Sunday, November 27, 2011
Tangent Error Minimized Tracker - A Double Arm Drive
Double Arm Drives have been used to photograph the night sky for over 20 years. Originally designed by Dave Trott, based on the Haig or Scotch mount (otherwise known as a Barn Door Tracker), the Double Arm Drive is a platform used to track and capture images of celestial objects, using slow shutter speeds necessary for this type of photography. The proposed design, while conventional, attempts to refine the tracking performance of the double arm design. Hence, the Tangent Error Minimized (TEM) Tracker - this is the prototype.
Basic image acquisition
Basic image processing
Notes:
Alternate methods of tangent error reduction in barn door drives include cams and varying motor speed. The point of the Tracker design, is to minimize tangent error while retaining simplicity of construction and operation.
The Tracker need only be driven at a steady rate of 1 rpm by hand or with a drive mechanism - in this case a programmable microprocessor (Arduino), precisely governing the speed of a stepper motor - Google
Vibration is inevitable when using stepper motors. A reduction system such as a gear box, gear train, or pulley system between the motor and drive shaft will reduce vibration significantly - Google.
TEM Tracker
View complete set of Tracker images
Front and rear views, with the original resonance dampers - the cork and spring arrangement is surprisingly effective. A reduction drive is more effective. The original build is shown here for illustration purposes.
The Equatorial Wedge (EW) provides active adjustment of altitude, particularly useful for refining tracking performance on the fly - limited to a range of latitudes in which the device is expected to be used. If attached to an adjustable tripod, directly to the Altitude board, the Azimuth board is not required, and may be omitted. Although, an EW is a more rigid design and easier to set up.
Notes:
For simplicity of construction the Conventional Layout is recommended - some cross referencing of the Tracker Plan is required. Observe the dimensions and ensure that the Points of Rotation are aligned when the Tracker is closed. All Tracker dimensions are metric (unless otherwise stated), including the Drive Shaft thread.
For the non-metric world, imperial measurements for use with the 1/4 inch 20 tpi drive screw can be found at the bottom of the page in Appendix;
The algorithm used to calculate the Tracker dimensions was kindly supplied by my brother. For any combination of Drive Shaft thread (metric or imperial) and rate of rotation, the algorithm calculates Critical Dimensions - that is, Drive Arm and Camera Arm length and corresponding hinge-to-hinge distance. Any mistakes are mine!
“Section 1” Development and Testing
Double arm design seems to be a set of compromises, trade offs, to minimize deviation about mean performance. An in-depth analysis can be found here.
The dimensions of the TEM Tracker are set at their current values because, among other things, they provide very accurate tracking in the first 15 to 20 minutes and subsequent tracking error is minor to 60 minutes. A design goal was accurate tracking for up to 60 minutes. In practice, accurate performance has been observed beyond 60 minutes.
A simple method to resolve tangent error during the final 40 minutes of tracking was not immediately evident. Varying motor speed or fitting a cam, while effective, is not preferred because of undesired complexity, whereas, constant motor speed can be replicated in a variety of ways.
An alternative method was found and, for want of better terminology, is simplicity itself. While experimenting with arms and arcs, using a 2D CAD program, the answer to the problem became evident. Raising the Camera Arm hinge tilts the arc followed by the Camera Arm backwards, reducing tangent error, retaining accuracy during the early stages of operation.
Geometry
Definitions
Siderial rate: The rate at which the Earth rotates on its axis - approximately 15.0416 degrees/hour.
Drive cycle: From boards closed to 60 minutes (zero to nominally, 15.0416 degrees).
Contact Point: The physical point at which the Drive Arm lifts the Camera Arm - 349.95mm (350mm).
Optimal Contact Point: The position at which the contact point ‘would’ intersect the Camera Arm, if it were to move (optimally) throughout the drive cycle. In practice, too complex.
Points of Rotation: Hinge and pinion centres should line up when the Tracker is closed, except the Camera-arm hinge which is slightly elevated. Why is it important? The performance of the Tracker is predicated on this arrangement - its the zero datum. What really matters is that the geometrical relationship between the components is retained.
