Brown’s disk-wheel drive uses a spiral thread on the face of a rotating disk to turn a spur wheel on a perpendicular shaft. One complete disk revolution advances the spur wheel by one tooth. This is a face-spiral reduction mechanism, distinct from a crown wheel with many separate teeth around its face.
Disk-wheel and Spur Gear Interactive Calculator
Brown movement 29: a single face spiral advances the driven wheel by one tooth per disk revolution. Adjust wheel teeth, input speed, torque and assumed efficiency.
Equation Used
- Single-start face spiral; one wheel tooth advanced per disk turn.
- No tooth skipping or backlash in the kinematic ratio.
- Steady power transfer with entered overall efficiency.
- Module 4 display dimensions and illustrative tooth bodies.
Illustrative tooth and spiral bodies, not generated manufacturing flanks. No capacity or self-locking claim.
A spiral face thread advances successive teeth
The blue input shaft turns the gold disk. A single-start spiral rib runs outward across its face. The driven spur wheel stands perpendicular to that face, with its shaft tangent to the disk’s pitch region. As the disk turns, the spiral acts on successive spur-wheel teeth.
Brown’s movement 29 specifies one tooth of wheel advance per disk revolution. With Z teeth on the wheel, Z input turns produce one output turn. Both shafts turn continuously in this ideal kinematic demonstration.
The illustration uses a fixed module of 4 mm for the displayed wheel and the same 4Ï€ mm radial lead for the spiral. Changing tooth count changes the wheel radius and height while preserving that pitch relationship. The rib and tooth bodies illustrate the arrangement; they are not generated conjugate tooth surfaces.
Explore the historical right-angle reduction
Use the tooth-count control to compare reduction and output speed. Input speed changes both shaft speeds together. Torque and assumed efficiency provide a steady power-balance estimate rather than a load-capacity rating.
The main drawing shows the spiral face and upright wheel. The two end-on indicators separate the fast disk motion from the slower wheel motion. All views use the same reduced playback time scale.
One disk turn advances one wheel tooth
For one spiral start and Z wheel teeth, reduction i=Z. Output speed is nout=nin/Z, and wheel advance per input revolution is 360°/Z.
With an entered total efficiency η expressed as a fraction, Tout=Tin×Z×η. Input power is Pin=Tin×nin×π/30, and estimated loss is Pin(1−η). These equations describe steady power transfer. At zero speed, power is zero; the torque result remains a nominal ratio estimate and does not establish static holding capacity.
Example: a 24-tooth driven wheel
A 60 rpm disk drives a 24-tooth wheel at 2.5 rpm. Each disk turn advances the wheel 15°. With 1 N·m input torque and assumed 75% efficiency, estimated output torque is 18 N·m and power loss is 1.571 W.
A 60-tooth wheel at the same input speed turns at 1 rpm and advances 6° per input turn. More reduction does not itself establish a higher allowable tooth load.
Illustration versus a manufactured gear set
The original reference establishes the layout and one-tooth advance. It does not provide a generated flank profile, allowable load, efficiency curve or service-life rating. A working design needs conjugate contact geometry, clearance, bearings, materials and lubrication checked separately.
For the illustrated single-start spiral, the wheel tooth count fixes the speed ratio. Select efficiency and installation details from the actual gear set; the geometry alone does not establish them.
Disk-wheel drive questions
Is this a crown gear?
No. The disk carries a continuous spiral thread. Brown’s crown wheel is movement 26; this face-spiral drive is movement 29.
Why does the ratio equal the wheel tooth count?
One input turn advances one tooth. Z input turns therefore advance all Z teeth for one output revolution.
Does efficiency change the speed ratio?
No. It changes the idealized torque and power estimate, not the tooth-count relationship.
Can the drawing be used to cut the teeth?
No. The displayed rib and tooth forms explain the motion; they do not define production contact surfaces.
Construction reference
Brown, 507 Mechanical Movements, movement 29 identifies the spiral disk driving a spur wheel through one tooth per revolution. The original engraving appears on printed page 12, with its explanation on page 13. Compare movement 26 for the different crown-wheel arrangement.
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