SatNOGS Rotator v3
SatNOGS Rotator v3  

Rotator Information  
Type:  Az/El 
Cost:  ~200 USD 
Release Information  
Status:  Beta 
Latest Release:  Torx Flathead (v3.0.1) 
Repository:  [1] 
Documentation:  [2] 
Contents
Intro
v3 marks a major rehaul of the SatNOGS Rotator design, with learnings from v2 applied. You can see a lot of the thinking and background research that was conducted prior to v3 development in this thread.
Also in this list is presented different rotators, either commercial or DIY builds.
Specifications
SatNOGS v3 Rotator  
Plastic Parts  26 
Non Printed Parts approx.  345 
Cost  ~ $220 
Controller Electronics  SatNOGS Rotator Controller 
Type  AZ/EL (possible X/Y) 
Motors  2x NEMA 17 Stepper or 2x DC Motors 
Frame Material  Aluminum Tslot 20x20 
Speed (deg/sec)  ? (Stepper motor), ? (DC motor) 
Torque (Nm)  ~? (Stepper motor), ~? (DC motor) 
Brake Torque (Nm)  ? 
Dimensions (mm)  306.5x197x142.5 (AZ/EL) 
Weight (kg)  6.2 
Pro  
Con  
Brake Torque
The greatest force the tracker needs to withstand is the force created by strong wind. The worst case is when one antenna is elevated at 90 degs, facing the direction of the wind. We based our calculations on an article found online after comparing it to others. We “translated” the second table in metric (because we don’t understand imperial and because we needed same units system in our calculations)
Method  Wind Zone(km/h)  Height (m)  Pressure(N/m^2) 

EIA222C  160  N/A  1280 
EIA222F  128  14  1260 
EIA222F  128  21  1390 
EIA222F  128  30  1500 
UBC'97  128  14  1290 
UBC'97  128  21  1160 
UBC'97  128  21  1390 
UBC'97  128  30  1260 
UBC'97  128  42  990 
UBC'97  128  42  1360 
Generic Formula  150  N/A  1270 
and we applied the worst case model (EIA222F) in 3 different antennas: in the biggest one of our designs, and in two others, for which we obtained data from yaesu G800 rotator manual at page 3. We assumed that antennas are mounted in 1m away from the azimuth axis. For our antenna with 2m length (actual, not wavelength), made by 2cm square tube, the generated torque was ≈600Kg*cm. For the 144MHz 10elements Yagi from the article is ≈6000Kg*cm and for the third 430MHz, 12elements Yagi is ≈1800Kg*cm
Moment of inertia
Now for the moment of inertia: (for all installation methods we assumed that antennas are counterbalanced in the elevation axis) the worst case scenario here is to use two 3kg (our designs are less than 1kg) back mounted yagis with 3kg counterbalances both mounted in 0.75m away from azimuth axis. The torque you need in order to accelerate this system from ω=0deg/s angular velocity to ω=5deg/s (the math about angular velocity is below) in one second is about 60kg*cm.
Note: we suppose that the mass of antennas is near to the altitude axis, so the torque of this axis that is needed to accelerate is approximately 0.
 M1: torque of Azimuth axis
 L: length of center of mass of antennas from azimuth axis (0.75m)
 m: mass of antennas and of counterweight (3kg + 3kg = 6kg)
 I: moment inertia
 a: angular acceleration of azimuth axis 5deg/s^2
 I = I1 + I2 = m*L^2 + m*L^2 = 2*m*L^2 = 6.75 kg*m^2
 M1 = I*a = 6.75kgm^2 * 0.087rad/s^2 = 0.58 Nm = 5.8 kgm = 58 kgcm
Angular velocity
(How well do you remember trigonometry?)For the angular velocity max needed in altitude axis the things are straightforward. The closer is the satellite the larger the velocity. According to the wikipedia article about LEO, the lowest height limit is 160 km and the speed unit to orbit earth in this altitude is 7,8 km/s. As a result, maximum velocity in ALT axis is 2,8 deg/s. In ALT AZ rotator design there is a well known limitation: the closer something passes near zenith the biggest gets the velocity of the AZ axis. Therefore, we have analyzed this problem to figure out the optimal velocity and how high we are allowed to track a target in relation to AZ velocity. The picture below illustrates a ground station B which tracks a satellite Γ in X degrees altitude. The satellite velocity at this point is vertical to the screen (page) plane.
The equations that lead to maximum altitude at which we can track in relation to AZ angular velocity are
 ω : angular velocity of AZ DOF in rad/s
 H = ΑΕ + ΕΓ : Minimum Height of LEO, 160 km
 R = ΑΕ : Radius of Earth, 6500 km
 u : linear velocity of satellite that rotates in 160km height is 7.8 km/s
 ΒΔ = u / ω : ΒΔ in km
 α = atan(ΒΔ / R)
 δ = π  α
 γ = asin( sqrt(R^2+ΒΔ^2) * sin(δ) / (H+R) )
 ά = π  δ  γ
 ΓΔ = (H+R) * sin(ά) / sin(δ)
 χ = atan(ΓΔ / ΒΔ)
Below you can see the plot of the equations mentioned above, where horizontal axis represents angular velocity (ω) in deg/s and vertical axis shows the max track altitude (χ) for lower bound of LEO.