Methodology
A spreadsheet was used to calculate Drive Arm and Camera Arm dimensions with tracking tolerances set to 4 decimal places of a degree, using the following fixed parameters;
motor speed, 1 rpm ; drive screw pitch, 1 thread/mm (6M (6mm) or 8mm fine - which has the same 1 tpmm pitch as 6M).
Camera Arm - Drive Arm Trend
Optimised angular displacement of the Camera Arm was calculated to 4 decimal places at 1 minute intervals for 60 minutes; i.e., 15.0416/60. Optimal contact points were determined to match the displacement of the Camera Arm at these intervals. The start and end points being 349.95 (350mm) and 347.11mm, respectively.
With the contact point fixed at 350mm (349.95mm) the Camera Arm is driven through 14.9517 degrees (in 60 minutes). If the contact point is fixed at 347.11 mm the Camera Arm is driven through 15.0416 degrees, which is optimal, but problematic because error is introduced during the early part of the drive cycle. The object is to drive the Camera Arm between these two points and take advantage of accurate performance at both ends of the drive cycle. This can be achieved by raising the Camera Arm hinge 0.4mm (4 thicknesses of 80gsm paper).
Calculating 30 contact points (two minute intervals) made it possible to verify the arc derived from the CAD program; angles subtended from the Camera Arm hinge to the Camera Arm arc correspond very closely to the optimal contact points.
Performance
A Canon G9, fitted with a 2x tele-converter lens with the camera lens set at 24x digital zoom, an approximate focal length of 1600mm, was used to take 10 x 64 second exposures (Spica, southern hemisphere) over 22 minutes, of which 5 were stacked, showing no apparent trailing. The others, subject to atmospheric distortion and vibration, due to construction faults, were discarded. Similarly, trailing was not apparent. Spica1 and Spica5 are the first and last in the series of 10 exposures.
Accurate tracking was observed > 30 minutes; that is, 15 minutes to resolve polar alignment using the drift method, 10 minutes to verify tracking and 22 minutes of photography, including a period of approximately 5 minutes where the setup was unattended after the shooting cycle was complete.
Spica - 5 x 64 second exposures over 22 minutes
Software control of motor speed is optimal because it eliminates a variable that tends to mask other errors, such as construction faults and/or poor polar alignment.
Programming an ATMEL ATMEGA168 microprocessor on an ‘Arduino’ board mated with a motor shield is an effective solution (if you know what this means, you may wish to skip this section). This arrangement was used to test the tracker.
Alternatively, inexpensive electronic control, using one of the many circuits to be found on-line may suffice. Other methods include, utilizing a 1rpm clock motor, or gearing down a DC or Servo motor. Otherwise, the device may be hand driven by reference to a time piece to produce acceptable wide field images.
Electronic control may not provide consistent performance, particularly where variations in ambient temperature affects the timing of the circuit (a function of resistance). There are ways to compensate for this, and it is recommended that if choosing this type of circuitry, adding temperature compensation is essential. However, using an oscillator/crystal type circuit is probably a better solution.
Polar Alignment
Accurate Polar alignment is essential! (Google)
Note: First, level the tracker, preferably with a circle type spirit level, or these days, a smart phone level. Align the axis of the camera arm roughly true South (SH), true North (NH). A compass with magnetic variation applied, Google map, survey maps, street directory, GPS may assist with the direction of the poles in relation to property boundaries.
I use the following procedure and find it more accurate than optical polar alignment for this type of mount.
1. Point the camera comfortably (for your neck and back) near the Celestial Equator, closer to Zenith than the horizon.
2. Expose for 10 seconds and check the image for star drift (trails instead of points of light) - adjust the tracker in Azimuth opposite to the star drift (horizontally) and Altitude (vertically). During the next exposure of 20 seconds the star trails will hopefully be shorter. If you adjust the wrong way the star trails will get longer, so adjust back the other way, plus a bit more.,
3. Repeat this process, increasing the length of exposure with each try. Eventually, tracking error will be minimized to allow for approximately 3 minutes. Don’t expect to achieve 10, 20 or 30 minutes, besides which there is no point. Testing was done with specially made vernier adjustment, specifically for verification purposes.
