What are the “6 Degrees of Freedom”? 6DOF explained. (2024)

The six degrees of freedom is a common concept used in machinery, robotics, manufacturing, 3D modeling, video game design, vehicles, the human body, and many other designs.

The 6 degrees of freedom is a representation of how an object moves through 3D space by either translating linearly or rotating axially. A single degree of freedom on an object is controlled by the up/down, forward/back, left/right, pitch, roll, or yaw.

What are the “6 Degrees of Freedom”? 6DOF explained. (1)

The human head is a great example of an object that uses all of the 6degrees of freedom to move throughout 3D space. Your head can rotate in all three axes and can also move freely up/down, forward/back, and left/right.

6 Degrees of Freedom - Translation

Three of the 6 degrees of freedom are controlled through translation. Translation is an object’s movement in a 3D space in the Z axis (up and down), X axis (left and right), and Y axis (forward and back).

The linear translation degrees of freedom are controlled by defining the origin or the datum reference frame, which should all be perpendicular to one another respectively.

Note: If datums in the datum reference frame are parallel with one another, the datum reference frame will be unable to properly control the 3 linear translation degrees of freedom.

Translation does not have any effect on the rotation of a part. Theoretically, a part could be rotating in space and not have any movement or translation at all, like a spinning top.

What are the “6 Degrees of Freedom”? 6DOF explained. (2)

If an object cannot move freely about a specific axis, that means that the axis’ degree of freedom is not controlled, and it is subject to change if manipulated.

6 Degrees of Freedom - Rotation

The remaining 3 degrees of freedom are controlled through axial rotation of a part. Typically, a part’s origin is at the center of the datum reference frame, which would also be the pivot point for each of the 3 rotational degrees of freedom: U axis (pitch), V axis (roll), and W axis (Yaw).

The rotational degrees of freedom are controlled by either a level plane (which could simultaneously control two rotational degrees of freedom) or by a line (which could only control one degree of freedom that is dependent on your work plane).

Similar to the 3 linear translation degrees of freedom, the rotational degrees of freedom will be perpendicular to one another. The rotational degrees of freedom will be considered at the center axis of the linear degrees of freedom. XYZ linearly are respective to UVW rotationally.

What are the “6 Degrees of Freedom”? 6DOF explained. (3)

Controlling the Degrees of Freedom

The easiest way to understand if a degree of freedom is controlled is to look and see if that linear plane or axis can be moved. If it can, that degree of freedom is not fully constrained and is free to move upon manipulation.

When you control the 6 degrees of freedom you are essentially removing an object’s ability to translate and rotate in space. Typically, the degrees of freedom are controlled with a “three/two/one” alignment.

  • Three - The primary datum has three points of contact and will coincidentally control 3 degrees of freedom (Z origin, roll, and pitch)
  • Two - The secondary datum is two points of contact and controls one or two of the degrees of freedom (yaw and possibly X or Y origin)
  • One - The tertiary datum is a single point of contact that controls one or two degrees of freedom (X and Y origin).

What are the “6 Degrees of Freedom”? 6DOF explained. (4)

In the image above, the cube is being controlled by the bottom, front, and left planes.

  • The bottom plane controls the Z origin, the roll, and the pitch.
  • The front plane controls the yaw and the Y origin.
  • The left plane controls the X origin.

A building is a great example of an object that has all of the degrees of freedom controlled. You do not have to worry about a building moving up/down, forward/back, or left/right. You also do not have to worry about a building rolling or rotating.

If that building has an elevator in it, you can conclude that the elevator itself has 5 of the 6 degrees of freedom controlled; while 1 degree of freedom can be manipulated because the elevator is still able to freely move up/down.

What are the “6 Degrees of Freedom”? 6DOF explained. (5)

If an object can move freely on an axis, that means that the axis that it is moving on does not have that axis controlled. A train can move forward and back but cannot move up, down, left, or right.

A gyroscope is a device that is used to control 2 of the 3 rotational degrees of freedom autonomously. As the center axis (yaw) spins and creates centrifugal force, the remaining 2 rotational degrees of freedom (pitch and roll) are controlled and therefore held in place.

What are the “6 Degrees of Freedom”? 6DOF explained. (6)

When locating a cylinder there is an exception for controlling the 6 degrees of freedom. A perfect cylinder is theoretically identical, regardless of the position of the yaw. Therefore, it will be completely controlled with 5 degrees of freedom. If there are any rotationally specific features on a cylinder, such as a slot or a notch, you can use them to control the final degree of freedom.

Conclusion

The 6 degrees of freedom is a very simple concept that can also be very easy to apply, as long as you are aware of the few intricacies explained here. The six degrees of freedom are used in many industries such as robotics, modeling, CAD assemblies, and video game design. The whole world around us is using the six degrees of freedom for every moving application, whether we are aware of it or not.

