507 Ways to Move Part 3: Gear Fundamentals & Geometry

Introduction: The Language of Gears

                        
                        Series Overview: This is Part 3 of our 24-part Mechanical Movements & Power Transmission Series. Before we study specific gear types (spur, helical, bevel, worm), we must first master the fundamental geometry and terminology that applies to all gears.
                    

Mechanical Movements & Power Transmission Mastery

Your 24-step learning path • Currently on Step 3

1

Foundations of Mechanical Movement

Motion types, power transmission, history of machines

Completed

2

Pulleys, Belts & Rope Drives

Simple/compound pulleys, V-belts, chain drives

Completed

3

Gear Fundamentals & Geometry

Pitch, pressure angle, module, involute profile

You Are Here

4

A gear is a toothed wheel designed to mesh with another toothed wheel (or a rack) to transmit rotary motion and power between shafts. Unlike belts and pulleys which rely on friction, gears use positive mechanical engagement — tooth interlocking tooth — to guarantee exact speed ratios with no slip and high efficiency (typically 95-99% per mesh).

Before diving into specific gear types in Parts 4-10, we must build a solid foundation in the geometry, terminology, and mathematics that govern all geared systems. This knowledge is essential whether you're designing a watch movement with 0.2 mm module gears or a ship propulsion system with 3-meter diameter gears.

                        
                        Key Insight: Understanding gear geometry is not merely academic — it directly determines whether gears will run smoothly, quietly, and durably, or will vibrate, wear rapidly, and fail. Every parameter (module, pressure angle, number of teeth) has real-world consequences for noise, load capacity, and service life.
                    

What Is a Gear?

Purpose & Function

Gears serve four fundamental purposes in mechanical systems:

Change speed: A small gear driving a large gear reduces speed and increases torque (speed reduction/torque multiplication). The reverse increases speed and reduces torque.
Change direction: Bevel gears change the axis of rotation by 90 degrees; internal gears reverse rotation direction.
Transfer power: Gears transmit power between parallel, intersecting, or non-intersecting shafts with minimal loss.
Maintain synchronization: Meshing gears maintain exact angular relationships, critical in engines (camshaft timing), clocks, and machine tools.

Classification of Gears

Shaft Relationship	Gear Type	Parts in Series
Parallel Shafts	Spur gears	Part 4
	Helical gears	Part 5
	Herringbone (double helical)	Part 5
Intersecting Shafts	Straight bevel gears	Part 6
Intersecting Shafts	Spiral bevel gears	Part 6
Non-Intersecting, Non-Parallel	Worm gears	Part 7
	Crossed helical gears	Part 5
	Hypoid gears	Part 6
Linear Motion	Rack and pinion	Part 9

Gear Terminology

Pitch, Base & Root Circles

Every gear has several imaginary circles that define its geometry:

Pitch Circle (d): The most important circle. When two gears mesh, their pitch circles are tangent to each other, rolling without slipping. The pitch circle diameter determines the gear ratio. All gear calculations start from the pitch circle.
Base Circle (d_b): The circle from which the involute tooth profile is generated. Its diameter equals d_b = d * cos(pressure angle). The base circle is always smaller than the pitch circle.
Addendum Circle (d_a): The outermost circle of the gear, passing through the tooth tips. d_a = d + 2*addendum.
Root Circle (d_f): The innermost circle, at the bottom of the tooth spaces. d_f = d - 2*dedendum.

The pitch point is where the pitch circles of two meshing gears touch. The line of action (also called pressure line) passes through the pitch point at the pressure angle, and all tooth contact occurs along this line.

Addendum, Dedendum & Clearance

Each gear tooth extends above and below the pitch circle:

Term	Definition	Standard Value (for module m)
Addendum (a)	Height of tooth above pitch circle	a = 1.0 * m
Dedendum (b)	Depth of tooth below pitch circle	b = 1.25 * m
Clearance (c)	Gap between tooth tip and root of mating gear	c = b - a = 0.25 * m
Whole depth (h)	Total tooth height = addendum + dedendum	h = 2.25 * m
Working depth	Depth of tooth engagement = 2 * addendum	2.0 * m

The clearance prevents the tooth tip of one gear from jamming into the root of the mating gear, allowing for manufacturing tolerances, thermal expansion, and lubricant film thickness.

