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MotorShared InputP = -- W
Manual override
Harmonic Drive Configuration
Series & RatioInputsN_fs=100 / N_cs=102
Three-Port KinematicsZou 2015 / Timofeyev 2018
GENERAL CONSTRAINT (any port as input/output/fixed)
N_cs · ω_cs = N_fs · ω_fs + (N_cs − N_fs) · ω_wg
CS fixed: i = N_fs / (N_cs − N_fs) = N  |  ω_fs = −ω_wg / N
FS fixed: i = N_cs / (N_cs − N_fs) = N+1  |  ω_cs = +ω_wg / (N+1)
Active: CS fixed → i = N  |  N_fs = 100  |  N_cs = 102  |  ΔN = 2
Animated MechanismLive Canvas
WG (gray ellipse, fast input) · FS (blue oval, slow output) · CS (outer ring, fixed) · Red dots = engagement
Speed:
WG: 0.0° · FS: 0.000°
Kinematic ResultsOutput
--
Gear Ratio
i (unitless)
--
Output Speed
RPM
--
Output Torque
N·m rated
--
Peak Torque
N·m
--
Output Power
W
--
Torque Loss
N·m (1−η)
--
Efficiency
%
--
Output Direction
re. input
Geometry & Tooth AnalysisTimofeyev 2018 / Zou 2015
Pitch Diameters & Tooth Form
--
FS Pitch Dia d_f
mm
--
CS Pitch Dia d_r
mm
--
Addendum h_a
mm
--
Dedendum h_f
mm
--
Full Tooth Height
mm
--
Circular Pitch p
mm
Wave Generator & Deformation
--
WG Semi-major a
mm
--
WG Semi-minor b
mm
--
Radial Deform. w₀
mm
--
Rel. Deformation
w₀/r_fs %
--
WG Axis (≈ FS PD)
mm
--
Ellipticity
(a−b)/a
Tooth Engagement (Zou et al., eq. 3–5)
--
Engaging Teeth Z_R
both zones
--
Engagement
% of N_cs
--
Contact Ratio ε
approx.
0
Backlash
arcmin
Flexspline Strength (Timofeyev, Sec. 2)
--
Rim Thickness h_ml
mm
--
h_ml / d_f
normalized
--
d_mlf (endurance)
mm min.
--
Kinematic Error
arcmin typ.
FS Radial Deformation Profilew(θ) = w₀·cos(2θ)
Radial deformation w(θ) — positive = outward (mm)Engagement zones (major axis ±β)
Stiffness & Dynamic ModelZou et al. 2015 — eq. (1)–(3)
THREE STIFFNESS COMPONENTS — PROC IMECHÊ PART C, DOI 10.1177/0954406215621097
K_m = Z_R · K_ms    [Meshing stiffness — scales with engaging tooth count]
K_t = G·I_p / L_cup    [Torsional stiffness of FS cup cylinder]
K_b = E·h³_wall / (12(1−ν²)·R³)    [Radial stiffness of thin-walled bearing]
K_m ≈ -- N/mm  |  Cam angle α_n = --°
--
Cam Angle α_n
degrees
--
Z_R (engaging)
teeth
--
K_m estimate
N/mm
--
Power Density
W/kg typ.

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 -- Full Analysis
Drive ParametersInputsN_r=40 / N_d=39
Cycloidal Profile ModificationOptional
Animated MechanismLive
Disk 1 (green) -- Disk 2 (pink, Phase 2) -- ring pins (navy) -- output pins (purple) -- camshaft (gold)
Speed:
Input: 3000 rpm -> Output: --
Kinematic ResultsOutput
--
Transmission Ratio
i
--
Output Speed
RPM
--
Output Torque
N*m
--
Output Power
W
--
Avg Pressure Angle
deg
--
PA Range
deg
--
Disk Outer D
mm
--
Housing OD
mm
Single Pin Pressure Anglevs. rotation
Pressure angle alpha(theta) -- 0 to 360deg of disk rotation
Average Pressure Angle Variationcyclic
Mean alpha over one full output revolution
Contact & Stress AnalysisHertzian -- Li et al. 2022 method
Peak Housing Contact Stress--
Cycle-Max Housing Force--
Cycle-Mean Peak Force--
Force Distribution by Housing Pin--
Crank angle:
Selected: 30deg
Pin force (N) -- bar height proportional to contact load

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.

