This is the twenty-second post in the LocalPapa Notes dev-log series. Post twenty-one was an inertially stabilized platform handbook, and its Layer 3 laid out a complete torque formula chain: from aerodynamic drag to rotational inertia, multiplied by a friction ratio and a safety factor, then divided by Kt to get current. The whole chain can be worked out on paper, or checked against the motor sizing calculator.
But that chain is deliberately flattened. T_friction is handled by a single 15% ratio, Cd is filled in as 0.45, SF as 2.5, and Kt is treated as a constant — and each of those four numbers sits on top of its own research field. The handbook's goal was to let you compute something. This post's goal is to show you who researches each number, what they found, and when you can no longer use the simplified version.
If you've just read the handbook and the concepts click but you have no hands-on experience, this post is that handbook's literature index.
How this literature sorts out
Torque-analysis papers blur together easily — the titles all look like "Modeling and Control of Some Gimbal," while the problems they actually solve differ enormously. Sorting them by which term of the handbook's formula chain they refine clears this up fast:
- Cluster 1: rigid-body dynamics and cross-axis coupling → refines
T_inertia = J·α
- Cluster 2: friction torque modeling → refines
T_friction = 15%
- Cluster 3: cable harness drag → a term the handbook never listed separately
- Cluster 4: aerodynamic torque → refines
Cd and L_arm inside T_wind
- Cluster 5: motor-side torque non-idealities → refines
T = Kt·I
- Cluster 6: margin standards → refines
SF = 2.5
Cluster 6 is different in kind from the rest: the first five are academic papers, the sixth is aerospace engineering standards. For someone without experience, cluster 6 is arguably the one to read first — because it tells you directly how to derive a safety factor rather than guess at one.
Cluster 1: Rigid-body dynamics — J·α is one term of a much larger equation
The handbook's T_inertia = J·α assumes three things: a single axis, perfect balancing, and a diagonal inertia tensor. What this literature does is remove those assumptions one at a time.
Ekstrand, B. (2001). Equations of Motion for a Two-Axes Gimbal System. IEEE Transactions on Aerospace and Electronic Systems, 37(3), 1083–1091.
This is where the whole line starts, with 100+ citations. It derives the full equations of motion for the yaw–pitch two-axis configuration, but explicitly assumes no mass unbalance and no inertia disturbance. In other words, it gives you the clean-case baseline. Its value isn't in how much it covers — it's that it pins down what the equations look like in the ideal case, which is the reference every later paper measures its deviations against.
Abdo, M., Vali, A. R., Toloei, A. R., & Arvan, M. R. (2013). Research on the Cross-Coupling of a Two Axes Gimbal System with Dynamic Unbalance. International Journal of Advanced Robotic Systems. DOI: 10.5772/56963
This one drops Ekstrand's assumption. It derives the torque relationships from the base body's angular motion and dynamic unbalance, then wires the two axes' stabilization loops together through a cross-coupling unit, validating in MATLAB/Simulink and SimMechanics.
Two key conclusions: coupling affects both the azimuth and elevation channels and impacts system stability; and the higher the base angular rate, the more pronounced the overshoot in gimbal response. The second point matters especially for airborne use — the harder the vehicle maneuvers, the higher the price of coupling, and none of that appears anywhere in the handbook's formula chain.
It's worth distinguishing two kinds of unbalance here. Static unbalance is the center of mass sitting off the rotation axis (what Layer 5 of the handbook covers — balancing fixes it). Dynamic unbalance is a non-diagonal inertia tensor, meaning the payload's principal axes of inertia aren't aligned with the rotation axes. Even with static unbalance driven to zero, dynamic unbalance still produces coupling torque under rotation.
Dynamic Modeling and Coupling Characteristic Analysis of Two-Axis Rate Gyro Seeker (2018). International Journal of Aerospace Engineering, Article 8513684.
Puts cross-coupling, mass imbalance, and disturbance torque into a single model, and identifies the servo motor transfer function in the frequency domain. For anyone building a full model, its value is in demonstrating how modeling connects to parameter identification — equations without parameters are an empty model.
Huang, Q., et al. (2024). Modeling and Control of a Two-Axis Stabilized Gimbal Based on Kane Method. Sensors, 24(11), 3615.