Tooth Thickness, Face Width & Backlash

Tooth thickness is measured along the pitch circle arc and ideally equals the space width (gap between teeth) for exactly half the circular pitch. In practice, teeth are cut slightly thinner than the space to provide backlash — a small gap that prevents binding, allows for thermal expansion, and provides space for lubricant.

Face width is the length of the tooth in the axial direction. AGMA recommends face width between 8m and 16m (8 to 16 times the module), with a common design guideline of approximately 10m. Too narrow increases tooth stress; too wide causes uneven load distribution due to shaft deflection and misalignment.

Standard backlash allowances range from 0.04m to 0.10m depending on the application quality grade. Precision instruments may require anti-backlash gear designs (split gears, spring-loaded), while heavy industrial gears may use 0.1m or more.

Pitch Systems & Module

The "size" of gear teeth can be expressed in three interrelated ways. Which system you use depends on your country and industry.

Circular Pitch (p)

Circular pitch is the distance from one tooth face to the corresponding face of the adjacent tooth, measured along the pitch circle. Mathematically: p = pi * d / N, where d is the pitch diameter and N is the number of teeth. Two gears must have the same circular pitch to mesh correctly.

Diametral Pitch (P)

Diametral pitch is the number of teeth per inch of pitch diameter: P = N / d (teeth per inch). This is the traditional system used in the United States and UK. A higher P number means finer (smaller) teeth. Common values range from P=3 (large industrial gears) to P=120 (fine instrument gears).

The relationship between circular pitch and diametral pitch is: p * P = pi.

Module (m) — Metric Standard

The module is the metric standard for tooth size, defined as: m = d / N (millimeters per tooth). It is simply the inverse of diametral pitch converted to metric: m = 25.4 / P.

Module is the preferred system worldwide (except in legacy US/UK applications). Standard module values follow a preferred series:

Series	Module Values (mm)	Typical Application
First Choice	1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10	Use whenever possible
Second Choice	1.25, 1.75, 2.25, 2.75, 3.5, 4.5, 5.5, 7, 9	When first choice does not suit
Fine Pitch	0.3, 0.4, 0.5, 0.6, 0.7, 0.8	Watches, instruments, small robots

                            
                            Quick Conversions: d = m * N (pitch diameter in mm). Addendum = m. Dedendum = 1.25m. Tooth height = 2.25m. Circular pitch = pi * m. These simple relationships make the module system elegant and easy to work with.
                        

Pressure Angle

14.5, 20 & 25 Degree Systems

The pressure angle is the angle between the line of action (along which tooth force is transmitted) and the tangent to the pitch circle at the pitch point. It fundamentally shapes the tooth profile and determines the direction of the force between meshing teeth.

Pressure Angle	Tooth Shape	Advantages	Disadvantages	Status
14.5 degrees	Tall, slender teeth	Smooth, quiet operation; higher contact ratio	Weaker teeth; prone to undercutting below 23 teeth	Obsolete (legacy only)
20 degrees	Medium, well-proportioned	Good balance of strength, smoothness; undercutting above 17 teeth	Slightly noisier than 14.5	Current standard worldwide
25 degrees	Short, stubby teeth	Strongest teeth; undercutting above 12 teeth	Lower contact ratio; noisier; higher bearing loads	Special applications only

Effects on Gear Performance

The pressure angle affects nearly every aspect of gear performance:

Tooth strength: Higher pressure angle = wider tooth base = stronger teeth
Bearing loads: Higher pressure angle = larger radial (separating) force on bearings
Contact ratio: Lower pressure angle = longer line of contact = smoother engagement
Minimum teeth: Higher pressure angle = fewer minimum teeth before undercutting occurs
Noise: Lower pressure angle generally produces quieter operation

Critical rule: Meshing gears MUST have the same pressure angle and the same module (or diametral pitch). You cannot mesh a 20-degree gear with a 14.5-degree gear — the tooth profiles are incompatible and will produce incorrect conjugate action, accelerated wear, and noise.

