Difference between revisions of "Rotation matrix"
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A 24-step switch can be used for angle adjustment in 15° steps. These 4x24 switches are available on Aliexpress for less than $10. | A 24-step switch can be used for angle adjustment in 15° steps. These 4x24 switches are available on Aliexpress for less than $10. | ||
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(Picture) | (Picture) | ||
The switch must be disassembled and the limiter must be removed, so that the axis can be rotated over the full 360° range. | The switch must be disassembled and the limiter must be removed, so that the axis can be rotated over the full 360° range. | ||
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(Picture) | (Picture) | ||
| − | In those planes that make the sin() and -sin() signals, the contact must be removed from the A position and inserted in position B, which is 90° from A. For the -sin() signal, the phase shift is in the other direction. | + | In those planes that make the sin() and -sin() signals, the contact must be removed from the A position and inserted in position B, which is 90° phase shifted from A. For the -sin() signal, the phase shift is in the other direction. |
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(Picture) | (Picture) | ||
For yaw, pitch and roll rotations you need three switches. | For yaw, pitch and roll rotations you need three switches. | ||
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(Picture) | (Picture) | ||
This is the schematic for half of the switch. It has an A input and two outputs A*sin(alpha) and A*cos(alpha). | This is the schematic for half of the switch. It has an A input and two outputs A*sin(alpha) and A*cos(alpha). | ||
The schematic for the other half is identical, but the contact in the switch is phase shifted in the other direction so that the outputs are -A*sin(alpha) and A*cos(alpha). | The schematic for the other half is identical, but the contact in the switch is phase shifted in the other direction so that the outputs are -A*sin(alpha) and A*cos(alpha). | ||
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(Picture) | (Picture) | ||
This is the main schematic: | This is the main schematic: | ||
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(Picture) | (Picture) | ||
Revision as of 19:40, 24 October 2021
Only two dimensions x,y can be shown on an oscilloscope screen. If you have a circuit with three outputs x,y,z you can see only two of them. But with a rotation matrix you can rotate the x,y,z space so that you can see a two-dimensional image from an arbitrary direction.
A 24-step switch can be used for angle adjustment in 15° steps. These 4x24 switches are available on Aliexpress for less than $10.
(Picture)
The switch must be disassembled and the limiter must be removed, so that the axis can be rotated over the full 360° range.
(Picture)
In those planes that make the sin() and -sin() signals, the contact must be removed from the A position and inserted in position B, which is 90° phase shifted from A. For the -sin() signal, the phase shift is in the other direction.
(Picture)
For yaw, pitch and roll rotations you need three switches.
(Picture)
This is the schematic for half of the switch. It has an A input and two outputs A*sin(alpha) and A*cos(alpha). The schematic for the other half is identical, but the contact in the switch is phase shifted in the other direction so that the outputs are -A*sin(alpha) and A*cos(alpha).
(Picture)
This is the main schematic:
(Picture)
