#003 Right Angle Gears
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Definition

A Gear is a rotating round mechanical part with "teeth" that mesh to transmit rotational power. They can be made of plastic or wood, but the most common material is metal, due to the wearing effect on the teeth.

There are many forms of gears that shift the axis rotation by 90 degrees

  • Bevel gears are the most well-known gears sets. The diving and following gears do not have to have the same angle. Gears are often sold in pairs to deliver a specific gear ratio and angle.
  • Miter gears are a subset of bevel gears where both gears have an angle of 45 degrees and the same number of teeth. This results in the two shafts rotation speed and torque being the same.
  • Spiral Bevel gears are a variation where the teeth profile spirals instead of being straight. These are more complex to make, but have the benefit of distributing the contact point between the gears.
  • Worm gears combine a long screw gear with a worm wheel. A worm wheel can be a simple flat spur gear, but angled or helical teeth are more efficient. Worm gears turn a full rotation to move the wheel one tooth. This results in greatly slowing down the rotaion and increasing torque. Worm gears usually cannot be 'back driven', as shown that guitar strings do not unwind.
  • Crossed helical gears are a unique orientation of the three dimensional helical thread. A second helical gear with matching curves can be driven by the first. Helical gears are complex to make, but very efficient as the contact point between the gear is spread across the curved thread.
  • Hypoid gears (short for hyperboloid) are "skew" gears; the shafts are neither parallel like flat gears, nor intersecting like bevel gears. Hypoid are much more complex to manufacture, but have excellent noise and efficiency. They can be found in automobile differentials. More at
  • Cage gears are an ancient design for wooden gears, commonly found in old mills.

Key Facts

This page builds on Reduction Gear, which contains explanations for many basic gear terms and ideas. See the below Research section.

Engineering Rules of Thumb

  • Keep in mind the friction losses for the total gear train. A page on efficiency Here is a 1980 paper from NASA on Spur-Gear-System Efficiency at Part and Full Load
  • Lubrication is an essential part of any gearing design, poor lubrication can waste up to 8% efficiency in one report.
  • Multiple Gear design calculators exist online, for example from KHK Gears
  • Longevity is very important in many gear applications. You can reduce wear on the teeth when you choose odd ratios. teeth on a 50:10 ratios will meet every 5 rotations. 49:10 or 50:11 it takes many more rotations before same teeth meet and make wear more even.
  • Although the most popular helix angle for screw gears is 45 degrees, any helix angle greater than zero degrees is possible.

View in 3D

iPhone Augmented Reality Viewer

Display

This model demonstrates different types of right angle gears.

  1. The driving gear in the center turns 4 bevel gears at a 48:12 (4:1) ratio.
  2. The top left Worm gear turns a helical ring gear at 1:36 ratio.
  3. The top right Hypoid gear pair at a 10:40 (1:4) ratio.
  4. The bottom right matched Helical gear pair at a 1:1 ratio.
  5. The bottom left is a fanciful Sprocket ring gear at a 10:60:10 ratio.
Right Angle Gear display in Mechanical Library
Right Angle Gear display in Mechanical Library
Source: mechanical-library.org
Right Angle Gear model
Mechanical Library Right Angle Gear Model
Source: mechanical-library.org

Images

Bevel Gears

Pair of bevel gears
Pair of bevel gears
Source: Tim Green from Bradford, via Wikimedia Commons
Pair of Miter gears
Matched pair of miter gears
Source: unknown
Bevel gears that drive a speed governer on one of the Steam engines at the London Science Museum
Bevel gears that drive a speed governer on one of the Steam engines at the London Science Museum
Spiral Bevel Gear
Spiral Bevel Gear
Myriam Thyes, Public domain, via Wikimedia Commons

Worm Gears

Worm gear
Worm Gear
Source: Catsquisher, via Wikimedia Commons
Levin classical guitar tuners
Levin classical guitar tuners
Source: Anders Ljungberg, Wikimedia Commons

