Saturday, November 26, 2011

Tangent Error Minimized Tracker: a Double Arm Drive

EDIT: When I first wrote this, it followed several years of dabbling in various designs and versions, hand and motor driven. There are of course many way to skin a cat, and this is just one of them. Think of this blog as useful information, if in-fact it is useful. I am a fan of the curved rod design for it’s simplicity. This design was probably a response to frustration over the inherent tangent arm error with flat board,straight shaft designs - anyway, if this is helpful, have fun…

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 camera platform used to track and capture images of celestial objects using long exposure times. This design is conventional and attempts to refine the tracking performance of the double arm drive. Hence, the Tangent Error Minimized “Preloaded” (TEM) Tracker - this is a prototype.

However, before proceeding this neat little design may be preferable for some readers. It is small and compact and can be driven using the Arduino electronics described later in this post, if desired. I really like what Gary Seronik has done with this design.

This how to is intended for a wide audience, consequently, there is lots of info and does not assume previous experience…

Mathematics of the Double Arm Drives at Dave Trott’s site - for the mathematically literate.

A few useful notes?

The unit had to be easy to build and accurate. A steel rule, sharp pencil, basic tools and a small drill, should be all that’s needed. Having said that, built-in adjustments can be used to fine tune performance to overcome minor fabrication errors.

I’ve provided as much detail as possible, along with the Arduino code, PCB template and Eagle board, for those who would like to have a commercially made Arduino shield.

In hindsight, the conventional layout is best - the camera arm, as shown in the images of the prototype, is not too stable and needs restraining to prevent the camera and lens toppling.

Although stepper motors are reliable and accurate, vibration can be a problem. A solution is gearing, which also increases torque at the drive shaft or using an Easy Driver with micro stepping.

Together, the dimensions of the tracker and packing the camera arm hinge with 4 thicknesses of 80GSM A4 paper (0.4mm), improves tracking overall.


Image Processing

Linux/MacOS RAW image preprocessing bash script with graphical interface and instructions. This should properly calibrate your RAW images, preparing them for deBayering, alignment and stacking.

The reader may want to postprocess their images. A low cost solution is GIMP, however, Deep Sky Stacker and Star Tools is a more sophisticated image processing solution.

Basic image processing Part 1
Basic image processing Part 2

TEM Tracker

Front and rear views - the reduction drive is more effective. Increasing torque at the drive screw and minimizing stepper motor resonance.


The Lagoon Nebula M8 and M20 the Triffid Nebula. Composite of 9, 30 second frames.Tail of Scorpio toward the centre of the Galaxy - M7, M6, the Butterfly Cluster and Cats Paw Nebula - 21 30 second frames. Taken with a FujiFilm XPro1, 60mm, f/2.4, iso800 and preprocessing in Pixinsight (Deep Sky Stacker is free) and post processing in Star Tools. I went to the trouble of taking bias, dark and flat calibration frames.

The Equatorial Wedge (EW) provides adjustment of altitude (latitude), 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, as shown above.


For simplicity of construction the Conventional Layout is recommended. Accurate dimensions and ensuring that the Tracker is flat when closed will ensure that it performs as expected. 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 the appendix;

Design and performance testing

The dimensions of the TEM Tracker provide for very accurate tracking in the first 15 to 20 minutes of operation and subsequent tracking error is minor to 60 minutes. A design goal was accurate tracking for up to 60 minutes. In practice, performance is very accurate up to 90 minutes.



Some helpful 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 centers should line up when the Tracker is closed, except that the Camera-arm hinge is slightly elevated. The performance of the Tracker is predicated on this arrangement - its the zero datum.

temrotationpoints.jpg and riser detail.

Straining at Gnats

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 tpm 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 and 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 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.

How did it shape up - 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 - true!

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

To show that the images are aligned and verify the ‘authenticity’ of tracking, in-camera software (CHDK) was used to combine/stack the Spica images. Compare the 5 sub exposures.

