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Last updated: May 2026
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Harmonic Drive (Strain Wave Gear) Calculator
Kinematics
General three-port constraint: N_cs·ω_cs = N_fs·ω_fs + ΔN·ω_wg. With CS fixed: i = N_fs/ΔN. Standard configuration has ΔN = 2, giving i = N_fs/2 = N. Output torque: T_fs = N·T_wg·η.
Geometry (Timofeyev et al., IOP Conf. Ser. 468, 2018)
Flexspline radial deformation: w₀ = (ΔN/N_fs)·γ·r_fs. Profile: w(θ) = w₀·cos(2θ). Rim thickness limit: h_ml ≤ 0.018·d_f. Endurance diameter: d_mlf = 165·∛(T/((0.03U−1)·σ_F0)).
Engagement (Zou et al., Proc IMechE Part C, 2015)
Number of engaged tooth pairs: Z_R = floor(N_cs·β/π) — typically 30–40% of all teeth load simultaneously. Contact ratio far exceeds standard spur gears. Backlash is theoretically zero. Meshing stiffness: K_m = Z_R·K_ms.
Ratios 30:1 to 320:1 single stage. Used in space robotics, collaborative robots, surgical systems, CNC machining centres, and semiconductor wafer handling.
Cycloidal Drive Calculator
Ratio: i = N_r/(N_r-N_d). Standard configuration has N_d = N_r - 1 giving i = N_r. Cycloid profile equations: x(t) = R*cos(t) - e*cos(N*t), y(t) = R*sin(t) - e*sin(N*t), offset normally by pin radius. Pressure angle varies cyclically across each lobe -- lower average means better efficiency and load capacity. Stress analysis applies Hertzian line contact theory between cycloidal disk and ring pin under load distribution per Li et al., Machines 2022, 10, 672. High shock resistance (loaded by ~half the pins simultaneously). Used in robotics joints, AGV drives, and high-precision positioning.
Cable / Capstan Drive Calculator
Capstan drives transmit torque through cable friction: T1/T2 = e^(u*theta) (Euler-Eytelwein). Maximum transmissible force F_max = T0*(e^(u*theta)-1) depends on pretension and total wrap angle. Keep D/d >= 20 for cable fatigue life. Zero backlash makes capstans popular in haptics, telescopes and robot joints.
Archimedes / Traction Drive Calculator
Smooth-roller planetary drives transmit torque through preloaded traction contacts instead of teeth: silent, zero backlash, but torque-limited by T_slip = u*F_N*n_p*r_s. Ratio follows the planetary relation i = 1 + d_r/d_s with the ring fixed.
V-Belt Drive Calculator
The V-groove wedging effect multiplies friction: u' = u/sin(groove/2), so the tension ratio becomes F1/F2 = e^(u'*alpha). Belt length L = 2C + pi(d1+d2)/2 + (d2-d1)^2/(4C). Keep the small-pulley wrap above 120 deg and belt speed below 30 m/s.
Chain Drive Calculator
Sprocket pitch diameter d = p/sin(pi/z). Chain length in pitches L_p = 2C/p + (z1+z2)/2 + ((z2-z1)/2pi)^2 * p/C, rounded to an even link count, then the exact center distance is solved back. Chordal (polygon) speed variation (1-cos(pi/z1))*100% drops fast above 17 teeth.
Lead Screw Calculator
Raising torque T_R = F*d_m/2 * (L + pi*u*d_m*sec a)/(pi*d_m - u*L*sec a) (Shigley). The screw self-locks when pi*u*d_m*sec a > L: the load cannot back-drive. Efficiency is the lift work per revolution over the input work, typically 25-45% for sliding threads versus ~90% for ball screws.
Linear Actuator Calculator
Stacks the shared motor with a gearbox and screw: v = rpm/i_g * L / 60 and F_max = 2*pi*T*i_g*eta_g*eta_s / (L/1000). Use it to size stroke time against load capacity before picking a COTS actuator.
ISO 286-1 Fits Calculator
Tolerance grade IT defines size of tolerance zone. Position letter (uppercase = hole, lowercase = shaft) defines location relative to nominal. Common reference: H for holes (EI = 0) and h for shafts (es = 0). Clearance fits (H7/g6, H9/d9), transition fits (H7/k6, H7/n6), interference fits (H7/p6, H7/s6). Range: 1-500 mm. Values per ISO 286-1:2010.
Shaft Tolerances
For position letters a-h, the upper deviation es <= 0 (zone below nominal). For j-zc, the lower deviation ei >= 0 (zone above nominal). IT grade controls tolerance width. Most common shaft classes: g6 (sliding), h6 (reference), k6 (light transition), n6 (drive transition), p6 (interference).
Metric Thread Tolerances
Basic geometry: D2 = D - 0.6495*P and D3 = D - 1.2269*P for ISO metric profile. Class 6g is standard for external (bolt) threads; 6H standard for internal (nut) threads. Class digit gives tolerance grade, letter gives position (g, e = clearance; H = reference; lowercase external, uppercase internal). Values per ISO 965-1.
Geometric Dimensioning and Tolerancing
GD&T (ISO 1101 / ASME Y14.5) defines feature geometry beyond basic +/- dimensions. Use form tolerances for individual features (no datum needed). Orientation, location, and runout tolerances require datum references. Apply material modifiers (MMC, LMC) for functional gauging and bonus tolerance.