Planetary Gearbox
Gear CountsInputs
Planetary SchematicVisual
S P P P 3 planets shown RING SUN CARRIER
SunPlanetsRing
ResultsOutput
--
Total Ratio
i
--
Ratio / Stage
i_s
--
Output Speed
RPM
--
Output Torque
N*m
--
Output Power
W
--
Total Efficiency
%
--
Torque / Planet
N*m
RV Reducer
RV InputsInputs
ResultsOutput
--
Total Ratio
i
--
Output Speed
RPM
--
Output Torque
N*m
--
Output Power
W
Timing Belt Drive
Belt & PulleysInputs
Timing Belt SchematicVisual
DRIVE z1 DRIVEN z2 C belt wraps both pulleys / ratio i = z2/z1
Drive pulleyDriven pulley
ResultsOutput
--
Speed Ratio
i
--
Output Speed
RPM
--
Output Torque
N*m
--
Belt Velocity
m/s
--
Belt Pitch Length
mm
--
Teeth in Mesh
z_m
--
Drive PD
mm
--
Driven PD
mm
--
Tangential Force
N
--
Wrap Angle
degrees
Worm Gear
Worm GearInputs
Worm Gear SchematicVisual
WORM (n_w starts) input shaft WHEEL (Z_g teeth) i = Z_g / n_w
Worm (driver)Wheel (driven)
ResultsOutput
--
Gear Ratio
i
--
Output Speed
RPM
--
Output Torque
N*m
--
Calculated n
%
--
Self-Locking
L < phi ?
--
Worm PD
mm
--
Wheel PD
mm
Bevel Gear
Bevel GearInputs
Bevel Gear SchematicVisual
PINION Z1 GEAR Z2 90deg cones share apex i = Z2/Z1
PinionGear
ResultsOutput
--
Gear Ratio
i
--
Output Speed
RPM
--
Output Torque
N*m
--
Pitch Angle d1
degrees
--
Pitch Angle d2
degrees
--
Pinion Mean PD
mm
Ball Screw -- Rotary to Linear
Ball ScrewInputs
Ball Screw SchematicVisual
NUT linear motion rotation v_lin = rpm x L / 60
Screw shaftNut
ResultsOutput
--
Linear Velocity
mm/s
--
Linear Velocity
m/s
--
Output Force
N
--
Required Torque
N*m
--
Lead Angle
degrees
--
Back-drivable
yes / no
Rack & Pinion
Rack & PinionInputs
Rack & Pinion SchematicVisual
RACK (linear) PINION Z v_linear omega v = pi * m * z * rpm / 60
RackPinion
ResultsOutput
--
Linear Velocity
mm/s
--
Linear Velocity
m/s
--
Rack Force
N
--
Pinion PD
mm
--
Travel / Rev
mm
Cable / Capstan Drive
Capstan DriveInputs
Euler-EytelweinCapstan equation
T_tight / T_slack = e^(u*theta) , theta = 2*pi*wraps
F_max = T0 * (e^(u*theta) - 1) -- slip limit at pretension T0
i = d2 / d1 -- zero backlash, drum-to-drum cable
ResultsOutput
--
Drive Ratio
i
--
Output Speed
RPM
--
Output Torque
N*m
--
Output Power
W
--
Tension Ratio e^(u*th)
--
--
Tangential Force
N
--
Max Force (slip)
N
--
Slip Safety
F_max/F_t
--
Drum/Cable D/d
>= 20
--
Cable Velocity
m/s

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
Traction PlanetaryInputs
KinematicsRing fixed
i = 1 + d_r / d_s -- sun in, carrier out, ring fixed
T_slip = u * F_N * n_p * (d_s/2) -- traction limit at sun contact
d_planet = (d_r - d_s) / 2
ResultsOutput
--
Drive Ratio
i
--
Output Speed
RPM
--
Output Torque
N*m
--
Output Power
W
--
Planet Diameter
mm
--
Slip Torque (sun)
N*m
--
Traction Safety
T_slip/T_in
--
Traction / Contact
N

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
Belt & PulleysInputs
V-Belt SchematicVisual
DRIVE d1 DRIVEN d2 C groove wedge: u' = u / sin(groove/2)
Drive pulleyDriven pulley
ResultsOutput
--
Speed Ratio
i
--
Output Speed
RPM
--
Output Torque
N*m
--
Belt Length
mm
--
Wrap (small)
degrees
--
Belt Velocity
m/s
--
Tension Ratio
e^(u'a)
--
Effective Pull
N
--
Tight Side F1
N
--
Slack Side F2
N
--
Shaft Load
N

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.