Involute Tooth Profile

Why Involute Is Standard

An involute curve is the path traced by the end of a taut string as it is unwound from a circle (the base circle). This simple geometric construction produces a curve with remarkable properties that make it ideal for gear teeth:

Constant velocity ratio: Involute gears maintain a perfectly constant angular velocity ratio regardless of small variations in center distance. This is the fundamental requirement for smooth power transmission.
Separability: Each gear's tooth profile is generated independently from its own base circle. Any two involute gears of the same module and pressure angle will mesh correctly, regardless of their numbers of teeth.
Manufacturing simplicity: A single hob or rack-type cutter can generate involute profiles for any number of teeth of a given module and pressure angle.
Center distance tolerance: Small changes in center distance do not affect the velocity ratio — only the pressure angle changes slightly. This provides critical manufacturing tolerance.

                            
                            Historical Note: The involute was first proposed for gear teeth by Philippe de La Hire in 1694 and later by Leonhard Euler in 1754. However, it took until the mid-19th century for manufacturing technology to catch up. Before involute gears, cycloidal tooth profiles were common (and are still used in clocks), but they require exact center distances — any deviation causes speed variation and rapid wear.
                        

Conjugate Action

Conjugate action means that the angular velocity ratio between two meshing gears remains constant throughout the engagement of each tooth pair. This is equivalent to saying that the common normal at the point of contact always passes through the same fixed point (the pitch point) on the line of centers.

This property is known as the fundamental law of gearing. The involute satisfies it perfectly: because the contact between involute teeth always occurs along a straight line (the line of action), and this line always passes through the pitch point, the velocity ratio is inherently constant.

Contact Ratio

The contact ratio (also called profile contact ratio, epsilon_alpha) is the average number of tooth pairs in contact at any instant. It is defined as the length of the path of contact divided by the base pitch.

For smooth, continuous power transmission, the contact ratio must be greater than 1.0 — meaning that before one tooth pair disengages, the next pair has already begun contact. Typical values for spur gears range from 1.2 to 1.9:

1.0 - 1.2: Marginal — noisy, high dynamic loads
1.3 - 1.6: Good — standard for most applications
1.7 - 2.0: Excellent — smooth and quiet
> 2.0: High Contact Ratio (HCR) gears — special designs with modified addendum

Contact ratio increases with more teeth, lower pressure angle, and larger addendum. This is why fine-pitch gears (many small teeth) tend to run more smoothly than coarse-pitch gears of the same diameter.

Gear Manufacturing

Hobbing

Hobbing is the most common method for producing gears in volume. A hob is a cylindrical cutting tool with helical cutting teeth shaped like a worm gear. The hob and the gear blank rotate simultaneously in a precise relationship (one hob revolution advances the gear blank by one tooth), and the hob is fed axially across the gear face.

Advantages of hobbing include high productivity (continuous cutting process), good accuracy (AGMA quality 8-10), and the ability to use a single hob for any number of teeth of the same module and pressure angle. Hobbing can produce spur gears, helical gears, worm wheels, and splines. Modern CNC hobbing machines achieve AGMA quality 12 or better with appropriate hobs.

Shaping & Grinding

Gear shaping uses a reciprocating cutter (either a pinion-shaped cutter or a rack-shaped cutter) that moves up and down while the gear blank rotates. Shaping is the preferred method for internal gears (which cannot be hobbed) and for gears with shoulders or obstructions that prevent hob access.

Gear grinding is a finishing process that produces the highest quality gears (AGMA quality 12-15). Grinding removes a small amount of material from a previously rough-cut gear to achieve precise tooth profiles, excellent surface finish (Ra < 0.4 micrometers), and tight tolerances. Methods include form grinding (grinding wheel shaped to match tooth space), generating grinding (threaded grinding wheel), and profile grinding.

3D Printing & Modern Methods

3D printing of gears has evolved from prototyping to production use for certain applications. Methods include:

FDM (Fused Deposition Modeling): Nylon and PEEK gears for low-load applications. Layer lines can create stress risers at tooth roots.
SLA/DLP (Resin): Higher accuracy than FDM; suitable for fine-pitch prototype gears and molds for injection molding.
SLS (Selective Laser Sintering): Nylon PA12 gears with good mechanical properties; suitable for low-to-medium load applications.
Metal AM (DMLS/SLM): Stainless steel and titanium gears for aerospace and medical applications where traditional machining is difficult (e.g., internal features, lattice structures for weight reduction).

