Zeroes, Scalings and Kinematics on a Motion
Control Rig
The following data is based on experience with Mark Roberts Motion Control Milos and
Cyclops. However, the theories could be expanded to work for other rigs.
Definitions
Zeroes
The position for an axis that is considered to be a numerical value of 0.00.
For rotational axes, this is normally pointing straight down the tracks and parallel to
them or exactly at right angles. For linear axes, it is usually some arbitrary
position that is precisely known in its relationship to other axes or the configuration of
the rig.
Scalings
The figure which converts the actual movement of a motor in terms of encoder slots
or stepper pulses into the physical universe units: length for translational axes, and
degrees of rotation for rotational axes. The units usually used on a Milo or Cyclops
system are centimetres and degrees.
Kinematics
This term has been stolen from mathematics and is used to mean the shape and
configuration of the rig with particular regard to the lengths and relationships between
each of the joints. The length of the arm is one of the simplest kinematics values.
Principles
For accurate data transfer and scaling of moves, the zeroes and kinematics on a rig
need to be very accurate. Linear measurements generally should be within 0.5mm (20
thou) and rotational zeroes/measurements should be accurate to within 0.05 degrees.
If you can get it better, then by all means do so.
In any shoot, the setup and care taken with the measurements etc. will be inversely
proportional to the amount of pressure, so any work that can be done carefully before the
shoot to set things up should be done to very high tolerances as the output result will be
the sum (or product) of the inaccuracies. So the more care taken to start with, the
better the result can be.
Zeroes should be set, in as much as possible, axis for axis totally independent of the
other axes. If the rotate zero is wrong, one can correct for this to some degree
with the pan zero. The result will look all right, but it will be inaccurate.
Zeroes and the optical result depend heavily on the lens. Lenses with aberrations
in their optics or in their mounting etc. can cause all the effort spent before to be
wasted. Take care when mounting the lens to get it in the right place, and as far as
possible get the production company to obtain good lenses from a reputable rental house,
preferably Panavision Primos as these seem to be the most reliable.
Scalings are best started with the figure worked out from the gear ratios and encoder
lines for each axis. Since there can be an error in these figures, they should not
be taken as gospel, but they are always a good starting point.
There is a law of diminishing returns that dictates that the gain of accuracy per unit
of time spent reduces as you get more accurate, so there is a point where one has to stop
and let the shoot go ahead. With a standard repeat motion control shot, the accuracy
is not totally crucial as long as it does not move, you will generally be OK since there
are no elements to match. The moment you get into scaling a move or matching it to
CG, then you have to get more accurate. The shot and how the images are going to be
used really dictates the accuracy you need to use. Only experience can give you
this, it is really impossible to lay down exact rules. As a rule of thumb, work out
how accurate you think it needs to be and then set it up twice as well.
A note on Thermal Expansion. When aluminium and steel warm up, they expand.
This is not likely to make a big difference on rotational axes as even if the
rotator ring gets bigger, it is still composed of 360 degrees. On translational
axes, you can estimate a percentage change of between 0.0117 and 0.0234 % for a 10 degree
Celsius temperature change. This equates into a change of between 14 and 28 thou in
10 feet depending on the material. Steel expands less than aluminium.
In general, scalings are checked first for all axes, then zeroes and then any
kinematics values. This is a guide to the order to do it in, and cannot be followed
exactly. Obviously get those axes done first which are not dependant or checked
against any other axes, and then do the rest.
Procedures
Track
The track zero is actually the least important as long as it is repeatable. Any
offsets in the track zero can easily be mopped up in data transfer or in move offset, so
it is not as critical. However the alignment and levelness of the rails is extremely
important to the results of the shoot as well as the accuracy of the rest of the zeroes.
The rails should be set up as straight and level as humanly possible. The
more time that can be put into this the better. The track scaling can be checked by
moving the rig as far as possible and measuring how far it has moved; obviously the
distance it has moved should match the distance it has reported it has moved.
Lift
With a rotational or boom lift that swings, the correct zero will be with the arm
totally horizontal (parallel to the tracks). The line of the arm is generally from
the rear arm pivot to the front arm pivot. With a Milo with extend or a Cyclops, the
lift zero is with the extend axis parallel to the rails. If you have no extend, the
lift zero is set so that the height of the lift pivot above the rails is the same as the
head pivot. This can be hard to measure and will vary system to system; if the rails
are level, then you can use a precision level on a machined surface. The scaling on
the lift on a Milo is done through the gear ratios and then checked against a tape measure
as the lift motion is effected through a ball screw. On a Cyclops, it is best to
work it out from the gearings and then test it from - 40 degrees to + 40 degrees with an
inclinometer. This is not inherently very accurate, but should work for change in
angle and will be good enough as a cross check on the gearings.