After studying this diagram, we came up to the conclusion that an angular velocity of 5 deg/s is adequate. For this decision, we took into consideration the main lobe of antenna (Δ3db) which in most situations is about 20 deg.
General Specifications
Together with the above mentioned specifications, we would also like for the 3rd version of SatNOGS rotator to be:
 inexpensive (less than €300, if possible)
 lightweight and portable (~6Kg, size:~300x~150x~150mm)
 rigid and durable
 easy to build and fix (try to use easily available materials)
 weatherproof
 electromagnetically shielded, so that noise in reception is reduced
 accurate (<1deg, backslash reduction and use of encoders at the axis)
Sourcing
3d Printing at a Fab Lab or your local hackerspace: If you don't have your own 3d printer, then a local Fab Lab or hackerspace may be able to do it for you. Fab Labs and hackerspaces are places that have invested in the machinery and you can take the designs to them. Generally they need .stl files to import into the software that runs the machines, but this should be discussed with the Fab Lab or hackerspace. You then pay for the material, time or a combination of the two for each of the parts or any other agreement in place.
Most people building the rotator have had success builds with simple ABS material for the 3D printing parts.
T Slot  If you don't want to cut the pieces yourself, then you may be able to find a supplier that will do this for you. (Here's one in the United Kingdom.)
Hidden corner connectors  AliExpress gave the cheapest supplier
A good US source is MISUMIUSA; they will also cut to length. MISUMI has several other global locations [3].
Beware, the 20series Tslot from 80/20 Inc. in the US has slots that are only 5.2mm wide. The hidden corner connectors from e.g. AliExpress will not fit.
Stepper Motors  eBay
Belts  eBay
Fixings / Pipe  eBay
Part Fabrication
Most of the parts could be fabricated by a FDM 3Dprinter. Some parts have only 2D geometry so could be fabricated by a laser cutter. Other parts have modifications of common(hardware) parts like threaded rods or aluminum pipes.
Build Sequence
 Make sure you have all parts
 Follow the instructions for mechanical assembly
 Once mechanical assembly is ready, construct the SatNOGS Rotator Controller and connect it to the assembly.
 You are ready! Proceed with testing.
Mechanical Analysis [WIP]
Horizontal distance between pulleys (P1, P2) is 58mm. Vertical distance between pulleys (P1, P2) is w = 9.5mm.
Pulleys and Belt are GT2, 2mm pitch. Belt width, 6mm. Belt thickness, 1.38mm (0.76 tooth).
Wrap angle in both pulleys is larger than 60deg. At least 6 teeth in contact with the pulley at any given time. In practice that means you want a minimum of a 12 tooth pulley, and usually try to get at least 18 teeth.
Outer Diameter of pulleys:
P(T)  OD(mm)
16  10.2
20  12.7
36  22.9
40  25.5
Belt calculation (according to calculator):
Ratio  P1(T)  P2(T)  Belt(T)  L(mm)
2.25163685/8658.65/59.66
1.8203686/87/8857.78/58.78/59.78
2.5164087/8858.5/59.5
2204089/9058.65/59.66
Motor Maximun noload speed, 200RPM = 1200deg/s Motor Maximum stalltorue, 1.2Nm
Position of idler do not care, or min 1.3*P1, max 1.5*P1 (for 20T, ~16mm/~20mm).
Belt gear selection:
 20/36 with 1.8 ratio and 86T/172mm belt without idler
 20/40 with 2 ratio and 90T/190mm belt with idler
To calculate Deflection force, (page T31, sdp  designguidelines)
 Y = 2.05, Tst = 1.3kg
 span length, t = 57.64mm
 Belt pitch length, L = 180mm
 Fd,min =
 Fd,max =
 2.8kg Working Tension [shapeoko  Belts and Pulleys](https://www.shapeoko.com/wiki/index.php/Belts_and_Pulleys#Tensile_Cord_Materials)
P3
/ \
P1 P2

P4P5
 Determination of design load
According to perfomance graph of DC motor, the optimal output power is Tm = 0.6Nm with efficiency of 0.2 and 100RPM = 600deg/s. Select a service factor of 1.5 (service factors between 1.5 and 2.0 are generally recommended when designing small pitch synchronous drives). Tpeak = SF*Tm = 1.5*0.6 = 0.9Nm
 Choice of belt pitch
Due to backslash and accuracy in both directions of movements and volume constrains, we choose GT2, pitch 2mm.
 Check belt pitch selection based on individual graphs
Due to Tpeak = 0.9Nm Noload speed,(Speed of fastest shaft) = 100RPM = 600deg/s GT2 pitch 2mm belt is the better solution for our application.