Other modern methods include powder metallurgy (sintered metal gears for high-volume automotive components like oil pump gears), injection molding (plastic gears for consumer products), and wire EDM (for hardened steel gears and very fine profiles).

Gear Standards

AGMA, ISO, DIN & JIS

Standard	Organization	Region	Key Standards
AGMA	American Gear Manufacturers Association	USA (global influence)	AGMA 2001 (rating), AGMA 2015 (accuracy), AGMA 6013 (industrial)
ISO	International Organization for Standardization	International	ISO 6336 (rating), ISO 1328 (accuracy), ISO 53 (basic rack)
DIN	Deutsches Institut fur Normung	Germany (EU influence)	DIN 3990 (rating), DIN 3961-3967 (tolerances)
JIS	Japanese Industrial Standards	Japan (Asia influence)	JIS B 1702 (accuracy), JIS B 1701 (tooth profile)

AGMA and ISO quality grades both range from lower numbers (less precise) to higher numbers (more precise), but the numbering is inverted: AGMA Q8 is roughly equivalent to ISO Grade 6. Modern practice increasingly uses ISO standards, with AGMA providing supplementary application-specific guidance.

History of Gears

Era	Development	Significance
c. 300 BC	Wooden peg gears in Greek water mills	Earliest known geared mechanisms for grinding grain
c. 100 BC	Antikythera mechanism	Bronze gears with triangular teeth; first analog computer for astronomical calculations
1200s	Lantern (cage) gears in medieval mills	Cylindrical pins replacing flat pegs; better load distribution
1694	Philippe de La Hire proposes involute	Mathematical foundation for modern tooth profiles
1765	Leonhard Euler formalizes involute gearing	Rigorous proof of constant velocity ratio property
1835	Whitworth develops first precision gear-cutting machine	Industrial-scale production of accurate metal gears
1897	First commercial gear hobbing machine	Mass production of high-quality gears
1950s	CNC gear grinding introduced	AGMA quality 14+ achievable; precision aerospace gears

Case Studies

Case Study 1: Watch Gear Manufacturing

A luxury mechanical watch contains 100-300 gears with modules as small as 0.10-0.20 mm. The escape wheel of a typical Swiss watch has module 0.15 mm and 20 teeth, giving a pitch diameter of just 3.0 mm. These gears are manufactured by wire EDM from hardened steel blanks, then polished to sub-micron surface finishes. Pivot holes are jeweled (synthetic ruby) to minimize friction, and the entire gear train achieves remarkable accuracy: a well-regulated mechanical watch loses less than 5 seconds per day, meaning the gear train maintains angular precision to within 0.006% over 24 hours.

Case Study 2: CNC Gear Hobbing in Automotive

A modern automotive transmission gear (e.g., a 3rd-gear helical gear with module 2.5, 30 teeth, 20-degree pressure angle, 25-degree helix angle) goes through multiple manufacturing steps. First, the gear blank is forged from 20MnCr5 case-hardening steel, then rough-turned on a CNC lathe. Hobbing removes the bulk of tooth material at a rate of 1-2 minutes per gear. After hobbing, the gear is case-carburized at 920 degrees C to achieve a surface hardness of 58-62 HRC with a tough core. Finally, hard finishing by generating grinding or honing brings the gear to AGMA quality 11-12, with tooth-to-tooth composite error under 5 micrometers.

Python Calculations

import math

class GearGeometry:
    """Complete gear geometry calculator based on module system."""

    def __init__(self, module, num_teeth, pressure_angle_deg=20.0):
        """
        Args:
            module: Module in mm (e.g., 2.0)
            num_teeth: Number of teeth (e.g., 30)
            pressure_angle_deg: Pressure angle in degrees (default 20)
        """
        self.m = module
        self.N = num_teeth
        self.phi = math.radians(pressure_angle_deg)
        self.phi_deg = pressure_angle_deg

    # --- Fundamental Diameters ---
    @property
    def pitch_diameter(self):
        """Pitch circle diameter (mm)."""
        return self.m * self.N

    @property
    def base_diameter(self):
        """Base circle diameter (mm)."""
        return self.pitch_diameter * math.cos(self.phi)

    @property
    def addendum(self):
        """Addendum height (mm)."""
        return self.m

    @property
    def dedendum(self):
        """Dedendum depth (mm)."""
        return 1.25 * self.m

