# Modifying a transformation based on yaw-pitch-roll or phi-theta-psi

• amrbekhit
In summary, the conversation discusses the use of a triangular platform with markers in a 3D simulation program. The platform can translate and rotate, and there is a special marker that is always at the centroid of the platform. The goal is to constrain the orientation of this marker in a specific way using transformations, including yaw-pitch-roll and phi-theta-psi. There is some confusion about the phi-theta-psi transformation and the pictures provided are cluttered. Clarification is requested about converting between the two transformations.
amrbekhit
[I've tried asking this question on math.stackexchange.com, but haven't got any responses, so I thought I'd try here]

I’m building a model in a 3D simulation program (MSC Adams) and part of that model is a triangular platform which can translate and rotate in the virtual world, as shown in the 2 images below:

There are some markers on this platform that, when it is at its home orientation, are aligned with the global axis system (which is the orientation of markers A, B and C in the first image). These markers move and orient with the platform so that they represent the platform’s orientation with respect to the global axis system.

Now, I have a special marker (TOP_ORIGIN) that is coded so that it is always at the centroid of the corners of the triangle that form the platform (average of the coordinates A, B and C). What I’m trying to do is to also constrain the orientation of the marker as follows:

• The X-Y plane is the same as the platform’s plane with the Z axis putting “up” away from the model.
• The angle between the X axis and the vector XA is set to an angle, theta, which I calculate elsewhere.
• The software gives me two ways of getting and setting the orientation of objects: yaw-pitch-roll (rotation about Z then rotation about the new Y, then rotation about the new X) and phi-theta-psi (rotation about Z then rotation about the new X, then rotation about the new Z).

How can I apply these transformations to get the marker to the orientation I want?

The yaw-pitch-roll transformation looks fairly standard but your description of the phi-theta-psi transformation doesn't look right. Two Z rotations is unusual, and not what I would expect from "phi-theta-psi." (P.S. I can't see what axes you are talking about because the pictures are very cluttered.)

I am not sure what you are asking, amrbekhit. Do you want to convert between yaw-pitch-roll and phi-theta-psi? Can you clarify your question?

## 1. What is the difference between yaw-pitch-roll and phi-theta-psi transformations?

The main difference between these two transformations is the order in which the rotations are applied. In a yaw-pitch-roll transformation, the rotations are applied in the order of yaw (rotation around the z-axis), pitch (rotation around the y-axis), and roll (rotation around the x-axis). In a phi-theta-psi transformation, the rotations are applied in the order of phi (rotation around the x-axis), theta (rotation around the y-axis), and psi (rotation around the z-axis).

## 2. How do I modify a transformation based on yaw-pitch-roll or phi-theta-psi?

To modify a transformation based on yaw-pitch-roll or phi-theta-psi, you will need to use a rotation matrix or quaternion. These mathematical representations can be used to perform the necessary rotations in the correct order to achieve the desired transformation.

## 3. Can I use yaw-pitch-roll or phi-theta-psi to rotate an object in 3D space?

Yes, both yaw-pitch-roll and phi-theta-psi transformations can be used to rotate an object in 3D space. These transformations are commonly used in computer graphics and robotics to orient objects in a specific direction.

## 4. Are yaw-pitch-roll and phi-theta-psi interchangeable?

No, yaw-pitch-roll and phi-theta-psi are not interchangeable. The order in which the rotations are applied can greatly affect the resulting transformation. It is important to use the correct transformation for the desired outcome.

## 5. Can I combine yaw-pitch-roll and phi-theta-psi transformations?

Yes, it is possible to combine these transformations, but it is important to use the correct order of rotations. For example, if you want to combine a yaw-pitch-roll transformation with a phi-theta-psi transformation, the yaw-pitch-roll rotation should be applied first, followed by the phi-theta-psi rotation.

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