If you have a system that does have an extend type axis (arm length can increase and
decrease) then the best way to set up the lift (and rotate) zero is to put them as close
to zero as possible with the pan and tilt also as close to zero as possible. Enter a
move that has the track and extend do equal and opposite moves so that the camera stays in
the same place. This will eliminate from the equation any inaccuracies in the pan
and tilt zeros, as well as lens aberration, as you will not be changing the distance from
the camera to the target. When the extend is in, adjust a cross to line up exactly
on the cross hairs. When the arm is out, adjust the lift zero. Repeat these 2
steps until the movement of the track against the extend produces no vertical shift of the
image against the cross hairs.
This method will tend to compensate for any droop of the arm as you extend out.
This droop will be minimal in a rigid system, and is the physical universe limitation of
how accurate you can get the system.
Rotate
With a arm extend, the rotate zero is set the same way (and at the same time) as the
lift zero. If you do not have an extending arm, the rotate zero is best set up by
dropping a plumb bob from the centre of the pan axis and ensuring that it is directly
above the centre of the rails assuming that the rotate centre is directly above the centre
of the rails. Rotate scaling is best checked by turning the turret through as many
turns as it easily feasible and checking that something lined up at 0 matches at 360 &
720 & 1080 degrees etc. etc.
Lift pivot offset
In the Milo system, the lift pivot is not directly above the centre of rotate.
This is an important offset as it is directional with the rotate. This figure is
best obtained from the manufacturer, or can be checked through other tests - see later.
Arm Length
The length of the arm has to be measured accurately. Generally on a complex
system, one cannot run a tape measure along the arm as the tape measure will usually not
run straight and parallel to the arm. If you drop a plumb line onto the floor from
the head pivot, rotate to 180 degrees and then track until the plumb bob matches the
earlier mark, you get the lengths of the arm doubled (if the lift pivot offset is 0.0).
You can do the same trick side to side and then use a tape measure, but remember
that the result depends on the arm being exactly level and the lift pivot offset known as
the measurement you get will be 2 * (arm length - lift pivot offset).
With the Mark Roberts Flair program, the arm length can also be checked in the
following manner: Place a thin cotton thread across the rails at right angles to the
rails. This can be checked by using the rig and rotating to an exact angle either
side, and making the thread line up on the cross hairs. Once this is done, place the
rotate at 0, tilt down to about -85 degrees and with the pan also at zero, focus on the
thread. Engage "cartesian control" in the "locked world" mode.
If you move the camera and target in Y only, then the camera should track exactly
along the string. If the string appears to drop below the cross hairs as you move
away from the middle of the rails, then the arm length should be increased, otherwise
decreased. This method should allow you to get it to within 1mm if not more
accurately.
Extend
The zero on the extend is such that the arm length is correct when the extend is
zeroed! Scaling is done the same way as the lift. This scaling can easily be
checked by moving the track against the extend with the arm level. The camera should
not move, so you can line up cross hairs and check that.
Angle
The angle axis is a system used by Mark Roberts Motion Control on their rigs and
basically changes the angle of the pan tilt head to the arm. This can be used to
give greater height and reach. The angle scaling is checked against the tilt.
The tilt should be set up as covered later, and once this is done, put the angle in a
vertical position and place a precision level on the top of the camera, and attach it
securely. Move the tilt until the level is horizontal and zero the tilt. Move
the angle to +90 degrees and the tilt to -90 degrees. If the level is still reading
level, then the angle scaling is good. If you have an extend, then the extend should
be pulled back as far as possible to lessen any bending in the arm. The zero on the
angle is checked against the rails. If you line up a point in front of the camera,
and then swing the camera around it so that the pan changes to 180 and the only other axis
to move is the track, you will be looking at it from the other direction. If the
object on the screen is the same height, then the angle is correctly zeroed. This
procedure can also be used to check systems with a parallelogram head as these also need
to be very accurate.
Roll
It is a good idea to get the roll correctly set up as well as the camera mounting
before proceeding with the rest of the head as inaccuracies in the roll will cause other
problems. The roll scaling is checked as any other rotational axis by doing many
turns and checking that it is a multiple of 360 degrees. The roll zero is such that
the horizon is level. The centring and alignment of the camera is critical.
