Hiscox item 133 describes oblique bevel gears on shafts at right angles and crossing out of axial plane. Explore the schematic arrangement and calculate an ideal tooth-count ratio and nominal reference diameters from entered values.
Oblique-Bevel Tooth-Count Calculator
Enter declared driver and driven tooth counts, nominal module and a schematic axis offset. The worksheet reports ideal ratio and nominal reference diameters only; it does not generate oblique bevel tooth surfaces or rate a drive.
Equation Used
- The two declared tooth counts define an ideal external gear ratio with no slip or loss.
- Nominal reference diameters use the entered module identity d=mz; they do not define a complete oblique-bevel geometry.
- The source fixes the shaft relationship at right angles and out of axial plane; the entered offset is an illustrative display quantity.
- Cone apex, mounting distance, face width, pressure angle, spiral/obliquity angle, tooth form, undercut, backlash, contact pattern, lubrication, efficiency, heat, loads, bearings, strength, manufacture and safety are excluded.
Tooth counts set the ideal rotation ratio. The offset appears as a schematic annotation; tooth surfaces, contact geometry and drive capacity are not calculated.
Right-angle shafts cross out of axial plane
Hiscox item 133 gives one concise definition: the oblique bevel gears operate on shafts at right angles and crossing out of axial plane. The plate shows the paired gears and their skewed shaft arrangement.
The animation illustrates the shaft arrangement and ideal tooth-count ratio. It does not generate a tooth surface for manufacture.
A historical power-transmission gear form
The arrangement transfers rotation between right-angle shafts that are displaced out of one axial plane. Applying it in a drive requires a defined gear geometry and engineering data beyond the tooth-count relationship shown here.
Ratio and nominal reference diameters
These identities do not solve offset bevel-gear pitch surfaces, mounting distances or contact geometry.
Declared tooth-count example
For z1=18, z2=36 and m=3 mm, the nominal reference diameters are 54 and 108 mm. The driven gear makes -0.500 revolution per driver revolution, an ideal 2.000:1 reduction magnitude. The 25 mm offset is schematic only.
Ratio calculations and offset gear geometry
Shaft offset changes the geometry needed for tooth contact. A tooth-count ratio and nominal module alone do not establish pitch surfaces, mounting distances or contact patterns. Those require a defined tooth system; strength and operating conditions require further design data.
Oblique bevel-gear questions
Does this calculator design the teeth?
No.
Does zero entered offset convert this to a standard bevel calculation?
No. Offset only changes the schematic annotation.
Is the nominal module a recovered Hiscox dimension?
No. It is an entered value used to calculate nominal reference diameters.
Oblique bevel-gear reference
- Hiscox, Mechanical Movements, page 43, item 133: primary public-domain figure and caption defining the right-angle, out-of-axial-plane shaft arrangement.
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