    @property
    def outside_diameter(self):
        """Outside (addendum) circle diameter (mm)."""
        return self.pitch_diameter + 2 * self.addendum

    @property
    def root_diameter(self):
        """Root circle diameter (mm)."""
        return self.pitch_diameter - 2 * self.dedendum

    @property
    def whole_depth(self):
        """Total tooth depth (mm)."""
        return self.addendum + self.dedendum

    @property
    def clearance(self):
        """Bottom clearance (mm)."""
        return self.dedendum - self.addendum

    @property
    def circular_pitch(self):
        """Circular pitch (mm)."""
        return math.pi * self.m

    @property
    def base_pitch(self):
        """Base pitch (mm)."""
        return self.circular_pitch * math.cos(self.phi)

    @property
    def diametral_pitch(self):
        """Equivalent diametral pitch (teeth/inch)."""
        return 25.4 / self.m

    @property
    def tooth_thickness(self):
        """Tooth thickness at pitch circle (mm)."""
        return self.circular_pitch / 2

    @property
    def min_teeth_no_undercut(self):
        """Minimum teeth to avoid undercutting."""
        return math.ceil(2 / (math.sin(self.phi) ** 2))

    @property
    def is_undercut(self):
        """Check if gear will experience undercutting."""
        return self.N < self.min_teeth_no_undercut

    def contact_ratio(self, mating_teeth):
        """
        Calculate contact ratio with a mating gear.
        Both gears assumed to have the same module and pressure angle.
        """
        r1 = self.pitch_diameter / 2
        r2 = self.m * mating_teeth / 2
        ra1 = self.outside_diameter / 2
        ra2 = (self.m * mating_teeth + 2 * self.m) / 2
        rb1 = self.base_diameter / 2
        rb2 = r2 * math.cos(self.phi)
        C = r1 + r2  # center distance

        # Length of path of contact
        La = (math.sqrt(ra1**2 - rb1**2) +
              math.sqrt(ra2**2 - rb2**2) -
              C * math.sin(self.phi))

        return La / self.base_pitch

    def summary(self):
        """Print complete gear geometry."""
        print(f"=== Gear Geometry (Module {self.m} mm, {self.N} teeth, "
              f"{self.phi_deg} deg PA) ===")
        print(f"Pitch diameter:    {self.pitch_diameter:.3f} mm")
        print(f"Base diameter:     {self.base_diameter:.3f} mm")
        print(f"Outside diameter:  {self.outside_diameter:.3f} mm")
        print(f"Root diameter:     {self.root_diameter:.3f} mm")
        print(f"Addendum:          {self.addendum:.3f} mm")
        print(f"Dedendum:          {self.dedendum:.3f} mm")
        print(f"Whole depth:       {self.whole_depth:.3f} mm")
        print(f"Clearance:         {self.clearance:.3f} mm")
        print(f"Circular pitch:    {self.circular_pitch:.3f} mm")
        print(f"Base pitch:        {self.base_pitch:.3f} mm")
        print(f"Tooth thickness:   {self.tooth_thickness:.3f} mm")
        print(f"Diametral pitch:   {self.diametral_pitch:.2f} teeth/inch")
        print(f"Min teeth (no UC): {self.min_teeth_no_undercut}")
        print(f"Undercut risk:     {'YES' if self.is_undercut else 'No'}")


# Example: Analyze a gear pair
pinion = GearGeometry(module=2.5, num_teeth=20, pressure_angle_deg=20)
gear = GearGeometry(module=2.5, num_teeth=45, pressure_angle_deg=20)

pinion.summary()
print()
gear.summary()

cr = pinion.contact_ratio(45)
print(f"\nContact ratio (20T / 45T): {cr:.3f}")
print(f"Gear ratio: {45/20:.3f}:1")
print(f"Center distance: {(pinion.pitch_diameter + gear.pitch_diameter)/2:.2f} mm")

Exercises & Self-Assessment

Exercise 1

Gear Geometry Calculations

Calculate the complete geometry for a gear pair:

Pinion: Module 3, 18 teeth, 20-degree pressure angle
Gear: Module 3, 54 teeth, 20-degree pressure angle
Find all diameters, tooth dimensions, circular pitch, and gear ratio
Calculate the contact ratio — is it acceptable?
Will the pinion suffer from undercutting? If so, what is the minimum number of teeth to avoid it?

