This is the twentieth post in the LocalPapa Notes dev-log series. Post eighteen covered how to measure LOS jitter, and post nineteen followed up on what the control side can do once you have a measured frequency response. Both posts shared an assumption — the gimbal already exists. This one goes back and fills in the piece before that: how the gimbal itself, at the mechanical level, actually gets designed.
Two foundational papers this series hadn't cited
The motor sizing calculator's methodology has cited Hilkert 2008 throughout, but that paper turns out to have a companion paper in the same journal issue that this series hadn't picked up until now:
Masten, M. K. (2008). Inertially Stabilized Platforms for Optical Imaging Systems. IEEE Control Systems Magazine, 28(1), 47–64. Published in the same issue as Hilkert's paper (vol. 28, no. 1), with a complementary angle — Hilkert covers the methodology of motor selection and control-loop design; Masten covers the overall architecture of stabilized platforms for optical imaging systems specifically. Together they're the actual complete primer on inertially stabilized platform (ISP) design; citing only one is reading half the picture.
The other is the key reference for mechanical architecture selection: Kennedy, P. J., & Kennedy, R. L. (2003). Direct versus Indirect Line of Sight (LOS) Stabilization. IEEE Transactions on Control Systems Technology, 11(1), 3–15. This paper compares two stabilization-loop architectures — direct sensing (the gyroscope is mounted directly on the payload, measuring LOS itself) versus indirect sensing (the gyroscope sits on the gimbal frame, and LOS is inferred through kinematic relationships) — and analyzes how disturbances couple into the LOS in each case. With 161+ citations, it's become the standard reference nearly every subsequent gimbal control paper cites when discussing architecture choice. This is arguably one of the earliest decisions in the entire gimbal design process — where the sensor physically goes directly caps what precision the control loop downstream can ever achieve.
The mechanism itself: why it's nearly always a direct-drive frameless motor
Several industry technical articles (CubeMars, Sierramotion, Automation International) agree on the same point: gimbals are almost universally built around frameless direct-drive torque motors, with no gear reduction. The reason is direct — even a small amount of backlash, or the cogging torque inherent to a slotted motor, is enough to badly degrade pointing precision. Frameless motors, lacking a slotted iron core, have cogging torque approaching zero, and paired with a high-resolution encoder can achieve micron-level smooth precision.
This explains the physical reasoning behind an assumption the motor sizing calculator has made from the start — why it models torque/current relationships for a frameless direct-drive motor rather than the equivalent torque after gear reduction. It also explains why the knowledge base specifically emphasizes torque density (peak torque / weight): in a direct-drive architecture, the motor's own torque IS the final output torque — there's no gear ratio to amplify it — so the margin for error in sizing is much smaller than in a geared system.
The balancing mechanism: decoupling isn't a metaphor, it's a real mathematical relationship
The previous two posts already spent considerable space on why balancing matters. This literature sharpens that into something more precise:
- Simple Design of A Gravity-Independent Mass Balance
- Multi-axis center of mass balancing system for an optical gimbal assembly guided by inertial measurement (US patent)
- Stable imagery from a gimbal mounted camera using mass balance (Raptor Scientific technical note)
The shared conclusion across this literature: when a gimbal is properly balanced, the azimuth and elevation equations of motion decouple — each axis's angular rate depends only on the net torque applied to that axis, no longer influenced by the other axis's motion state. This is almost the textbook version of the "balance before sizing" entry in the motor calculator's knowledge base, just now with precise mathematical language attached: balancing isn't merely "reducing gravity torque" — without it, the equations of motion for the two axes pick up cross-coupling terms, meaning tuning the Pitch axis controller inadvertently affects Yaw axis behavior, and the two axes can no longer be designed or tuned independently. For control system design, that's a catastrophic jump in complexity.
The physical mechanism behind that cross-coupling, when balancing falls short, gets spelled out more concretely in another paper: Research on the Cross-Coupling of a Two Axes Gimbal System with Dynamic Unbalance points to dynamic unbalance — not just static center-of-mass offset, but the fact that if the payload's inertia tensor isn't diagonal (i.e., its principal axes of inertia aren't aligned with the rotation axes), rotation itself generates coupling torque. This goes a step further than the static balancing the previous posts discussed: even if static balancing is done correctly (center of mass on the rotation axis), a misaligned inertia tensor will still produce coupling under dynamic motion.
Dynamics modeling: why classical methods get stuck on two-axis gimbals
Modeling and Control of a Two-Axis Stabilized Gimbal Based on Kane Method (2024) points to a real modeling pain point: building a dynamic model for a two-axis gimbal with classical Newton-Euler or Lagrangian mechanics runs into trouble — the former requires analyzing constraint forces at the hinges, and while the latter sidesteps constraint-force analysis, it requires solving second-order differential equations, which is computationally inefficient. This paper instead uses the Kane method — deriving generalized velocities, deflection velocities, and angular velocities directly from generalized coordinates, then analyzing generalized active and inertial forces — trading in a simpler model structure and higher computational efficiency.