Start with 10 seconds (gross error check), increase to 20 seconds, then 30 seconds, achieving good tracking at each stage, and then increase to 60 seconds. If tracking is good at 60 seconds, there’s a very good probability that this is sustainable to 2 or 3 minutes.
4. Expose for 2 or 3 minutes, depending on whether you choose to expose for 2 or 3 minutes and check for drift. Resolving errors in Azimuth and Altitude.
Notes:
The reason this method is successful is that it accounts for refraction of the position of the Celestial Pole through the atmosphere.
If you’re in a suburban light polluted area, 3 minute exposures is as much as you will need (iso800). Any more and the sky glow will dominate the image, any less and the signal from the image you are taking will be drowned in noise.
If exposures are too long they will be over exposed. Lots of optimal exposures stacked together is the best method for a good image.
To verify the authenticity of tracking, in-camera software (CHDK) was used to combine/stack the Spica images (at that time they were not stacked using a computer program that automatically rotates and aligns images), further noise reduction and conversion to jpeg was done with GIMP. The more recent image was combined in GIMP. Very little adjustment was required to align the Spica images - a few pixels at most.
Spica
Note:
CHDK provides slow shutter speeds to 64 seconds (now much longer), besides other functions. Scripting allows automated multiple shots with a single press of the shutter. The process can be interrupted between exposures by pushing the shutter release button.
“Section 2” Design and Resources
Design criteria; construction possible using hand tools - a drill press is a handy addition;
simplicity retained throughout;
‘critical dimensions’ easily measured and reproducible;
tracking accurate up to 60 minutes - this seems adequate for most astrophotography;
final build tracking within 2 decimal places of a degree or better;
the device portable and easily deployed in the field;
lightweight and rigid.
Tracker Plan
Providing the Critical Dimensions, Points of Rotation and other design conventions are observed, performance should be consistent in various configurations.
Note:
The centre line through the Drive Arm hinge and the Drive Nut pinion, including the motor mount hinges (Points of Rotation), when the device is closed, represents the intersection of two planes. A third exists between the centre of the raised Camera Arm hinge and the Contact Point. These ‘virtual’ planes are the design datum; it is important that construction proceed with this concept in mind, otherwise design performance cannot be guaranteed.
Construction Tips
Not all pairs of boards are square, even if you had them cut at the timber yard. Choose the squarest end of each board and mark the edges; be careful to measure to these edges. The square ends should be at the drive end of the board the measurements referenced to a common datum. In other words, don’t introduce error during construction by assuming that the boards are square.
Preparing the drive end, before committing to other measurements, referenced to the centre of the Drive Shaft, is preferable, making sure that the 20mm (nominal) drive shaft holes in the top and bottom boards are aligned prior to marking the location of other components. That is, marking out the motor/drive shaft assembly end first, will minimize construction errors - readily corrected during this stage.
The boards pictured are 17mm ply coated with laminate - a cut-off picked up at a timber yard. This material is used for concrete form-work and is very stable - resists warping etc. The Camera Arm is cut out of the drive arm. 12mm waterproof ply is acceptable, but is getting a bit light.
Drive-end Construction
Notice that the motor is mounted on the top board and hinged. It may be mounted on the bottom board in a similar fashion - a matter of preference. Importantly, the centre of the drive shaft should be coincident with the centre of the motor mount hinge and the centre of the Drive Nut pinions. It may be necessary to ‘pack the motor up’ to provide clearance between the Drive Nut and the motor shaft.
An easy way to make Drive Shaft pinions, and have them match up with the Motor Mount hinges, is to cut the ends off the hinges to be used for the Motor Mount. The part with the pin is retained (see photo); additional holes are drilled to accept locking screws, once the Drive Nut pinions have been mounted and centered - use tape to hold things in place while drilling.
Another refinement is the use of springs on the pinions to minimize slack in the assembly. Alternatively, remove the pins and tap threads to fit grub screws for centering the Drive Nut (recommended). The most difficult task was drilling the holes in the sides of the Drive Nut and ensuring that they were concentric.
