**Related Resources: calculators**

### Gears Shafts Right Angles Exact Helix Design Equations and Calculator

**Machine Design and Engineering**

**Mechanical Gear Design and Engineering**

**Helical Gears Shafts at Right Angles Exact Design Equations and Calculator - **Gears will have same direction of helix. Sum of the helix angles will equal 90 degrees.

Sum of helix angles of gear and pinion must equal 90 degrees.

Related:

Helical Gears Shafts Parallel Center Distance Exact Design Equations and Calculator

Helical Gears Shafts Parallel Center Distance Approximate Design Equations and Calculator

Helical Gears Shafts at Right Angles Approximate Design Equations and Calculator

Preview ** Helical Gears Shafts at Right Angles Exact Design Calculator**

Design variables you should know:

- Position of gear having right- or left-hand helix depending on rotation and direction in which thrust is to be received,
- Pn = normal diametral pitch (pitch of cutter),
- R = ratio of number of teeth in large gear to number of teeth in small gear,
- α
_{a}= approximate helix angle of large gear, - C = exact center distance.

Number of teeth in pinion for any angle:

n = ( 2 C_{a} P_{n} sin α_{a} ) / ( 1 + R tan α_{a} )

Number of teeth in large gear formula:

N = n R

Exact helix angle of large gear ( exact angle found by trial and varying R sec α + cosec α )

α is the exact helix angle of large gear found by trial from the following equality

R sec α + cosec α = R / cos α + 1 / sin α = ( 2 C P_{n} ) / n

Exact helix angle of small gear

β = 90° - α

Pitch diameter of large gear

D = N / ( P_{n} cos α )

Pitch diameter of small gear

d = n / ( P_{n} cos β )

Outside diameter of large gear

O = D + 2 / P_{n}

Outside diameter of small gear

o = d + 2 / P_{n}

Lead of helix on karge gear formula:

L = π D cot α

Lead of helix on small gear formula:

*l* = π d cot β

Where:

C = approximate center distance (in, mm),

P_{n} = normal diametral pitch (in, mm),

N = number of teeth in large gear,

n = number of teeth in small gear,

α = angle of gear helix (deg),

β = angle of pinion helix (deg),

R = ratio of gear to pinion,

L = lead of helix on large gear (in, mm),

l = lead of helix on pinion (in, mm).

References:

Machinerys Handbook, 29th Edition