How to Convert Right-Handed to Left-Handed Coordinates and Quaternions In Unity

private Vector3 ConvertLeftHandedToRightHandedVector(Vector3 leftHandedVector)
        {
            return new Vector3(leftHandedVector.x, leftHandedVector.z, leftHandedVector.y);
        }

        private Quaternion ConvertLeftHandedToRightHandedQuaternion(Quaternion leftHandedQuaternion)
        {
            return new Quaternion(-leftHandedQuaternion.x,
                                   -leftHandedQuaternion.z,
                                   -leftHandedQuaternion.y,
                                     leftHandedQuaternion.w);
        }

Hello,

First of all thanks for the great the example!

I'm despairing about converting Quaternions to Axis-Angle.
Following situation:
I have developed a kinematized 3D model of a Universal Robot in Unity and would like to query the orientation of the Tool Center Point and transfer it to the real robot.
Unity uses a left-handed coordinate system (Y points upward, Z points to the right, and X toward the viewer) (positive rotation is clockwise).
Universal Robots uses a right-handed coordinate system (Z points up, y points to the right, and X points toward the viewer) (positive rotation is counterclockwise).

In Unity, I can query quaternions. The real robot can process Axis-angle representation. Definition of Universal Robots: "The length of the axis is the angle to be rotated in radians, and the vector itself gives the axis about which to rotate."

Therefore, I would like to convert the quaternions from Unity to Axis angle with the following formula:

qx = -qx_Unity
qy = -qz_Unity (switched)
qz = -qy_Unity (switched)
qw = qw_Unity

And then continue with:

angle = 2 * acos (qw)
x = qx / sqrt (1-qw * qw)
y = qy / sqrt (1-qw * qw)
z = qz / sqrt (1-qw * qw)

For the UR:
x_UR = x * angle
y_UR = y * angle
z_UR = z * angle

But I'm not sure if that's right. Especially when converting from left to right handed. Can I simply transfer your example?
Thanks for any help and comments!

Best regards
Niels