While it is important to ensure that everything is properly aligned during construction, it is recommended that the Tracker be started slightly open - say 10 - 15mm - to stabilize the drive shaft and pinion. With the Tracker closed the drive shaft tends to lean due to its proximity to the drive nut pinion assembly. A bit of triangularity stabilizes the drive.
Nylon nuts and bolts can be easily modified with side-cutters, and are useful replacements for hinge pins and pinions - they tend to reduce the transmission of motor resonance. Nylon threads are noticeably tighter.
Tip - place a small ball of Blutak on the end of the screw before pushing it into the hinge - this will further isolate hard surfaces without compromising rigidity.
Tracker - Drive End Assembly - Motor Mount - Contact Point
Drive Shaft & Nut Assembly (replaced with a nylon sleeve and plastic tube insert tapped to 6mm)
Azimuth and Altitude boards
If intending to mount the drive on an adjustable (sturdy) tripod, the azimuth board may be omitted. This part of the design is flexible.
Camera Mount
It is advisable to place a layer or two of Neoprene under the Camera Mount bracket to reduce transmission of resonance. Having said that, an improved Motor Mount is needed. Be careful of heavy telephoto lens that may topple the Camera Arm - restraint or a counter balance may be necessary.
Two hinges are better than one for the camera arm, tending to be more stable. A wider footprint for the camera arm and drive arm is recommended - use the alternate layout and build the unit a little wider for stability, but not so wide that it becomes cumbersome.
Electronics
The Printed Circuit Board (PCB) is designed as a motor shield and fits on top of the Arduino board. It utilises an L293D or SN754410NE H-Bridge bipolar stepper driver, and a ULN2003AN (or similar) to drive a unipolar stepper motor. Primarily, logic is used to control the motor function. A three position switch selects Forward, Stop and Reverse and a ‘Kill Switch’ stops the motor once the Drive Arm is back in the start position; the motor is held in position with its coils energised. Turn off supply power to rotate by hand, if necessary.
Limit (Kill) Switch
The L293D is probably a better choice because it has in-built protection to prevent damage to your Arduino from voltage spikes generated by the motor; the SN754410NE does not. However, the use of the Arduino pull-up resistors may well serve to provide additional protection; no problems have been experienced to date.
The L293D and SN754410NE use two separate power sources, one for the chip and one for the motor. As such, the motor shield is designed to provide several control configurations. For example, the SN754410NE may utilise a “power-off” kill switch, or the Arduino logic. Similarly, for the L293D, the board may also be configured to remove power from the logic and power supply. This is more derivative, through design evolution, than a deliberate feature.
The ULN2003AN Darlington Array, drives a 5 or 6 wire uni-polar motor. Changing the pin allocation in the ‘Global’ section of the ‘Wiring’ program is necessary with the current program.
Fitting a heat sink to the 780x (x = the motor supply voltage) IC and attaching a cooling fan will be necessary where more powerful stepper motors, consuming large amounts of current, are used. A 5 volt 4 wire 200 or 400 step bi-polar motor, or 5 or 6 wire unipolar is adequate for the job, unless you have other requirements. Besides, there are several motor shields available for the Arduino if you prefer an alternative, for some reason.
Motors
Stepper motors can be purchased at most electronic stores or on-line. Many sites speak of using motors from old dot matrix printers. A suitable motor with sufficient torque can be purchased for about $20. These motors usually have 200 steps/revolution. Less expensive hobby motors have as few as 48 steps (probably too coarse for digital photography at high magnification used without using a gear box). Don’t forget to change the motorStep line of your Arduino script to suit your motor. If using a gearbox of some kind, increase the speed of the motor for the gearbox reduction - for a ratio of 5:1: motorSpeed must be 5rpm to maintain 1rpm at the drive shaft.
Arduino motor shield
Arduino Resources
Direction and Kill Switch wiring
StepperDriver.brd (Eagle Board Milling)
StepperDriver.pdf (PCB Etching)
Notes:
Copy and Paste the Arduino code to your editor and upload to the board.
