A worm and its mating worm wheel use the same hand. Reversing both members from right-hand to left-hand reverses the wheel's signed response for the fixed input and drawing convention used here. Ideal ratio is wheel teeth divided by worm starts.
Right- and Left-hand Worm Gear Interactive Calculator
Compare ideal right- and left-hand worm-pair kinematics using a fixed signed drawing convention.
Equation Used
- Each worm and its mating wheel have the same hand.
- The right- and left-hand panels share one fixed axis and viewing convention.
- The tooth/start relationship is ideal with no slip, backlash or deformation.
- Geometry, lead angle, efficiency, forces, thrust, friction, self-locking, lubrication, heat, life and ratings are excluded.
The secondary figure uses the same worm starts, wheel teeth and fixed signed drawing convention.
How the selected handed worm pairs work
A worm is a screw-like gear whose threads mesh with a worm wheel on nonparallel, nonintersecting axes. One worm revolution advances the mesh by one lead; for a z1-start worm and a Z2-tooth wheel, the wheel advances z1/Z2 revolution.
The two panels hold the schematic axes, observation convention and signed worm motion fixed. The right-hand pair and left-hand pair therefore show equal wheel-turn magnitudes with opposite signs. Each wheel must match its worm's hand.
What this calculator demonstrates
Select worm starts, wheel teeth and signed worm revolutions. The calculator returns the ideal reduction ratio, wheel revolutions per worm revolution and the two signed wheel responses in this fixed schematic.
It does not calculate universal clockwise direction, geometry, lead angle, efficiency, torque, force, thrust, friction, lubrication, temperature, backlash, self-locking, strength, life or ratings.
Ideal tooth-count kinematics
Let z1 be worm starts, Z2 be wheel teeth and N be signed worm revolutions. The ideal reduction ratio is i = Z2/z1, and wheel-turn magnitude per worm revolution is z1/Z2.
For this page's fixed drawing coordinates, NRH = Nz1/Z2 and NLH = −Nz1/Z2. These signs are schematic coordinates, not universal clockwise labels; a physical direction statement must define viewing ends and axis orientation.
Default selected example
For a one-start worm, 40-tooth wheel and +1 signed worm revolution, i = 40:1 and wheel-turn magnitude is 0.025 revolution per worm revolution. In the fixed drawing, the right-hand result is +0.025 revolution and the left-hand result is −0.025 revolution.
The signs describe only the marked coordinates in this comparison. They do not establish a global clockwise direction for an installed drive.
Scope and correction boundary
The removed calculator labelled output directions clockwise and counterclockwise without defining the observer's viewing end or axis orientation. The replacement uses signed drawing coordinates and explicitly limits them to one fixed schematic.
The removed article also supplied universal efficiency, self-locking, backlash, temperature, service, failure and cost claims without an identified product and operating condition. KHK's technical references support same-hand mating, tooth/start ratio and handedness-dependent direction, but detailed selection requires the actual geometry, materials, supports, lubricant and duty.
Questions
Must the worm and wheel have the same hand?
Yes. KHK's terminology reference states that a worm and worm wheel in mesh have the same direction of hand.
Why avoid universal clockwise labels?
Clockwise depends on which shaft end the observer faces. This calculator instead defines positive and negative response in its fixed drawing.
How do worm starts affect ratio?
At the same wheel tooth count, more starts increase wheel travel per worm revolution and reduce the numerical reduction ratio.
Does the calculator predict self-locking?
No. Self-locking and backdrivability depend on geometry and friction conditions not entered here.
Primary technical references
- KHK, Standards in Terminology for Worm Gearing — a meshing worm and worm wheel have the same hand.
- KHK, Calculation of Gear Dimensions — worm threads correspond to tooth count and one worm revolution advances one lead.
- KHK, ABC's of Gearing, Part B — worm-pair ratio uses wheel teeth divided by worm starts and diagrams compare right- and left-hand sets.
- KHK, Direction of Rotation of Gears — worm output direction depends on helix direction.
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