If you have any questions, about the 6 degrees of freedom or any upcoming inspection or CMM programming needs, please contact us.

What are the “6 Degrees of Freedom”? 6DOF explained. (2024)

FAQs

What are the “6 Degrees of Freedom”? 6DOF explained.? ›

Specifically, the body is free to change position as forward/backward (surge), up/down (heave), left/right (sway) translation in three perpendicular axes, combined with changes in orientation through rotation about three perpendicular axes, often termed yaw (normal axis), pitch (transverse axis), and roll (longitudinal ...

What is the meaning of 6 degrees of freedom? ›

The 6 degrees of freedom is a representation of how an object moves through 3D space by either translating linearly or rotating axially. A single degree of freedom on an object is controlled by the up/down, forward/back, left/right, pitch, roll, or yaw.

What are the 6 spatial degrees of freedom? ›

6-DOF refers to the six directions in which an object can move in space. These directions are: up and down, forward and backward, left and right, up and down, left and right, and rotation.

What does 6DOF mean? ›

Six degrees of freedom, or 6DoF, is a term used to refer to the number of axes that an object can freely move within a three-dimensional space. The concept of the six degrees of freedom broadly describes an object's freedom of movement and rotation, specifically in three-dimensional spaces.

What is the 6 dof representation? ›

The 6DOF (Euler Angles) block implements the Euler angle representation of six-degrees-of-freedom equations of motion, taking into consideration the rotation of a body-fixed coordinate frame (Xb, Yb, Zb) about a flat Earth reference frame (Xe, Ye, Ze).

What is the 6DOF analysis? ›

Six degree of freedom (DOF) shock and vibration testing provides an avenue for improved mechanical qualification of a system or component. Six DOF testing allows for application of a test input that is more representative of actual operational environments.

What is the significance of 6 degrees? ›

Six degrees of separation is the idea that all people are six or fewer social connections away from each other. As a result, a chain of "friend of a friend" statements can be made to connect any two people in a maximum of six steps. It is also known as the six handshakes rule.

What is the 6 degree of freedom stage? ›

Specifically, the body is free to change position as forward/backward (surge), up/down (heave), left/right (sway) translation in three perpendicular axes, combined with changes in orientation through rotation about three perpendicular axes, often termed yaw (normal axis), pitch (transverse axis), and roll (longitudinal ...

What is degrees of freedom clearly explained? ›

Degrees of freedom are the number of independent values that a statistical analysis can estimate. You can also think of it as the number of values that are free to vary as you estimate parameters.

How many DOF does a human leg have? ›

After simplification of the leg structure to 7 DOF, one can distinguish three of them that are essential and necessary for proper performance of the basic tasks such as sitting down, getting up and walking.

How many degrees of freedom do humans have? ›

Architecture of human joints and their movement

A joint in three-dimensional space has maximum six degrees of freedom; three translation motions along the x, y, and z axis and three rotation motions around the x, y, and z axis, respectively, which one can say that degrees of freedom of a joint varies from 0 to 6 (Fig.

What is the difference between 3DoF and 6DoF? ›

In short, while 3 DOF allows you to look around, 6 DOF allows you to look around and move like in the real world, which provides a more immersive experience by allowing you to physically move within the virtual space, enabling a greater sense of presence and interaction.

Why does a rigid body have 6 degrees of freedom? ›

A rigid body has 6 configuration degrees of freedom because its most general configuration can be obtained by translating (3 degrees of freedom) and rotating (3 degrees of freedom) its initial configuration.

What is the 6DOF measurement? ›

6DOF pose perception means locating an object to position (X, Y, Z) and orientation (pitch, roll, and yaw). The test procedure for 6DOF will compare 6DOF estimates computed by a system under test to 6DOF ground truth values from a reference standard system with established accuracy.

What is 6 degrees of freedom virtual reality? ›

6-DoF means being able to track both rotational and translational motion. In addition to being able to track head movements, this means being able to detect whether the user has moved forward, backward, laterally, or vertically.

What is a 6DOF simulation? ›

A 6-DOF simulation has 6 degrees of freedom: three rotations and three translations. Since a vehicle both translates and rotates through the air, two coordinate systems keep track of the vehicle. The first is a known or fixed reference system, referred to here as a local-level coordinate system.

What is the meaning of sixth freedom? ›

Sixth Freedom – The right to carry passengers or cargo between two foreign countries via one's own country without a change of aircraft.

What does 6 degrees means? ›

Six degrees of separation is the theory that any person on the planet can be connected to any other person on the planet through a chain of acquaintances that has no more than five intermediaries.

What does 6 degrees of freedom mean in VR? ›

3 degrees of freedom (3DoF) refers to the 3 rotational axes, which allow turning left/right, looking up/down, and tilting the view. 6 degrees of freedom (6DoF) includes 3 additional translational degrees, which allow moving to the left/right, forwards/backwards, and upwards/downwards.

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