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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 provides astrophotographers with a platform 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.

Several other means have been employed to reduce tangent error in barn door drives, such as the use of a cam or varying motor speed- which are very effective. The point of the Tracker design was to find a method of minimizing tangent error while retaining simplicity of construction and operation. The Tracker can be driven by hand, at a steady rate of 1 rpm, or by using conventional electronics. In this case, using a programmable microprocessor. A Google search should provide an array of designs to suit personal taste and technical capabilities.

Addendum: This paper describes the design of a heavy duty double arm tangent arm in which the author mentions the use of offset points of rotation – the same idea applied to the Tracker – here. I discovered this some time after designing the Tracker and was encouraged to see that I was, at least in part, on the right track.

Philosophical Position

A Double Arm Drive, need not be a roughly constructed Barn Door. It’s possible, with basic tools, to produce an instrument of reasonable precision, in fact, remarkable precision, given a method of construction and a few simple guidelines. The first – don’t be in a rush to complete the project. Consider each step and analyze how you will implement the tool set and materials that you have, in view of what you want to achieve with the device, and how it will be driven. A hand driven unit is suitable for wide field photography, but more precision is required of the assembly if you intend using a telephoto – working to finer tolerances, is no more demanding! The second- “Measure twice, cut once.”

The most limiting aspect of any tangent arm design is the periodic error (PE) of the drive screw (lead screw), due to imperfections in the manufacturing process – a screw or threaded shaft is a helical gear and unless machined with precision is notorious for PE. Use tough plastic tube, that (in place of a metal nut – through which the drive shaft runs) expands into the drive shaft thread, eliminating backlash and clearances that promote periodicity – diminishing the effect. Concentric attachment of the drive screw to the motor shaft also reduces periodic error, significantly. Accurate placement of hinges and other components adds to overall precision. There is no need to be sloppy with construction. The final result may not be perfect, but some clever adjustments will all but eliminate inconsistencies in workmanship.

Think of your Tracker as a precision instrument. Keep in mind that most astrophotography involves taking multiple short exposures from 30 seconds to 4 or 5 minutes and stacking them together, well within the Trackers’ capabilities – 10 to 15 minutes with good polar alignment.

Notes

The information contained on this page, and related others, is intended to provide sufficient detail for would-be builders of the device and to provide an explanation of its design and performance so that readers can decide whether the Tracker is for them or not, and hopefully then, provide feedback. Comments are blocked because of incessant and increasingly intelligent spamming. If you wish to be in touch, please follow the usual email format on the Contact Me page.

There have been several improvements (marked ***) to the design – please read further down and here.

The Equatorial Wedge provides active adjustment of altitude, particularly useful for refining tracking performance on the fly – limited to a range of latitudes, North and South, 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.

If intending to build the Tracker – Please read this first: For simplicity of construction, the Alternate Layout is recommended, consistent with Tracker design conventions – 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 (millimeters, unless otherwise stated), including the Drive Shaft thread. Stepper motor resonance damping can be found here.

For the non-metric world, imperial measurements for use with the 1/4 inch 20 tpi drive screw may be found here

Northern Hemisphere: Please remember to place the Alt/Azimuth hinges on the other edge of the Tracker.

A personal note: 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!

A little nostalgia!

“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, while retaining accuracy, during the early stages of operation.

Dimensions

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 geometry 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)

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 60 contact points 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, the camera lens set at 24x digital zoom, was used to take 10 x 64 second exposures (Spica, southern hemisphere) over 22 minutes, of which 5 were stacked (here), showing no apparent trailing. The others, subject to inadvertent light pollution 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 for approximately 40 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.

The optical zoom of the G9 at 6x = 210mm. Multiply by 2 with a tele-converter lens = 420 mm. The digital zoom is 24x = estimated focal length of approx 1600mm. This however requires verification? Still, it was surprising to see Spica remain in position for such an extended period at high magnification.

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 and 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!

If polar alignment with a finder scope is not possible, for some reason (weather or terrain obscure the celestial pole), precision alignment can be achieved using an abbreviated form of the ‘drift method’ (suggest Google this). Google map is useful for determining the alignment of property boundaries and their relationship to the celestial pole (coarse alignment). Further adjustment can be made by observing the movement of a target star (on the display screen of a digital camera, a finder scope or with greater difficulty, the cameras view finder – pick a bright star) and finely adjusting in azimuth to eliminate further drift (with altitude set correctly to the observers latitude). The images of Spica at high magnification were possible with fine adjustments in azimuth.