The PCB pdf file prints the actual size of the shield to fit the Arduino (Decimilia or similar) - it was printed directly from Eagle. Print to a transfer medium then iron onto a single sided board for etching. It may be wise to print to paper first, cut out, and check for fit with the Arduino board. A Laser printer is required, as well as a 1mm and 0.8mm drills, fine hacksaw and file to cut to shape.
Refer to the parts list and use the image of the Arduino Motor Shield for guidance (note the two jumpers - logic setup). The 100uf capacitor is nearest the diode and 4 pin connection header, the 1uf capacitor is at the back of the shield. The L293D (SN754410NE) is the IC to the front of the image/board. The ULN 2003AN is located at the back of the board.
The Direction Switch is an 8 pin 3 position sliding switch. Terminal layout as shown, is 3 + 1 and 1 + 3. The limit switch, when closed, sets Pin2 LOW. Note, that in the Stop and Reverse positions Pin 3 is always LOW. Forward, sets Pins 2 and 3 HIGH, overriding the limit switch.
If problems are experienced getting the stepper motor to rotate; i.e., it ticks one way then the other, the motor wiring will need rearranging in the socket. If the motor turns the wrong way, plug the socket in the opposite way.
If intending to have a board made commercially, use the “Eagle Board Milling” file.
The “PCB Etching” file has bigger pads to improve adhesion during image transfer (ironing) and provides more copper for better adhesion to the board.
Warning the program makes use of the pull up resistors on the Arduino board for voltage protection. No resistors have been used in this design. Use of the L293D is recommended because it has in-built protection.
“Section 3” Concluding
It has been 2 years since designing the Tracker, and it is safe to say that it will consistently provide accurate tracking, consistent with accurate polar alignment, for 3 - 4 minute exposures, which is adequate.
Demonstrated performance, more than 30 minutes, was achieved under controlled conditions, specifically to verify the design parameters - which it did quite well
Appendix
Large Imperial version:
Similar profile to the Metric version, for exposures up to and beyond 60 minutes - say 90 minutes.
Drive Arm hinge - Drive Nut pinion / Drive Shaft centre = 16 inches; Drive Arm hinge - Contact Point = 14 inches; Drive Arm and Camera Arm hinge = 4 inches. Pack up the Camera Arm hinge with 2 layers of 80 gsm paper, because the uncorrected error after 60 minutes is half that of the metric version.
Compact Imperial version (see Section 3 Acknowledgements):
Indicates superior tracking up to 40 - 45 mins with no camera arm correction (packing up, as in the tracker design) and may be ideal for hand driven exposures of shorter duration. A computerised motor driven version should demonstrate exceptional tracking to 42 minutes - more than enough.
DA hinge - DN pinion / DS centre = 14” ; CA hinge - CP = 12.92” ; DA hinge - CA hinge = 1.9”. No packing is required. Calipers may be useful for measuring down to 1/100”.
Acknowledgements
Dave Trott,, the original designer of the Double Arm Drive, proposed the concept in the Sky and Telescope magazine, 1988. Containing a wealth of information, his web-site is also beautifully designed.
My brother, the interested sceptic, and the brains behind the spreadsheet. Without whom this project may not have had the impetus to continue. The spreadsheet enabled experimentation with various component dimensions.
Mike Mohaupt - whose Compact Imperial design prompted further research to optimise the performance of his very accurate design which provided the data for 1/4” 20tpi dimensions.
Open source software (Linux) - Qcad, without which the idea would have escaped my attention.
Eagle PCB software and the Arduino Decimilia provided the tools to develop the electronics platform to drive the stepper motor.
Not forgetting Stellarium an excellent open source desktop planetarium.
GIMP the image manipulation program, another open source astronomical imaging tool.
The CHDK developers and many excellent sites devoted to digital astrophotography and Double Arm Drive design.
Licence
This work is licensed under a Creative Commons Attribution-Noncommercial 2.5 Australia License.
Disclaimer
The information on this site is provided in good faith. The author/owner of the material of this site accepts no responsibility for reader/user outcomes, of any nature, directly or indirectly associated with this and/or any other site associated with, or affiliated, by any means or interpretation. Please use the information freely, at your own risk.