Difference between revisions of "Rotation matrix"
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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. | 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 | + | A 24-step switch can be used for angle adjustment in 15° steps. These 4x24 switches are available on Aliexpress for less than 10€. Search for "4*24 Rotary Switch". |
(Picture) | (Picture) | ||
| − | The switch must be disassembled | + | The switch must be disassembled to remove the limiter, so that the axis can be rotated over the full 360° range. |
(Picture) | (Picture) | ||
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(Picture) | (Picture) | ||
| − | This is the schematic for half of the switch. It has an A | + | This is the schematic for half of the switch. It has an input A 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). | ||
Revision as of 09:30, 25 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€. Search for "4*24 Rotary Switch".
(Picture)
The switch must be disassembled to remove the limiter, 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 input A 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)
