connection points

solve for P3,P5 given actuator distances.(2d)

PLOTS:

tertiary connection points

computing P3,P5 from actuator distances.

Abbreviations:

dmn - will be the distance in inches between points Pn,Pm.

Measuring the connection points in dome centerline coordinates.

On 04feb02 and 29mar02, the connection points were surveyed into
position.V1, V2, H1, H2, H3, B1, TG1, TG2, TG3, TG4, TG5. The measured
target positions with the left, right differences asymetries are shown
in the table below:

target | X position | y position | z position | XL-XR | YL+YR | ZL-ZR |

B1L | -204.0413 | 139.4230 | -385.0532 | |||

B1R | -203.6735 | -139.4130 | -384.8790 | -0.3678 | 0.0100 | -0.1742 |

V1L | -210.4762 | 138.2322 | -253.5995 | |||

V1R | -210.5884 | -139.6473 | -252.8725 | 0.1122 | -1.4151 | -0.7270 |

V2L | -209.7820 | 138.0292 | -260.7937 | |||

V2R | -209.7856 | -139.4416 | -260.0842 | 0.0036 | -1.4124 | -0.7095 |

H1L | -276.3333 | 137.1005 | -370.4733 | |||

H1R | -276.3822 | -139.0441 | -369.1217 | 0.0489 | -1.9436 | -1.3516 |

H2L | -277.6391 | 136.8182 | -378.7157 | |||

H2R | -277.8897 | -139.0551 | -377.4202 | 0.2506 | -2.2369 | -1.2955 |

H3L | -275.3072 | 137.4232 | -377.2410 | |||

H3R | -275.4639 | -139.5862 | -376.0341 | 0.1567 | -2.1630 | -1.2069 |

TG1 | -413.1730 | 0.2559 | -405.2392 | |||

TG2 | -411.9641 | -1.8014 | -408.4934 | |||

TG3 | -408.2801 | -1.6680 | -417.9370 | |||

TG4 | -407.3638 | 0.3457 | -420.3216 | |||

TG5 | -397.4426 | -1.9846 | -454.5385 |

The distances between P13, P23, and P45 can be varied via a motor to
move the tertiary in the x,z plane. The relative distance moved is measured
by an encoder attached to the motors.

The point P3 is the connection between the horizontal
and vertical actuators and is the axis of rotation for the tail gunner
motion.

Solve for P3,P5 given actuator distances. (2D)

- Measure all of the connection points for the nominal focus position using the theodolite. Record the encoder values of the motor at this position.
- Move the tertiary to another position and record the encoder positions. Knowing the encoder turns per inch, and the values measured in 1., you can compute the distances D13,D23. D12 is also known from 1.
- We know all 3 lengths of the triangle P1P2P3 so compute the included angle a (between d12,d23) using the law of cosines.
- Rotate P12 by angle a so it points along P23. Scale it to D23 and then add this vector to P2. This is P3 in dome centerline coordinate.
- To compute P5 use the same technique on triangle P3P4P5. Since we know all the lengths we can again compute the included angle b (between d34,d35). Compute P34=P3-P4 and then rotate it by angle b so it points along P45. Scale the value to d45 and then add it to P4. You now have P5 in dome centerline coordinates.
- Any other fixed point on the the tertiary say Pm can be converted to dome centerline coordinates if we know its distance from P3,P5 (which are fixed in the tertiary coordinates). Use triangle P3P5Pm with the above technique. See the figure above.

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