 Determine speed ratio
Speed ratio 1.82.25 according to specification of output rotation speed of 5deg/s.
 Check belt speed
V(m/s) = 0.0000524 x pulley PD (mm) x pulley rpm = 0.066548m/s Belt speeds up to 6,500 fpm (33.02 m/s) do not require special pulleys.
 Determine belt length
Table 'Belt calculation (according to calculator)' Teeth in mesh: 9
 Determine the belt width
From Table 43 torque = 0.17Nm Length Correction Factor = 0.9 width multiplier = 1.00 torque*Length Correction Factor*width multiplier = 0.17*0.9*1.00 = 0.153Nm Teeth in mesh: 9 Tpeak = 0.9Nm, so belt width is nice for our application
 Check the number of teeth in mesh
Teeth in mesh: 9 according to calculator
 Determine proper belt installation tension
SECTION 10, on page T50, look at 'To calculate Deflection force, (page T31, sdp  designguidelines)'
 Y = 2.05, Tst = 0.812*DQ/d + mS^2 = 12.8lb + 0 = 5.8kg
 DQ = Tpeak = 0.9Nm = 7.9lbin
 d = 12.7mm = 0.5in
 S = (0.5*100/3.82)/1000 = 0.0131ft/min
 m = 0.039
 span length, t = sqrt(CD^2  (PDpd/2)^2) = 57.64mm
 Belt pitch length, L = 180mm
 t/L = 0.32
 Fd,min = 0.8lb = 0.36kg
 Fd,max = 0.9lb = 0.41kg
 Safety factor 1.5
 P2 timing pulley torque  Maximum radial load of timing belt ball bearing 625zz
Tpeak = 0.9Nm TorqueP2 = 2*0.9Nm = 1.8Nm, PDp2 = 25.5mm Radial static load of 625ZZ is 0.38kN T39
 Maximum thrust load of timing belt ball bearing 625zz
 Maximum radial and thrust load of output ball bearings 6008zz
Calculate or evaluate correct loads for deep groove ball bearings radial static load = 11.6kN thrust static load = 0.7*11.6kN = 8.12kN This type of construction permits the bearings to support relatively high thrust load in either direction. In fact the thrust load capacity is about 70% of the radial load capacity. A ball bearing primarily designed to support radial load can also support high thrust load; because only few balls carry the radial load, whereas all the balls can withstand the thrust load.
 Maximum selflocking or backdrivable torque of gear box (according to more weak component)
It necessary to achieve [specs](https://community.libre.space/t/satnogsrotatorversion3/226), 60Nm (6Kg in 1 meter)
 Nominal torque of drivable torque of gear box (according to more weak component) and maximum rotational speed of gear box
Notes:
 sdp distance calculator
 belt GT26mm wide, 172mm
 belt GT26mm wide, 180mm
 idler pulley, noteethID3mmOD18mm
 brecoflex  designguidelines
 shreegeeimpex  designguidelines
 sdp  designguidelines
Worm Gear Box Calculations
 Gear ratio: i12 = 30
 Angle between axis of gears: δ = 90 deg
 Number of threads in worm: If i12 >= 30 then z1 = 1
 Number of teeth in worm wheel: z2 = i12*z1 = 30
 Center distance: initial case a = 45.5 mm
 Worm reference diameter: AGMA d01>= 11.5*(a/25.4)^0.875 = 19.15 mm, so d01 = 19.5mm
 Worm wheel reference: d02 = 2*a  d01 = 71.5 mm
 Axial module: ms = d02/z2 = 2.38 , so ms = 2.5
Recalculate d02, a with new axial module
 d02 = z2*ms = 75mm, a = (d02+d01)/2 = 47.25mm
 Axial pitch: ts = π*ms = 7.854mm
 Reference lead angle: γ0 = atan(d02/(i12*d01)) = 7.3 deg
 Worm tip diameter: dk1 = d01 + 2*hk = 24.5mm
 Worm teeth reference addendum in axial section: hk = hk* *ms = 2.5mm
 Worm tooth reference addendum coefficient: hk* = 1
 Worm root diameter: df1 = d01  2*hf = 13.5mm
 Worm tooth reference dedendum: hf = hf* _ms = 1.2_ms = 3mm
 Dedendum coefficient: hf* = 1.2
 Worm length: L = 2.5_ms_sqrt(z2+2) = 35.36mm
 Worm tooth thickness: smx1 = smx1* * ts = 3.927mm
 Tooth thickness coefficient: smx1* = 0.5
 Normal pressure angle: aon = 20 deg
 Worm wheel throat diameter: dk2 = d02+2*hk = 80mm
 Worm wheel root diameter: df2 = d02  2*hf = 69mm
 Worm wheel outside diameter: de2 = dk2 + 2*mx = 83.5mm
 Worm wheel tooth external addendum: mx = n*ms, 0.4<=n<=1.5
 Effective worm wheel face width: b2H,max = sqrt((2_a  df2)^2  (2_a  de2)^2) = 23mm
Test Sequence
Test sequence needed