This may be helpful to visualise the polar alignment problem using a digital camera. Note: the reason this method is successful is that it accounts for refraction of the position of the Celestial Pole through the atmosphere. Using a Polar Finder scope the results were OK, but the method below is more accurate – but time consuming.

Images

In-camera software (CHDK) stacked (summed) the Spica images (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 has been processed using imagej (see link).

CHDK provides slow shutter speeds to 64 seconds (now much longer), beside 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

Criterion;

construction be possible using hand tools – a drill press is a handy addition;
simplicity be retained throughout;
‘critical dimensions’ be easily measured and reproducible;
tracking be accurate up to 60 minutes – this seems adequate for most astrophotography;
final build tracking be within 2 decimal places of a degree or better;
the device be 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.

If these concepts are observed the drive can be started at any point in the cycle and provide consistent performance.

***Since testing and improving on the Tracker design, I find it preferable to start  the Tracker slightly open (15 – 20mm). This stabilises the unit, preventing the motor and drive shaft rotating out of alignment when the board is closed. Redesign of the drive assembly improved the stability and tracking capability of the unit by stiffening the connection between the motor and drive screw and by eliminating any clearance between the drive nut and drive screw.

***Simply, replace the metal drive nut thread with a nylon collar and flexible 10mm plastic tube insert and tap a 6mm thread in the plastic tube to accept the drive screw. Connect the motor shaft and drive screw using a sleeve made from the stiff barrel of a marker pen and a soft plastic tube insert. Push one end onto the stepper shaft (10mm) and thread the drive screw on to the other (18mm), leaving a 2mm space between the metal shaft ends.

***You will need to reset the limit switch setting – the Tracker starts slightly open with the improvements discussed above – but still observe the datum lines mentioned previously, when building the unit.

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. Work carefully and methodically.

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.

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, 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 15 or 20mm – 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. Eventually, the drive nut pinions will be replaced with nylon and be adjustable. A nylon drive nut should also reduce noise – at the moment – metal to metal. Nylon threads are noticeably tighter.

Tip – put 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.

Altitude – Azimuth Boards (Equatorial Wedge)

The Equatorial Wedge (hinged Altitude – Azimuth boards) is used to set the observers latitude and to provide fine adjustment during polar alignment. For example, if you live 38 degrees north or south you would set the angle of the EW 38 degrees, the drive may then be swivelled to affect alignment with the celestial pole and locked.

If intended to mount the drive on an adjustable (sturdy) tripod, the azimuth board may be omitted. This part of the design is flexible.  Though a little tedious, time spent refining polar alignment will produce superior results.

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 needful. Be careful of heavy telephoto lens that may topple the Camera Arm. It may be necessary provide restraint or a counter balance. Use tight hinges to avoid sideways movement of the Camera Arm under the weight of a heavy camera.

Electronics

The Printed Circuit Board (PCB) is designed as a motor shield, fitting 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.

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 uses 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, used to drive a 5 or 6 wire uni-polar motor, also has two power sources. 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.

Stepper motors can be purchased at most electronic stores or on-line shops. Many sites speak of using motors from an old dot matrix printer, and other sources. 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). Don’t forget to change the motorStep line of your Arduino script to suit your motor.

Arduino Resources

Arduino Code StepperDriver.brd (Eagle Board Milling) StepperDriver.pdf (PCB Etching) Parts list.

Copy and Paste the Arduino code to your editor and upload to the board.

The PCB pdf file should print 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 Kill 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 Kill 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.

Feedback and suggested improvements in this area would be most welcome. It is not an area of expertise. The work is essentially an adaptation of the circuit diagrams located at the ‘Arduino’ site. The program makes use of the pull up resistors on the Arduino board for voltage protection. Therefore, components are minimal.

“Section 3″ Concluding

The device has demonstrated accurate tracking at high magnification for approximately 40 minutes and requires further testing to 60 minutes. It’s time to remove it from its test bench and get it into the field.

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 this potentially very accurate Double Arm Drive.

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 and KStars, two excellent open source desktop planetariums. GIMP the image processor and ImageJ, another open source astronomical imaging tool.

The Arduino developers. The CHDK developers and the excellent sites devoted to digital astrophotography. The many sites dedicated to 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 contained on and within 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.