This paper doesn't affect the motor sizing calculator's current formulas (the calculator uses a simplified simple-harmonic-motion peak-acceleration estimate, not a full dynamic model), but it illustrates something: the calculator's formulas are a deliberately simplified design-stage estimate, not a precise dynamic model. If precise controller design is needed — especially anything involving compensating for cross-axis coupling — the work eventually has to reach the level of Kane's method or Lagrangian mechanics. The calculator only answers "how big a motor," not "how to tune the controller optimally."
Sensors and electronics: the other half of the gimbal
The previous two posts both focused on torque, current, and control algorithms. This literature fills in the other half — the electronics beyond the mechanism:
- Sensor fusion: multiple sources agree the standard gimbal configuration fuses gyroscope and accelerometer data through a Kalman filter or a complementary filter before feeding it into the PID loop. Complementary filters carry far less computational load than Kalman filters, making them more common on resource-constrained embedded gimbal controllers; Kalman filters are theoretically more accurate but require more accurate prior assumptions about the sensor noise model.
- Slip rings: a gimbal's Yaw axis needs to rotate without limit, so power and signal can't be routed through a simple flex cable — a slip ring is needed to maintain continuous electrical contact between the rotating and stationary parts. Small gimbals typically run 6–18 channels (signal and power combined); large gimbals can reach around 100 channels. Gold-to-gold contacts are the standard for low noise and high reliability. None of this affects the torque calculations in the motor sizing calculator, but it's an unavoidable part of mechanical design if you're building a gimbal from scratch — especially since, without an unlimited-rotation slip ring on the Yaw axis, the gimbal's entire slew range ends up bounded by cable length.
Passive isolation: complements active control, doesn't replace it
The ADRC, sliding-mode control, and friction compensation covered in the previous post are all active disturbance-rejection measures — sense the disturbance, compute a compensation, drive the motor to cancel it. This literature fills in the other half:
- Passive Isolator Design and Vibration Damping of EO/IR Gimbal Used in UAVs (2023)
- The Design and Validation of a Satellite Camera Vibration Isolation Platform Supported by Multi-Strut Damping Rods (2025)
Passive isolation (spring-damper systems, rubber mounts, multi-strut damping rods) and active control aren't an either/or choice — they divide labor. Passive isolation first filters out a portion of the high-frequency vibration energy (spring-damper systems are effective at attenuating high-frequency vibration, need no power, and can't be made worse by poor controller design), while active control then handles the low-frequency residual that passive isolation can't reach (passive isolation is poor at low frequencies, and low frequency is exactly the band an active control loop's bandwidth can cover). In practice the two are often combined, each handling the frequency band it's good at — the same logic as "use PSD analysis to tell insufficient servo bandwidth from an excited structural resonance" from the previous post, just applied on the mechanical side: figure out which frequency band the problem is in first, then decide whether a passive or active tool is the right fix.
All three posts together: a complete series
- How to Build an Optical LOS Measurement Rig: how to measure LOS jitter — autocollimator, laser + PSD, and target-board + camera architectures
- A Literature Review of Gimbal LOS Optimization: once you have a measured frequency response, what the control side can do — ADRC, sliding-mode control, friction compensation, structural optimization, reinforcement learning
- This post: how the mechanism itself gets designed — direct-drive motor selection, the balancing mechanism, dynamics modeling, sensors and slip rings, passive isolation
The first two both assumed "the gimbal already exists"; this one answers "how does the gimbal get designed from scratch." Together, the three form a complete loop from mechanical design, through measurement verification, to control optimization — matching the motor sizing calculator's own design philosophy of "compute the requirement first, size the motor, verify by measurement, then optimize" — just with the literature now filling in the physical reasoning behind the mechanical design piece.
References
- Masten, M. K. (2008). Inertially Stabilized Platforms for Optical Imaging Systems. IEEE Control Systems Magazine, 28(1), 47–64.
- Kennedy, P. J., & Kennedy, R. L. (2003). Direct versus Indirect Line of Sight (LOS) Stabilization. IEEE Transactions on Control Systems Technology, 11(1), 3–15. Link
- Hilkert, J. M. (2008). Inertially Stabilized Platform Technology: Concepts and Principles. IEEE Control Systems Magazine, 28(1), 26–46.
- Modeling and Control of a Two-Axis Stabilized Gimbal Based on Kane Method. (2024). PMC. Link
- Research on the Cross-Coupling of a Two Axes Gimbal System with Dynamic Unbalance. Link
- Passive Isolator Design and Vibration Damping of EO/IR Gimbal Used in UAVs. (2023). International Journal of Aviation Science and Technology. Link
- The Design and Validation of a Satellite Camera Vibration Isolation Platform Supported by Multi-Strut Damping Rods. (2025). Coatings. DOI: 10.3390/coatings16030278
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