Roller Chain Drive
Chain & SprocketsInputs
Chain Drive SchematicVisual
DRIVE z1 DRIVEN z2 C chordal speed variation = polygon effect
Drive sprocketDriven sprocket
ResultsOutput
--
Speed Ratio
i
--
Output Speed
RPM
--
Output Torque
N*m
--
Drive PD
mm
--
Driven PD
mm
--
Chain Speed
m/s
Links (even)
pitches
--
Chain Length
mm
--
Exact C
mm
--
Chordal Variation
%
--
Chain Tension
N

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 (Sliding Thread)
Lead ScrewInputs
ResultsOutput
--
Mean Diameter
mm
--
Lead L
mm/rev
--
Lead Angle
degrees
--
Torque to Raise F
N*m
--
Torque to Lower F
N*m
--
Efficiency
%
--
Self-Locking
yes / no
--
Linear Velocity
mm/s
--
Force @ Motor T
N
--
Lift Power @ F
W

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 (Motor + Gear + Screw)
Actuator StackInputs
ResultsOutput
--
Linear Velocity
mm/s
--
Full Stroke Time
s
--
Max Force (rated)
N
--
Max Force (peak)
N
--
Motor T for Load
N*m
--
Power @ Load
W
--
Travel / Motor Rev
mm

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
Fit SelectionInputs
Tolerance Zone DiagramVisual
deviation (um) 0 nominal D HOLE ES EI SHAFT es ei +um above line / -um below line
Hole zoneShaft zone
Hole LimitsOutput
--
Upper Dev. ES
um
--
Lower Dev. EI
um
--
Tolerance IT
um
--
Max Diameter
mm
--
Min Diameter
mm
--
Mid (mean)
mm
Shaft LimitsOutput
--
Upper Dev. es
um
--
Lower Dev. ei
um
--
Tolerance IT
um
--
Max Diameter
mm
--
Min Diameter
mm
--
Mid (mean)
mm
Fit AnalysisResult
--
Fit Type
classification
--
Max Clearance
um
--
Min Clearance
um
--
Mean Clearance
um
FIT CONVENTIONS -- ISO 286-1
Hole: D_max = D + ES, D_min = D + EI
Shaft: d_max = D + es, d_min = D + ei
Clearance = D_hole - d_shaft (negative = interference)

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 (ISO 286-1)
Shaft ParametersInputs
Shaft Section DiagramVisual
shaft cross-section nominal D zone position D es ei --
Shaft tolerance zoneNominal D
ResultsOutput
--
Class
letter+grade
--
Upper Dev. es
um
--
Lower Dev. ei
um
--
Tolerance IT
um
--
Max Diameter
mm
--
Min Diameter
mm
--
Mean Diameter
mm
--
Zone Position
vs. nominal

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 (ISO 965)
Thread ParametersInputs
Thread Profile DiagramISO Metric Profile
axis of rotation NUT (internal) BOLT (external) D2 D P D3
Bolt (external)Nut (internal)D = major / D2 = pitch / D3 = minor / P = pitch
Basic Thread GeometryOutput
--
Major D
mm
--
Pitch D2
mm
--
Minor D3
mm
--
Thread Height H
mm
Tolerance LimitsISO 965
--
Major Max
mm
--
Major Min
mm
--
Pitch D2 Max
mm
--
Pitch D2 Min
mm
--
Fund. Deviation
um
--
Tol. Td2
um

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 Tolerances (GD&T) Reference
Form TolerancesISO 1101
STRAIGHTNESS -- A line element must lie within a tolerance zone bounded by two parallel lines.
FLATNESS -- A surface must lie within a tolerance zone bounded by two parallel planes.
CIRCULARITY (roundness) -- Any cross-section perpendicular to axis must lie within two concentric circles.
CYLINDRICITY -- A cylindrical surface must lie within two coaxial cylinders.
Orientation TolerancesNeed datum
PARALLELISM -- Feature must be parallel to a datum within tolerance zone.
PERPENDICULARITY -- Feature must be at 90 deg to a datum within tolerance zone.
ANGULARITY -- Feature must be at specified angle to datum within tolerance zone.
Location TolerancesNeed datum
POSITION -- Located feature must lie within zone around theoretical position. Most common: hole patterns.
CONCENTRICITY -- Axis of feature must coincide with datum axis within zone.
SYMMETRY -- Median plane of feature must lie within zone around datum.
Runout TolerancesRotation axis
CIRCULAR RUNOUT -- Any single cross-section measured during rotation must vary within tolerance.
TOTAL RUNOUT -- Entire surface, measured along full length during rotation, must lie within tolerance band.
Profile TolerancesCurved features
LINE PROFILE -- Profile of cross-section must lie within tolerance zone around theoretical profile.
SURFACE PROFILE -- Entire surface must lie within zone formed by two surfaces offset from theoretical surface.
Material ModifiersISO 2692
M -- Maximum Material Condition (MMC) -- Bonus tolerance available as feature departs from MMC.
L -- Least Material Condition (LMC) -- Used to control min wall thickness or edge distance.
F -- Free State -- Used for flexible parts measured without restraint.
P -- Projected Tolerance Zone -- Tolerance extends beyond surface, used for threaded inserts.

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.

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