This paper addresses a methodological pain point. Modeling a two-axis gimbal with Newton–Euler requires analyzing constraint forces at the hinges; Lagrange sidesteps constraint forces but requires solving second-order differential equations and is computationally inefficient. It uses the Kane method instead — deriving generalized velocities and partial velocities directly from generalized coordinates, then analyzing generalized active and inertial forces — trading into a simpler model structure that computes faster.
Mapping back to the handbook: Layer 5 already disclosed honestly that "this layer is not in Hilkert's paper." These four papers fill that gap. The practical judgment: if your vehicle's angular rates are low and your payload is well balanced, the single-axis J·α estimate is enough. If the vehicle makes large maneuvers, or the payload is irregularly shaped (principal axes hard to align), the coupling terms can't be ignored, and you need to move toward Ekstrand's or Kane's full model.
Cluster 2: Friction torque — 15% is only a placeholder
The handbook writes friction as "15% of the sum of the first two terms," noting it's an empirical ratio. What this literature does is replace that 15% with an actual model.
The evolution of the models is worth getting straight first, or the papers won't parse:
- Coulomb + viscous: the simplest static model, friction as a function of velocity alone. Discontinuous at zero crossing, which makes simulations chatter.
- Dahl (1968): introduces an extra state variable, describing friction in the pre-sliding regime through micro-displacements. Fixes the zero-crossing problem, but has no Stribeck effect.
- LuGre (Åström and Canudas-de-Wit): extends Dahl by putting the Stribeck effect back in. It can reproduce stick-slip, the pre-sliding hysteresis curve, friction lag in the sliding regime, and the break-away force at the static-to-dynamic transition.
Why do gimbals care so much? Because a gimbal spends most of its time in low-speed micro-motion — stabilization is fundamentally a continuous stream of small counter-corrections, so velocity hovers near zero crossing. And the Stribeck regime (where friction falls as velocity rises, at low speed) sits exactly there. That's also why the linear assumption "friction is a fixed ratio of the total" fails most easily on gimbals specifically.
Jia, R., Nandikolla, V. K., Haggart, G., Volk, C., & Tazartes, D. (2017). System Performance of an Inertially Stabilized Gimbal Platform with Friction, Resonance, and Vibration Effects. Journal of Nonlinear Dynamics, 2017, Article 6594861. DOI: 10.1155/2017/6594861
This one unusually puts friction, structural resonance, and vibration into a single system model, then compares four grades of gyro against overall performance. Its main contribution is really sensor selection — but for torque analysis, the value is in showing these three factors don't simply add independently: mechanical resonance amplifies friction-induced disturbance, and the gyro's noise floor determines whether you can even observe that amplification.
Two-Axis Optoelectronic Stabilized Platform Based on Active Disturbance Rejection Controller with LuGre Friction Model (2023). Electronics, 12(5), 1261. DOI: 10.3390/electronics12051261
Stabilization of two-axis line-of-sight system using active disturbance rejection control (2025). Multibody System Dynamics. DOI: 10.1007/s11044-025-10110-z
These two represent the current mainstream: LuGre for modeling, ADRC for compensation. The latter implements a separate LuGre model for each joint of the platform, which is worth noting — friction parameters are per-axis. The azimuth and elevation axes have different bearing arrangements, different preloads, different cable routing. Using one parameter set for both is wrong.
Unified Model of Disturbances Acting Upon Gimbal Seeker in Anti-Tank Guided Missile. Journal of Automation, Mobile Robotics and Intelligent Systems (JAMRIS).
This paper does something few others do: it links LuGre's Coulomb component to the normal force induced by the missile's lateral acceleration. That is, friction torque isn't a fixed parameter — it varies with maneuvering load. The same holds for airborne gimbals: during high-g maneuvers, bearing normal forces rise, friction torque rises with them, and that is precisely when you most need stabilization performance.
Mapping back to the handbook: 15% is a reasonable starting point for early design, but know its two limits. First, LuGre has six parameters (σ0, σ1, σ2, Fc, Fs, vs) to identify — that's measurement work, not table-lookup work. Second, friction is not a fixed fraction of total load: on a high-speed airborne gimbal where aerodynamics dominate, 15% may be an overestimate; on a low-speed, low-drag ground or indoor application, friction may be the dominant term and 15% badly underestimates it. The test is simple: look at the T_wind share in the handbook's Layer 3 breakdown. If T_wind is under half, friction is a term you have to measure seriously.
