Moment at quadarm–frame connection point

Mnet = H · (Fy − Fz · tan θ)  —  both forces act simultaneously about the same axis (X), so they add algebraically. Fy bends the connection; Fz partially counters this via the lateral foot offset. At θopt they cancel exactly: Mnet = 0.  |  θopt is coupled to θfwd via 3D geometry: larger forward tilt amplifies lateral foot offset, requiring less outward angle.

16.0° leg angle (0–30°)  |  FEM optimum leg stress: 16°
50 N vertical impact force  →  vz = 1.40 m/s  |  drone 12.5 kg
20 N lateral drift force  →  vy = 0.40 m/s
mm connection height  |  standard 200 mm (ground clearance to connection point)
H = 200 mm drone body F_z F_y X Z Y
Connection moment   Mnet = H · (Fy − Fz · tan θ)
0.00 Nm
—
θopt   =   arctan(Fy · cos θfwd / Fz)  —  coupled to forward angle via 3D geometry
16.0°
At this angle M_net = 0
Mnet vs θout  —  at current vz and vy. Zero crossing = θopt (green), coupled to θfwd.

Side view — forward leg angle θfwd

Mfwd = H · Fz · tan θfwd  —  bending moment in the X-Z plane due to vertical landing force on a forward-tilted leg.  |  Trod = H · Fy · tan θfwd  —  torsion on the carbon rod due to lateral drift (lever arm = horizontal foot offset).  |  θfwd also shifts θopt of the outward angle via 3D coupling.

9.0° forward leg angle (0–30°)  |  default ≈ 9° (FEM-optimum stability sweep)
N/mm lateral stiffness of leg foot in X-direction  |  to be determined via FEM bending analysis
H = 200 mm quadarm drone body F_z F_y Y Z X
Bending moment X-Z plane   Mfwd = H · Fz · tan θfwd
0.00 Nm
—
Torsion carbon rod   Trod = H · Fy · tan θfwd
0.00 Nm
—
Foot deflection in X   δ = Fz · tan θfwd / kleg
0.0 mm
—
Mfwd and Trod vs θfwd  —  at current Fz and Fy. Both increase linearly with tan θfwd.

Combined 3D connection moment

θout governs Mx (lateral bending).  |  θfwd governs My and Mz (sagittal + horizontal).  —  The two angles act on orthogonal moments: they add in quadrature, not algebraically. At θopt, Mx = 0, but My and Mz remain — |Mtotal| is then dominated by θfwd. θopt itself shifts with θfwd due to 3D geometry coupling.

Mx — lateral bending
0.00 Nm
H·(Fy − Fz·tan θout)
My — sagittal bending / torsion
0.00 Nm
H·Fz·tan θfwd
Mz — horizontal bending
0.00 Nm
H·Fy·tan θfwd
|Mtotal|   =   √(Mx² + My² + Mz²)
0.00 Nm
3D vector magnitude at connection point
|Mtotal| vs θout  —  at current θfwd, Fz, Fy. Green floor = optimal |Mtotal| when θout = θopt (Mx = 0). Residual is set by θfwd.