Focusing with the tertiary

19mar02

SECTIONS:
connection points
solve for P3,P5 given actuator distances.(2d)
PLOTS:
tertiary connection points
computing P3,P5 from actuator distances.

Introduction.

    The tertiary can be used to focus the telescope. It is mounted with two vertical actuators, two horizontal actuators, and a tail gunner (for rotations). It is constrained in the Y direction (toward the stairwell) by two rubbing blocks. The dome centerline coordinate system uses Z vertical, X along the azimuth arm, and Y toward the stairwell. The focus coordinate system is a rotation about the Y axis of about 18 degrees so the tertiary points back towards the secondary. To focus the tertiary we change the actuator distances. This change in distance must be mapped into motion in the focus coordinates. The sections below describe the  connection points, how to compute the position of the moveable connection points given the distance, and the inverse of  how to compute the actuator distances given the requested motion in the focus coordinate system.
Abbreviations:
  • CP - connection point for actuator or tertiary.
  • DC  -  dome centerline coordinates (X along the azimuth arm, Z vertical, Y toward the stairwell).
  • LB1 - Lynn baker measurement with theodolite circa 1992
  • LB2 - Lynn baker measurement with theodolite 04feb02,29mar02
  • P1..P5,R - connection points (see tertiary connection points diagram).

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

    Measuring the connection points in dome centerline coordinates.

        To go from actuator distances to focus coordinates, you need to know the connection points of the tertiary in dome center line coordinates for a known value of the actuators. Targets were placed close to the connection points when the tertiary was in the standard focus positinon. The connection points are shown in tertiary connection points while the target locations and measured offsets are shown in connection point target locations.

      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:
     
    Measured target positions in dome centerline coordinates
    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

     
    tertiary connection points (survey/020204/reduc/targetpostocp)
     
    latestCoord (DC)
    x,y,z
    		 origin of data
    P1L  upper vertical CP
    (fixed in DC coords)    		 -208.833, 135.789, -262.731 L 
     -210.307,?            ,-262.410    		 LB2, then measured offsets targets
    LB1
    P1R upper vertical CP -208.833     -137.201     -262.030 R LB2 then used left side target offsets
    P2L horizontal CP
    (fixed in DC coords)    		 -275.307      134.798     -377.241 L
    -280.000,             ?,         -376.000    		 LB2 then yoffset measured (assumed all y)
    LB1
    P2R -275.464     -136.961     -376.034 R LB2  then yoffset measured (assumed all y)
    P4 tail gunner
    (fixed in DC coords)    		 -414.621     -1.62156     -402.958
    -445.122,?                       ,-427.144    		 LB2  and measured offsets.
    LB1
    P3L,ver/hor intersection
    (fixed on tertiary)    		 -204.041      136.983     -385.053L
    -204.000,                       ,-389.000    		 LB2 then measured offset (assumed all y)
    LB1 (this may be Rl not P3)
    P3r,ver/hor intersection -203.673     -136.973     -384.879R LB2 then used -right offset.
    P5 tail gunner
    (fixed on tertiary)    		 -397.443    -0.234600     -454.539
    -397.00,               ?            ,-459.000    		 LB2 measured offset (assumed all y)
    LB1
        There is a discrepancy of 4 inches in the P3L position from LB1,LB2. It looks like one of the positions is P3, and the other is Rl (rotation axis of tail gunner).

    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.

    processing: survey/020204/reduc

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

        We can compute P3,P5 (the moveable points) in dome centerline coordinates if we have the actuator distances and  we know the positions of the above connection points in dome centerline coordinates for a given position of the  tertiary (say the nominal focus position).(see actuator distances to dome centerline).  We can also convert any fixed point on the tertiary if we know it's distance from the fixed tertiary points P3,P5.The algorithm is:
    1. Measure all of the connection points for the nominal focus position using the theodolite. Record the encoder values of the motor at this position.
    2. 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.
    3. We know all 3 lengths of the triangle P1P2P3 so compute the included angle a (between d12,d23) using the law of cosines.
    4. 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.
    5. 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.
    6. 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.
    This computation probably needs to be repeated for the left and right P3 positions since it appears that these point have different X,Z coordinates. 
     home_~phil