Cluster 3: Cable harness drag — the term the handbook never listed separately
The handbook folds cable harness drag into the 15% T_friction. But the central claim of this literature is that cable drag is physically not friction — it's a spring.
Dynamic simulation and disturbance torque analyzing of motional cable harness based on Kirchhoff rod model (2012). Chinese Journal of Mechanical Engineering, 25(2), 346–354. DOI: 10.3901/CJME.2012.02.346
This paper builds a dynamic model of a moving cable harness using Kirchhoff rod theory, accounting for geometric nonlinearity and simulating the internal bending and torsional restoring torques — so that disturbance torque can be predicted at the cable-routing design stage. Validation compares simulation against measurements from a binocular-vision optical measuring instrument.
Why reach for something as heavy as rod theory? Because harness behavior is strongly angle-dependent — the same cable produces very different restoring torque at mid-travel versus at the travel limits, with hysteresis. Approximating it with a constant friction term means mistaking a position-dependent spring for a velocity-dependent damper. The two behave completely differently in a control loop: friction makes trouble near zero crossing (limit cycles, stick-slip), while harness spring torque makes trouble at the travel limits, and the position loop sees it as a sustained load.
Yu, et al. (2017). A Uniform Method of Mechanical Disturbance Torque Measurement and Reduction for the Seeker Gimbal in the Assembly Process. Mathematical Problems in Engineering, 2017, Article 2179503. DOI: 10.1155/2017/2179503
This paper comes at it from a completely different angle — the production line. It establishes a model relating assembly parameters to mechanical disturbance torques, builds a measuring system that directly measures the torque motor's driven torque, then adjusts each disturbance-related assembly parameter with the goal of flattening and minimizing that driven torque.
For someone without experience, this may be the more valuable of the two, because it admits something important: a large share of disturbance torque is assembled in, not designed in. Same drawing, same parts, different assembly technique — and you get different bias and fluctuation in disturbance torque. That explains why measured values so often fail to match the model: the model computes the design value, and what you measured is this particular unit's assembly outcome.
Mapping back to the handbook: if your gimbal has a slip ring, cable drag can usually stay inside the 15%. If the harness crosses the rotation axis directly (common on small gimbals), this term deserves its own estimate — and it must be measured across the full travel, not just at center.
Cluster 4: Aerodynamic torque — where Cd = 0.45 comes from
The handbook's Layer 3 example works out T_wind at 85% of the total — the dominant term by far. Being dominant, its assumptions are the ones most worth checking.
Gordeyev, S., & Jumper, E. J. Aerodynamics of a Generic Optical Turret. Journal of Aircraft. DOI: 10.2514/1.36804
The baseline reference for optical turret aerodynamics, studying the flow around a sidewall-mounted hemisphere-on-cylinder configuration at Mach 0.3–0.5. This line of work is mainly concerned with aero-optics (how flow disturbance degrades imaging), but the flow structure itself is also what determines the forces and moments acting on the turret.
Aerodynamic Investigations of UAV Sensor Turrets — A Combined Wind-tunnel and CFD Approach (2021). AIAA SciTech Forum. DOI: 10.2514/6.2021-1535
This is the most useful one for torque estimation. It runs unsteady RANS on eight realistic EO/IR sensor turret geometries, validated against wind-tunnel drag data.
The key finding: realistic turrets have drag coefficients more than 40% higher than a clean hemisphere-cylinder. The cause is that real turrets have protruding window surfaces and rotational-mechanism edges, and those sharp features drive substantial flow separation; the simulations also show horseshoe and wake vortices. Related work in the same line notes that EO/IR turrets and fixed landing gear are the main reasons UAV parasitic drag runs so much higher than on manned aircraft.
Wind-tunnel and CFD investigations of UAV landing gears and turrets — Improvements in empirical drag estimation (2020). Aerospace Science and Technology.
The same group feeds their CFD and wind-tunnel results back into improved empirical drag estimation formulas — the missing layer between table-lookup and full CFD.
Mapping back to the handbook: this literature offers two corrections, but they are not equally important.
First, Cd may be underestimated. 0.45 is a typical clean-bluff-body value; if your gimbal has a protruding window and exposed rotational seams, the real value may be 40%+ higher. The conservative move is to raise Cd, or to hand that uncertainty to SF (see cluster 6 — that's exactly what the standards do).
