Mechanisms — Gear Ratio

Recent Blogs

Internal Spur Gear and Pinion diagram
Internal Spur Gear and Pinion: Pitch Geometry Calculator | FIRGELLI
Calculate ideal fixed-axis internal gear ratio, center distance and same-direction ring speed. Tooth interference, capacity and planetary motion are not calculated.
Going Train diagram
Going Train Calculator: Clock Gear Ratios and Speeds | FIRGELLI
Calculate speeds and barrel period through four clock-train gear stages. Explore direction reversals and distinguish gear ratios from escapement timing.
Two-speed Gear diagram
Two-speed Gear: Ideal Ratio Comparison Calculator
Compare two ideal gear ratios and their speed and torque relationships. See a schematic sliding jaw clutch select between two gear paths.
Transmission of Two Speeds diagram
Transmission of Two Speeds: Ideal Ratio Comparison
Compare two entered input-to-output speed ratios and their ideal torque multipliers. The calculator does not define a gearbox or simulate shifting.
Transmission of Rotary Motion diagram
Rotary Motion Transmission: Ideal External Spur-gear Pair
Calculate ideal speed, torque and direction ratios for one compatible external spur-gear pair. Tooth geometry, efficiency and load capacity are not evaluated.
Strain Wave Gearing diagram
Strain-Wave Gearing: Animation and Ratio Calculator | FIRGELLI
Explore a fixed circular spline, wave-generator input and flexspline output. Calculate tooth difference, reduction and signed output travel.
Spiral Gearing diagram
Spiral Gearing Mechanism Explained: How It Works, Parts, Spiral Bevel and Hypoid Gear Uses
Spiral gearing transmits power between non-parallel shafts with curved teeth. Learn how it works, the formulas, and where it shows up in real machinery.
Skew Worm and Wheel Gear diagram
Skew Worm and Wheel Gear Mechanism Explained: How It Works, Diagram, Parts and Uses
Skew worm and wheel gear explained — how the offset axis transmits power, sizing formulas, and real industrial uses in conveyors, mixers, and packaging lines.
Oblique Bevel Gear diagram
Oblique Bevel Gear: Hiscox Right-Angle Out-of-Plane Pair
Explore Hiscox's oblique bevel-gear arrangement on right-angle, out-of-plane shafts. Calculate ideal tooth-count ratio and nominal reference diameters.
Gear Train diagram
Compound Gear Train: Two-Stage Ratio and Speed Calculator | FIRGELLI
Calculate stage ratios, total ratio and ideal output speed for two external gear pairs linked by a common intermediate shaft. Includes examples and animation.
Crown Wheel diagram
Crown Wheel Mechanism: How It Works, Diagram, Gear Ratio Formula and Uses Explained
Explore a crown wheel and perpendicular spur pinion. Compare tooth counts, input/output revolutions, speed ratio and ideal torque multiplication.
Bicycle Gear diagram
Bicycle Gear Mechanism Explained: Drivetrain Parts, Gear Ratio Formula, Diagram and Calculator
Compare bicycle chainring and rear-sprocket ratios, wheel revolutions, ideal torque factor and distance travelled per complete crank revolution.
Rack and Pinion diagram
Rack and Pinion Mechanism: How It Works, Diagram, Formula, Calculator and Real-World Uses
Rack and Pinion explained — how the gear-and-bar mechanism converts rotation to linear motion, with formulas, real automotive steering examples, and design tradeoffs.
Variable Circular Motion by Crown-wheel and Pinion diagram
Eccentric Crown Wheel and Pinion: Local Ratio Calculator
Explore an eccentric crown wheel and perpendicular pinion. Calculate a local ideal reduction ratio and lossless torque factor; complete tooth geometry and drive capacity are...
Two-velocity Gears on Same Shaft diagram
Two-velocity Gears on One Shaft: Alternative Speed Comparison
Compare two selectable ideal gear paths to one output shaft. Check their ratios and the tooth-count condition for a shared center distance at common module.
Spur Gears diagram
Spur Gears Mechanism Explained: How They Work, Parts, Diagram, Formula and Uses
Explore spur-gear motion and compare tooth-count ratios, output speed and ideal torque multiplication, with reference dimensions and a worked 5:1 example.
Spur Gear Train diagram
Spur Gear Train Mechanism: How It Works, Diagram, Formula and Calculator
How a Spur Gear Train works, the speed and torque math, real applications in machine tools, and the trade-offs versus helical and planetary alternatives.
Revolution of a Pinion diagram
Revolution of a Pinion: Rack Travel, Speed and Tooth-Passage Calculator
Calculate how far a straight rack travels per pinion revolution, plus ideal rack speed and tooth-passage frequency, from module, tooth count and RPM.
Planetary Motion diagram
Planetary Motion: Exact Fixed-Ring Speed Geometry
Planetary motion in gearing — how sun, planet and ring gears combine to deliver high torque density in robotics, automotive transmissions and wind turbines.
Oblique-tooth Gears (form 2) diagram
Oblique-Tooth Gears Form 2: Brown Movement 41
Explore the double-oblique gear pair in Brown movement 41. Calculate ideal driven speed, reduction ratio and mesh-event rate from tooth counts and input speed.
Oblique-tooth Gears (form 1) diagram
Oblique-Tooth Gears Form 1: Brown Movement 40
Explore the single-oblique tooth pair in Brown movement 40. Calculate ideal driven speed, reduction ratio and mesh-event rate from tooth counts and input speed.
Internal Worm-gear Wheel diagram
Internal Worm Wheel: Ratio and Assumed-Efficiency Calculator | FIRGELLI
Calculate an ideal worm-input reduction, wheel speed, torque and power loss using an entered efficiency. Physical contact and self-locking are not determined.
Epicyclic Train (form 1) diagram
Epicyclic Train (form 1) Mechanism Explained: How It Works, Parts, Willis Ratio and Uses
Explore a fixed-ring planetary reduction. Derive planet teeth from sun and ring counts, then compare carrier speed and ideal torque multiplication.
Epicyclic / Planetary Gear Train diagram
Epicyclic / Planetary Gear Train: How It Works, Parts, Ratio Formula, Diagram and Uses Explained
Explore a fixed-ring planetary reduction and check tooth-count compatibility. Compare sun input, carrier speed and required planet geometry.
Differential Speed diagram
Differential Speed: Fixed-Idler Gearing and Coaxial Counter-Rotation
Explore a fixed-idler gear train with coaxial counter-rotation. Calculate the required ring tooth count, signed idler and output speeds, and reduction ratio.