Entwistle’s arrangement doubles rotation on a common shaft axis using a moving bevel-pinion carrier. One side bevel gear is fixed to the frame. The input shaft carries a radial stud and pinion around that fixed gear, driving the opposite, freely rotating side gear and its pulley at twice carrier speed.
Doubling a Revolution on Same Shaft Interactive Calculator
Follow the carrier stud around a fixed bevel gear. The orbiting pinion drives the coaxial output pulley at twice input speed; all three gear tooth counts remain equal.
Equation Used
- Fixed side gear and equal tooth counts on three illustrated bevel gears.
- Input through-shaft carries the radial planet stud.
- Output sleeve runs freely on the input shaft.
- Ideal lossless torque comparison.
Equal 45-degree pitch-cone gears with simplified tooth ribs. No manufactured tooth, bearing, friction or load rating.
A fixed bevel gear makes the moving carrier a speed increaser
The blue input pulley turns the through-shaft and the radial carrier stud. The gray planet pinion spins on that stud as it travels around the stationary bevel gear A. Its opposite mesh turns the gold side gear C and the output pulley C′, which run freely around the input shaft.
The cutaway uses three equal, 45-degree pitch-cone gears with a common pitch apex. The right-hand side gear remains fixed to its support while the planet both orbits and spins. The output sleeve and pulley rotate twice as fast as the input shaft in the same direction.
Tooth ribs are simplified for viewing, not manufacturing tooth profiles. The even common tooth-count control changes all three illustrated gears together, retaining equal ratios and the shown tooth phasing.
Inspect a carrier-driven speed doubler
Change the common tooth count to inspect the three equal gears, and enter the number of input carrier revolutions to compare output travel. Zero input revolutions holds the mechanism still. The demonstration is slowed for inspection.
This page studies the historical coaxial bevel arrangement. It is not an ordinary two-spur-gear speed ratio, nor a gearbox strength, lubrication, bearing or service-life calculation.
The two side speeds average to carrier speed
For equal side gears, ωA+ωC=2ωcarrier. Gear A is fixed, so ωA=0 and ωC=2ωcarrier. Thus one input carrier revolution produces two output revolutions in the same direction.
In an ideal lossless model, output torque magnitude is half the input torque magnitude because output speed is doubled. The fixed gear transmits a reaction torque to the frame even though it does no work. The common angular tooth pitch is 360/N degrees.
The fixed side gear and moving carrier determine the two-to-one output. Changing all three equal tooth counts together changes tooth spacing while preserving that ratio.
Example: one carrier revolution
With three equal 24-tooth bevel gears, one carrier revolution makes the output pulley turn twice. Common tooth pitch is 15°. Doubling speed gives a 100% increase and an ideal torque-magnitude factor of 0.5.
Changing all three gears to 48 teeth changes tooth pitch to 7.5° but retains the same speed ratio. The ratio comes from the fixed side gear and moving carrier, not from unequal side-gear tooth counts.
The fixed gear support is part of the mechanism
Gear A must remain fixed to the frame for this operating mode. Releasing it adds another degree of freedom and the two-to-one relation no longer follows from carrier speed alone.
The planet follows pitch-line rolling around the fixed gear while its stud travels with the input shaft. It omits bearing details, backlash, elasticity, friction and manufactured tooth contact stresses.
Coaxial speed-doubler questions
Which part is the input?
The through-shaft and radial carrier stud, shown blue. The fixed side bevel gear is not the driver.
Does the planet merely spin in place?
No. It rotates about its radial stud and orbits around the common shaft axis.
Why are the tooth counts linked?
This model uses three equal bevel gears. Independent tooth counts would require a different pitch-cone geometry and speed model.
Does twice the speed provide twice the power?
No. Ideal power is unchanged, so output torque magnitude is half input torque magnitude.
Historical construction reference
Hiscox, Mechanical Movements, Powers and Devices, printed page 246, figure 975 (PDF page 256), identifies Entwistle’s patent, the fixed side gear, moving stud and freely rotating output bevel gear and pulley.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