Second, and more important: the real error source is probably L_arm, not Cd. The handbook itself computed that L_arm sensitivity far exceeds J sensitivity. And L_arm physically means the distance from the center of pressure to the rotation axis, not from the geometric center — and on a bluff body with separated flow, the center of pressure moves with angle of attack. That is not something a ruler can measure.
So the right move for accuracy isn't to go back and fix Cd — it's to take the hinge moment directly from CFD or the wind tunnel. CFD outputs moment about a specified axis natively; the Cd × A × L_arm decomposition isn't needed at all in between. ½ρv²·Cd·A·L_arm is the estimator for early design when you have no CFD. Once you have CFD results, it should be replaced, not calibrated.
Cluster 5: The motor side — Kt is not a constant
The handbook's Layer 4 converts torque to current with T = Kt · I and warns about the Kt/KV unit trap. But there's a second trap: Kt itself fluctuates with rotor angle.
Li, H., Yang, S., & Le, Y. (2023). Torque Ripple Minimization of Low-Speed Gimbal Servo System Using Parameter-Optimized ESO. IEEE Journal of Emerging and Selected Topics in Power Electronics, 11, 2094–2103.
Targeting the gimbal servo system of a control moment gyro (CMG), it proposes composite control with sliding mode in the speed loop and PI plus feed-forward compensation in the current loop. What's notable in the approach is its use of three independent ESOs, estimating disturbances on the d-axis current, the q-axis current, and the load torque separately — splitting electrical-side disturbance from mechanical-side load disturbance rather than lumping everything into one total disturbance.
Speed Ripple Reduction of Direct-Drive PMSM Servo System at Low-Speed Operation Using Virtual Cogging Torque Control Method (2020). IEEE Transactions on Industrial Electronics.
Straight to the point: at low speed, cogging torque is the main factor degrading drive performance, and can even induce speed oscillation. Cogging torque comes from stator slotting and is periodic in rotor position; add non-ideal back-EMF waveforms, current measurement error, and phase imbalance, and together they give you periodic torque ripple.
Anti-Disturbance Gimbal Control via Adaptive Proportional-Integral-Resonant Controller and ESO for Control Moment Gyroscope with Vibration Isolator. Actuators, 15(4), 215.
Uses a PIR (proportional-integral-resonant) controller aimed at periodic disturbance at specific frequencies — a natural fit for torque ripple, since ripple frequency is a known multiple of shaft speed and a resonant controller can put high gain exactly there.
Mapping back to the handbook: treating Kt as constant is correct at the sizing stage — you're asking whether the motor's average torque suffices, and ripple barely affects the average. But the assumption fails at the performance verification stage: ripple gets filtered out by rotational inertia at high speed, but at low-speed micro-motion it turns directly into LOS jitter. This is why post twenty emphasized that gimbals almost always use slotless frameless direct-drive motors — not for torque density, but to eliminate cogging at the source. Put another way: if you use a slotted motor, this literature is something you will come back to. If you picked slotless frameless from the start, your component choice already routed around the entire problem.
Cluster 6: Margin — how to actually derive SF = 2.5 (read this first if you lack experience)
The first five clusters are academic papers. This one is engineering standards. The problem they solve: what should that SF = 2.5 in the handbook actually be, and on what basis.
NASA-STD-5017B (2022). Design and Development Requirements for Mechanisms.
This standard defines torque margin as an equation:
torque margin = T_avail / (Σ Kf·Tf + Σ Kv·Tv) − 1
T_avail is the minimum torque the mechanism can generate under worst-case environmental conditions. The key feature of the denominator is that it splits resistance into two classes, each with its own factor:
Tf: resistances relatively well determined in direction and magnitude (friction and similar)Tv: resistances with high variability and less certainty
And the size of the factor depends on how you obtained the number:
- Obtained via theory or analysis:
Kf = 1.5, Kv = 3.0
- Obtained via test of flight-like hardware:
Kf = 1.25, Kv = 2.0
When test-verified, an operating margin of ≥ 1.0 is required — meaning available torque must be at least twice the weighted resistance.
ECSS-E-ST-33-01C Rev.2 (2019). Space engineering — Mechanisms.