Crossed Helical Gears

Crossed Helical Gears
mechanical-library.org

Hypoid Gears

Spiral Hypoid gear
Spiral Hypoid gear showing Ring gear (1) and Pinion (2)
Source:Sam novo, via Wikimedia Commons
1963 Ad for Rockwell Standard Hypoid Gearing
1963 Ad for Rockwell Standard Hypoid Gearing
Source: Unknown

Cage Gears

A traditional wooden cog wheel and cage gear
A traditional wooden cog wheel and cage gear

Videos

Bevel Gears

Making gears from scratch

Spiral Bevel Gears

HELIX AND SPIRAL GEAR CALCULATIONS
HELICAL BEVEL GEAR bevel gear in Fusion 360
SPIRAL BEVEL GEAR PINION

Worm Gears

Crossed Helical Gears

Crossed helical gears video
Title
Bevel Gears vs. Crossed Helical Gears

Hypoid Gears

Hypoid Ring and Pinion Gears Explained

CAD and 3D Modeling

Gears in general

Gear Parameters and Design Tradeoffs (This whole series is excellent)
How to Create Gears in Fusion 360
How To 3D Print Gears Like a Boss

Bevel Gears

Bevel Gear - Fusion 360
Fusion 360 to design a set of bevel gears
Fusion 360 Bevel Gears
Straight, Zerol and Spiral Bevel Gear (Tredgold's approximation), parametric (Fusion 360)

Worm Gears

Unusual 3D printed Worm Gear that can be backdriven
This is why worm gears are so cool...
Worm Gears Explained, Calculated & Modeled
Fusion 360: How to create a Worm Gear
How to model Worm Gears (Gears pt 7/?)
Worm Gears in Fusion 360
Simulating WORM GEAR MOVEMENT in Fusion 360 with Joints - demonstrates Motion link how to use a downloaded STEP from McMasterCarr

Crossed Helical Gears

Design Helical Gears for 3D Printing

Hypoid Gears

Hypoid Gear set for automotive drive axle
Hypoid Gear set for automotive drive axle
What do I need for hypoid gear modeling
Hypoid Crossed 1 Fusion 360 - Hypoid/Hyperboloidal Gear
Tutorial: The Math Behind Hyperboloidal Gears and How to Design Them in Blender

Software in Fusion 360

3D Printing - files not tested

Bevel Gears

Bevel Gear Drive Model
Bevel Gear Drive Model

Worm Gears

Worm-Gear Reducer
Worm-Gear Reducer
Worm Gear Desk Toy
Worm Gear Desk Toy
Worm Gear Drive - Print In Place
Worm Gear Drive - Print In Place
Worm-Gear
Worm Gear
Worm Gear
Worm Gear

Crossed Helical Gears

Helical Gear Stand
Helical Gear Stand
Crossed Helical Gear Set
Crossed Helical Gear Set
Helical Gear Stand
31 piece crossed helical gears set Module 1
Screw (Crossed Helical) Gear Drive Model
Screw (Crossed Helical) Gear Drive Model

Hypoid Gears

HYPOID GEARS 2
Hyperboloidal Gear Drive, 11:40, 60° Shaft Angle
Helical Gear Stand
HYPOID GEARS 2

Cage Gears

Cage & Peg Gears, 1984

Mechanism in Legos

Legos have long supported gears in their models.

History

Early gears were made from wood with cylindrical pegs for cogs and were often lubricated with grease from animal fat. Gears were used to change the rotational speed from water wheels or wind mills to power pumps or grain mills. The speed of a horse was typically too slow to use, so wooden gears increased the speed. Right angle gears may have preceeded flat gear trains, given the large amount of friction in early machines, for example, connecting water wheels to grindstones.

The industrial revolution of the 1800's saw an explosion in the use of metal gearing. A science of gear design and manufacture rapidly developed through the century.

Reconstructing the Library Display

The Mechnical Library Gear Reduction display is composed of

Research