The Rigid Transform block specifies and maintains a fixed spatial relationship between two frames during simulation. The spatial relationship can include a translation and a rotation.

The block has various methods to specify the position and orientation of the follower frame with respect to the base frame. For more information, see Rotation and Translation.

Examples

Creating Frames Using Rigid TransformsThe 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

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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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Rotation

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

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.

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.

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.

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 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 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 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 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.

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 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 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.

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.

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

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.

Extended Capabilities

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

Version History

Introduced in R2012a

See Also

World Frame | Variable Brick Solid | Reference Frame | Transform Sensor

Topics

  • Creating Connection Frames
  • Model a Simple Link
  • Working with Frames
  • Visualize Simscape Multibody Frames

MATLAB Command

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Fixed spatial relationship between frames (3)

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Fixed spatial relationship between frames (2024)

FAQs

What is the frame of reference in philosophy? ›

A “frame of reference” is a standard relative to which motion and rest may be measured; any set of points or objects that are at rest relative to one another enables us, in principle, to describe the relative motions of bodies.

What is the difference between inertial reference frame and non inertial reference frame? ›

A non-inertial frame of reference is one that does exhibit acceleration, which is any change in speed or direction. This is the opposite of an inertial frame of reference, in which there is no acceleration. Another difference in a non-inertial frame of reference is that the law of inertia appears to not hold.

What is the absolute frame of reference? ›

Absolute frame of reference is also a binary system in which the location of an object is defined in relation to arbitrary fixed bearings, such as cardinal directions (North, South, East, West).

What is the ideal inertial frame of reference? ›

An inertial frame of reference is a frame where Newton's law holds true. That means if no external force is acting on a body it will stay at rest or remain in uniform motion.

What are frames in philosophy? ›

A frame of reference, or point of view, refers to the way we look at a given situation. How a person views that situation can affect her understanding of the facts and influence how she determines right from wrong. Some frames minimize or even omit the ethical aspects of a decision.

What is a simple definition of a frame of reference? ›

A frame of reference is a particular set of beliefs or ideas on which you base your judgment of things.

What is the difference between inertial and fixed reference frame? ›

A fixed frame is a reference frame that is fixed. A moving frame is a reference frame that moves with the body. A moving reference frame can translate and/or rotate. When a reference frame is either fixed or moving with a constant velocity, it is an inertial frame.

Why is the earth not an inertial reference frame? ›

Earth rotating about its own axis causes an external force that results in the acceleration of the motion of objects. This indicates that the Earth is not an inertial reference frame.

Do inertial frames exist? ›

This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity.

What is the most commonly used frame of reference? ›

All measurements of motion will be compared to a frame of reference. Therefore, the most commonly used frame of reference is Earth itself, even though it moves.

What is the best example of frame of reference? ›

Example of Frames of Reference

Suppose a train is moving and a person is sitting inside the train watching a tree pass by. In this case, the train is the frame of reference and the tree appears to be moving. If we consider the opposite of it, a person on the platform will look at the tree as a stationary object.

Why is the frame of reference important? ›

Choosing a frame of reference requires deciding where the object's initial position is and which direction will be considered positive. Frame of reference are particularly important when describing an object's displacement. Displacement is the change in position of an object relative to its reference frame.

How do you know if you are in an inertial reference frame? ›

If you are in an inertial frame of reference, an accelerometer will show no reading.

Why does inertia exist? ›

Inertia is the force that holds the universe together. Literally. Without it, matter would lack the electric forces necessary to form its current arrangement. Inertia is counteracted by the heat and kinetic energy produced by moving particles.

What is an example of a spatial frame of reference in communication? ›

Abstract. In everyday communication, people effortlessly translate between spatial cognitive frames of reference. For example, a tourist guide translates from a map (“the fountain is north-west of the church”) into a cognitive frame for a tourist (“the fountain in front of the church”).

What is the frame of reference theory? ›

The theories within the learning frame of reference support the ethos that the individual's capacity to learn may promote positive change in occupational performance. This learning may be in acquisition of new knowledge and skills or insights into their behaviour.

What is a frame of reference in layman's terms? ›

noun. 1. a set of basic assumptions or standards that determines and sanctions behaviour. 2. any set of planes or curves, such as the three coordinate axes, used to locate or measure movement of a point in space.

What is theory of reference in philosophy? ›

1 The theory of reference. A theory of reference is a theory which pairs expressions with the contribution those expressions make to the determination of the truth-values of sentences in which they occur. (Though later we will see that this view of the reference of an expression must be restricted in certain ways.)

What are the principles of frame of reference? ›

One's frame of reference is the context, viewpoint, or set of presuppositions or evaluative criteria within which a person's perception and thinking seem always to occur; and which constrains selectively the course and outcome of these activities.

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