The European counterpart, similar in logic but different in wording: each resistive contributor is first multiplied by its own uncertainty factor, and the total is then multiplied by a motorization factor ≥ 2.0. Likewise, the uncertainty factors are tied to how well verified the number is — for bearing and harness resistive torques, for example, the factor can drop from 3 to 1.5 once measured under thermal-vacuum conditions.
Nalbandian, R., Blais, M., & Horth, R. (2014). A Recommended New Approach on Motorization Ratio Calculations of Stepper Motors. 42nd Aerospace Mechanisms Symposium, NASA Goddard.
Compares how NASA, ESA, and AIAA each compute margin on electrically driven drives, and proposes a correction for stepper motor behavior under low duty cycles. Even if you don't use steppers, the three-way comparison alone is worth reading — it shows that "margin" has no single right answer, just different ways of apportioning uncertainty.
Mapping back to the handbook: the handbook collects every unmodeled uncertainty into one SF = 2.5. The standards split that into two layers.
- Per-term weighting: each resistive term gets its own uncertainty factor, sized by whether that number was computed or measured.
- Overall margin: the weighted total is then multiplied by a motorization margin of roughly 2.
This gives SF two things the handbook doesn't. First, a defensible provenance — you don't guess 2.5, you derive it from a standard, and the derivation is something you can walk someone through. Second, and more useful: a path to bringing SF down. The standards say it outright — for the same resistive term, the factor is 1.5 or 3.0 when analyzed, and 1.25 or 2.0 when measured. So SF isn't a permanently fixed number: the better you measure, the more you can lower it.
For someone without experience, this is the single most useful point in this post: it converts "what safety factor should I use," a question you have no basis to answer, into "was this number computed or measured," a question with a definite answer.
If you only read four
Following the six clusters above, here's a minimal reading order.
- Hilkert (2008) — the methodological skeleton. The source of the handbook's Layer 3 formula chain; establish the overall frame first.
- The torque margin section of NASA-STD-5017B — gives
SF a basis. Shortest of the four and the fastest to put to use.
- Ekstrand (2001) — the dynamics baseline. See what the equations look like in the ideal case, so that any later coupling or unbalance paper has something to be compared against.
- A recent LuGre + ADRC paper (the Electronics 2023 one above, for instance) — see friction go from a 15% ratio to a six-parameter model requiring measured identification.
Save clusters 4 and 5 (aerodynamics, motor ripple) until you know which kind of design you have. Airborne, aerodynamics-dominated gimbal: read cluster 4. Low-speed high-precision ground gimbal: read cluster 5. Reading both is a waste of time.
Three practical notes on reading this literature
The three traps that catch people without hands-on experience:
- Check for a parameter table first. Many papers give equations but no numbers, or report non-dimensionalized results. For sizing work, a paper without concrete parameter values has limited value — you can't check your own numbers against it. Skip to the simulation section and see whether it lists actual values for inertia, friction coefficients, and motor parameters.
- Separate "modeling papers" from "control papers." The titles look alike, but the purposes are opposite. Modeling papers (Ekstrand, the Kane method work) ask where torque comes from — useful for sizing. Control papers (ADRC, sliding mode) ask how to compensate when the torque isn't right — nearly useless for sizing, because they assume the motor is already chosen. It's easy to read a stack of control papers and realize afterward you still have no answer on how big a motor to buy.
- Look at the verification method. Pure simulation, hardware-in-the-loop, and real hardware measurement differ enormously in credibility. This matters especially for friction and cable harness: pure simulation results largely just reflect the parameters the author typed in. The assembly-process paper mentioned above is worth reading in large part because it works backward from real measurements.
Scope of the citations in this post
While compiling this, most publisher sites (IEEE, MDPI, Springer, Wiley, AIAA) were not directly reachable for full text in this environment. So descriptions of each paper's method and contribution are based on abstracts, public information, and search results, and I have not quoted experimental values I couldn't verify directly. The one set of exceptions is the explicitly attributed standard figures (NASA-STD-5017B's Kf/Kv, the ECSS motorization factor) — treat the standards' own text as authoritative, and verify the revision and clause numbers yourself before citing them in a design document.
DOIs and links for every entry are listed below so you can pull the full text through an institutional account or library.