There are 2 factors here, one is the positioning of the camera so that the centre of the
film (academy of full gate) is exactly in the centre of the roll. The other more
important factor is if the film plane is exactly parallel to the roll ring. A
positional offset of 1mm will only produce an error of 1mm at the target, if the cross
hairs would drift across 1mm of the target - not terrible. However an angular offset
will cause a greater error, the farther away you look. These both should be set up
so that if you roll the camera, the cross hairs stay in the same place. Easier said
than done, but worth the effort. This of course has to be done with a
"perfect" lens. The lens should have been tested and checked beforehand,
as should the flange depth and alignment of the camera. (The lens mount and film plane
must be parallel).
Pan
The pan scaling is checked in the same way as the rotate. Pan around as many
times as feasible (up to 4 or so) and check that the result is an exact multiple of 360.
The pan zero can be checked with the lens on by tracking the camera back and forth.
The cross hairs should not drift side to side as you track in. (This assumes
that the roll has been set up as above). An alternative method to this is to put a
flat pressure plate in the gate, turn the camera to exactly 90 degrees, and put a depth
gauge onto the film plane, and then check for run out as you track back and forth.
Once this is set correctly, then pan back exactly 90 degrees and your film plane is
correctly aligned at 90 degrees to the track.
Tilt
The tilt scaling can be harder to check as tilts do not always travel a full 360.
However with most systems, they can be forced to go 360 even if you have to cheat
the limits slightly. The zero is set up in the same way as the pan. The extend
should be about half way through its travel in this case so that any bending of the arm is
averaged.
Lens offsets
The nodal point of the lens is normally required to give an exact match to CG systems.
The precise definition of the nodal point seems to have a certain amount of
variation, but for our purposes, the nodal point could be considered to be the same as the
entrance pupil and could be defined as that point, a pan about which causes no parallax
shift in the image. The finding of the Nodal Point is then done by adjusting the
nodal offset and panning until there is no parallax shift. As this can only be
checked as the image slides across the lens, you are at the mercy of the spherical
aberrations in the lens. An alternative is to get a lens that has this data readily
available (Panavision Primos).
The Nodal Offsets is NOT critical to Mark Roberts Motion Control Target Tracking
software. Major changes in the Nodal offset do not generally make much of a
difference to the move, and it will almost never make a difference to how well you track
an object.
Lens Measure Offsets
In the Mark Roberts Motion Control Flair computer program, the other offsets that make
a major difference to the accuracy of the target tracking and the XYZ output information
are the position of the measurement point. The computer has to know exactly where
that point is in relation to the pan tilt intersection in order to get the position of the
object in space correct. There are 2 offsets that define this. One is the
Measure Optical Offset which is the distance that the measure point is forward of the pan
tilt intersection measured parallel to the optical axis. This distance should be
measured to within 1mm or better if possible. The other offset the Measure Normal
Offset is not as important though it does have an effect when you are close up. The
purpose of this second offset is to compensate for the fact that the measure tape goes
from the side of the lens to the centre of the target whcih is a diagonal, not a straight
measurement. The software uses simple pythagorus to determine the correct optical
distance based on the measured distance. This distance is from the optical axis to
the measure hook, measured at right angles to (normal to) the optical axis.
Outer arm length
On a system that has an outer arm, its length is vital to the kinematics if this arm is
going to move off of the vertical. When it is vertical and stays like that, as with
other vertical offsets that do not change such as the height of the central turret or
column, then we are not really concerned with its length. The composite of all these
is usually sorted out by defining the height of the camera above ground when all axes are
at 0.0. To get an accurate measurement for this arm length, repeat the tests done
for the arm length but with the angle out at 90 degrees, and the tilt looking straight
down at the thread. Do not move the arm away from the horizontal as that will only
confuse the issue. Given that the arm length is correct as set up before, adjust the
outer arm length such that a side to side motion keeps the cross hairs on the thread. (see
above)
Testing
Once all the above has been done, one can assume that the rig is fully set up.
However, testing must always be done to see how good the results are.
The best way to test a Flair system is with "Cartesian Control". In
"World" or "View" mode, you can move the camera around in 3D space and
it should track the target perfectly. Zooming in and out and rolling round the
object should produce no drift in the image. Another test that can be done in this
mode is to move one of the rig "master" axes, and test that the camera does not
move in space. With the "master" axes, there will be a slight lag in the
motion of the other axes, but at rest, the camera should be in the same position.
If there is motion in the image, then the errors need to be isolated. If you do
get drift, check to see if it happens with just a simple side to side motion. This
uses only the rotate, pan and track, so it narrows the target down. By a process of
testing, hypothesising and experimentation errors can be traced and corrected. Be
very wary of changing variables and seeing if it works better; it is often possible to
correct an error in one particularly situation by compensating in another variable.
This might work for one particular movement, but will not work for many others.
Perfectly right is the only answer.
Simon Wakley
Senior Programmer
Mark Roberts Motion Control.