Spica Astro-TEM-20110603-SpicaCompositeTestImage.jpg

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 ‘Arduino’ board, fitted with a motor shield provides very accurate and consistent motor speed. This arrangement was used to test the tracker. Alternatively, Google other types of conventional circuitry.

Polar Alignment

Planning is the key to acquiring quality exposures, which depends, in part, on proper polar alignment.

Device leveling, latitude setting and finding True North or True South (depending on hemisphere) is essential to accurate polar alignment - finding TN or TS can be the most difficult and frustrating nightly chore. Setting up references/datums during the day minimizes efforts in the dark when we should be imaging.

If you have access to Google Maps. TN/TS can be referenced to natural lines, buildings or fence lines, by measuring the angle between a reference line and TN/TS (which is, of course, vertically up and down the page (screen shot)).

Locate two legs of the tripod on the reference line and the third perpendicular to the reference line. Now point the axis of the drive arm hinge to TN/TS; that is, the angular difference between the reference line and TN/TS measured from Google map.

Next level the azimuth/base board of the tracker, set the latitude at your location by adjusting the altitude board up or down and check alignment with TN or TS for accuracy.


Having completed this task once, nightly set up at the same location and datums, perhaps marked on the ground, is a 3 minute job. If you have a GPS equipped phone/tablet, record the latitude and longitude of the location.

A polar alignment scope, if you have one, is the traditional polar alignment method - wide field imaging at short focal lengths is tolerant of small polar alignment error.

Shoot an image and check for drift - elongated stars. Make very small adjustments in azimuth (rotating the azimuth board) and latitude (adjusting the angle of the altitude board) to further improve polar alignment. That is, until stars are round for the chosen exposure time.

I haven’t tried this and you may prefer the curved rod tracker design.

Construction Notes


Providing the Critical Dimensions, Points of Rotation and other design conventions are observed, performance should be consistent in various configurations.

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, in particular the placement of hinges.

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.

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 - 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).

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.

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.


Note: Drive Shaft & Nut Assembly (replaced with a nylon sleeve and plastic tube insert tapped to 6mm)

Azimuth and Altitude

If intending to mount the drive on an adjustable (sturdy) tripod, the azimuth board may be omitted.


Camera Arm

Be careful of heavy telephoto lens that may topple the Camera Arm - restraint is necessary.


EDIT: Update - for L293D read L293NE, which seems to run the stepper smoothly. Half stepping included in Arduino code - see acknowledgements for author credit.

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. 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 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 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.

Ebay has a plethora of unipolar 5v geared stepper motors for sale from Hong Kong (28BYJ-48 - advertised at 64 steps, it actually has 32 steps/rev and 1/64 gear ratio) - set the stepper speed and change the motorStep line of your Arduino script to suit your motor. Otherwise steppers come in various grades and steps - gearing of some type is highly recommended to reduce resonance.

Arduino motor shield


Arduino Resources

Direction and Kill Switch wiring


Arduino Code (incl. half stepping)



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 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 provides very accurate tracking up to 90 minutes, consistent with accurate polar alignment.


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”.


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. The spreadsheet enabled experimentation with various component dimensions.

Mike Mohaupt - whose Compact Imperial design prompted further research to optimise performance, which provided the data for 1/4” 20tpi dimensions.

Open source software (Linux) - Qcad.

Eagle PCB software and the Arduino Decimilia provided the tools to develop the electronics platform to drive the stepper motor.

Arduino half step library Note: The Stepper.cpp file above has been modified to suit Arduino 1.x (WProgram.h changed to Arduino.h)

Not forgetting Stellarium an excellent open source desktop planetarium.

GIMP the image manipulation program, another open source astronomical imaging tool.

Ivo Jaeger’s Star Tools


The CHDK developers and many excellent sites devoted to digital astrophotography and Double Arm Drive design.


This work is licensed under a Creative Commons Attribution-Noncommercial 2.5 Australia License.


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