How to work through this with me
If you want to apply any of these models to your own gimbal, having these numbers ready makes the conversation much faster:
- Whether your design is aerodynamics-dominated or inertia/friction-dominated (use the Layer 3 breakdown table in the handbook to decide)
- Bearing arrangement, preload method, and whether cables route through a slip ring or cross the axis directly
- Whether the motor is slotted or slotless frameless
- For each resistive term, whether the number was computed or measured (this determines how far
SF can come down)
References
- Hilkert, J. M. (2008). Inertially Stabilized Platform Technology: Concepts and Principles. IEEE Control Systems Magazine, 28(1), 26–46.
- Masten, M. K. (2008). Inertially Stabilized Platforms for Optical Imaging Systems. IEEE Control Systems Magazine, 28(1), 47–64.
- Ekstrand, B. (2001). Equations of Motion for a Two-Axes Gimbal System. IEEE Transactions on Aerospace and Electronic Systems, 37(3), 1083–1091. Link
- Abdo, M., Vali, A. R., Toloei, A. R., & Arvan, M. R. (2013). Research on the Cross-Coupling of a Two Axes Gimbal System with Dynamic Unbalance. International Journal of Advanced Robotic Systems. DOI: 10.5772/56963
- Dynamic Modeling and Coupling Characteristic Analysis of Two-Axis Rate Gyro Seeker (2018). International Journal of Aerospace Engineering, Article 8513684. Link
- Huang, Q., et al. (2024). Modeling and Control of a Two-Axis Stabilized Gimbal Based on Kane Method. Sensors, 24(11), 3615. Link
- Jia, R., Nandikolla, V. K., Haggart, G., Volk, C., & Tazartes, D. (2017). System Performance of an Inertially Stabilized Gimbal Platform with Friction, Resonance, and Vibration Effects. Journal of Nonlinear Dynamics, 2017, Article 6594861. DOI: 10.1155/2017/6594861
- Two-Axis Optoelectronic Stabilized Platform Based on Active Disturbance Rejection Controller with LuGre Friction Model (2023). Electronics, 12(5), 1261. DOI: 10.3390/electronics12051261
- Stabilization of two-axis line-of-sight system using active disturbance rejection control (2025). Multibody System Dynamics. DOI: 10.1007/s11044-025-10110-z
- Unified Model of Disturbances Acting Upon Gimbal Seeker in Anti-Tank Guided Missile. Journal of Automation, Mobile Robotics and Intelligent Systems. Link
- Dynamic simulation and disturbance torque analyzing of motional cable harness based on Kirchhoff rod model (2012). Chinese Journal of Mechanical Engineering, 25(2), 346–354. DOI: 10.3901/CJME.2012.02.346
- Yu, et al. (2017). A Uniform Method of Mechanical Disturbance Torque Measurement and Reduction for the Seeker Gimbal in the Assembly Process. Mathematical Problems in Engineering, 2017, Article 2179503. DOI: 10.1155/2017/2179503
- Gordeyev, S., & Jumper, E. J. Aerodynamics of a Generic Optical Turret. Journal of Aircraft. DOI: 10.2514/1.36804
- Aerodynamic Investigations of UAV Sensor Turrets — A Combined Wind-tunnel and CFD Approach (2021). AIAA SciTech Forum. DOI: 10.2514/6.2021-1535
- Wind-tunnel and CFD investigations of UAV landing gears and turrets — Improvements in empirical drag estimation (2020). Aerospace Science and Technology. Link
- Li, H., Yang, S., & Le, Y. (2023). Torque Ripple Minimization of Low-Speed Gimbal Servo System Using Parameter-Optimized ESO. IEEE Journal of Emerging and Selected Topics in Power Electronics, 11, 2094–2103. Link
- Speed Ripple Reduction of Direct-Drive PMSM Servo System at Low-Speed Operation Using Virtual Cogging Torque Control Method (2020). IEEE Transactions on Industrial Electronics.
- Anti-Disturbance Gimbal Control via Adaptive Proportional-Integral-Resonant Controller and ESO for Control Moment Gyroscope with Vibration Isolator. Actuators, 15(4), 215. Link
- NASA-STD-5017B (2022). Design and Development Requirements for Mechanisms. NASA Technical Standard. Link
- ECSS-E-ST-33-01C Rev.2 (2019). Space engineering — Mechanisms. Link
- Nalbandian, R., Blais, M., & Horth, R. (2014). A Recommended New Approach on Motorization Ratio Calculations of Stepper Motors. 42nd Aerospace Mechanisms Symposium, NASA Goddard Space Flight Center. Link
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