Exercise 2

Pressure Angle Comparison

Using the Python GearGeometry class:

Create three versions of the same gear (module 2, 25 teeth) at 14.5, 20, and 25 degrees pressure angle
Compare the base diameters, contact ratios (meshing with a 40-tooth gear), and minimum teeth for no undercutting
Explain which pressure angle you would choose for (a) a quiet instrument gear, (b) a heavily loaded industrial gear, (c) a small pinion with only 14 teeth

Exercise 3

Manufacturing Method Selection

For each application, recommend a manufacturing method and justify:

10,000 identical spur gears per month, module 2, 30 teeth, AGMA Q10
An internal ring gear for a planetary gearbox, module 4, 80 teeth
A prototype gear for a student robotics project, module 1.5, 24 teeth
An aerospace helicopter transmission gear, module 3, AGMA Q14
An oil pump gear pair, module 3, 500,000 units per year, moderate accuracy

Exercise 4

Reflective Questions

Why did the involute tooth profile ultimately replace the cycloidal profile for nearly all applications except clocks? What specific property of the involute makes it superior for general engineering use?
Explain why the contact ratio must be greater than 1.0 for continuous power transmission. What would happen physically if it were exactly 1.0? What if it were 0.8?
A gear designer wants to reduce noise by increasing the contact ratio. What three parameters could they adjust, and what are the trade-offs of each approach?
Why is the module system preferred over diametral pitch in modern international practice? What practical challenges arise when a US company needs to source replacement gears for a German machine?

Gear Specification Document Generator

Generate a professional gear specification document. Download as Word, Excel, PDF, or PowerPoint.

Draft auto-saved

All data stays in your browser. Nothing is sent to or stored on any server.

Gear Name *

Gear Type *

Module (mm) *

Number of Teeth

Pressure Angle

Material

Quality Grade

Application

Author Name

Conclusion & Next Steps

You now have a solid foundation in gear geometry and terminology. Here are the key takeaways from Part 3:

Module (m = d/N) is the fundamental tooth-size parameter — all other dimensions derive from it
Pressure angle (standard 20 degrees) determines tooth shape, strength, contact ratio, and bearing loads
The involute profile provides constant velocity ratio, center distance tolerance, and manufacturing simplicity — explaining its universal adoption
Contact ratio > 1.0 is essential for smooth power transmission; values of 1.3-1.8 are typical for good gear design
Gear manufacturing ranges from hobbing (general production) to grinding (precision finishing) to 3D printing (prototyping and special cases)
AGMA and ISO standards provide the engineering framework for specifying, manufacturing, and quality-controlling gears worldwide

Next in the Series

In Part 4: Spur & Internal Gears, we apply these fundamentals to the simplest and most common gear type. You'll learn external and internal spur gear design, gear ratio calculations, tooth interference, friction gearing, and a step-by-step spur gear design procedure.

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507 Ways to Move Part 3: Gear Fundamentals & Geometry

Table of Contents

Introduction: The Language of Gears

Mechanical Movements & Power Transmission Mastery

Foundations of Mechanical Movement

Pulleys, Belts & Rope Drives

Gear Fundamentals & Geometry

Spur & Internal Gears

Helical, Herringbone & Crossed Gears

Bevel, Miter & Hypoid Gears

Worm Gears & Self-Locking

Planetary & Epicyclic Trains

Rack & Pinion, Scroll & Sector

Gear Trains & Differentials

Cams, Followers & Eccentrics

Cranks, Linkages & Four-Bar Mechanisms

Ratchets, Pawls & Intermittent Motion

Screws, Toggle Joints & Presses

Escapements & Clockwork

Governors, Regulators & Feedback

Parallel & Straight-Line Motions

Hydraulic & Pneumatic Movements

Water Wheels, Turbines & Wind Power

Steam Engines & Valve Gear

Gearmotors, Sensors & Encoders

Efficiency, Backlash & Contact Ratio

Vibration, Noise & Failure Analysis

Materials, Lubrication & Standards

What Is a Gear?

Purpose & Function

Classification of Gears

Gear Terminology

Pitch, Base & Root Circles

Addendum, Dedendum & Clearance

Tooth Thickness, Face Width & Backlash

Pitch Systems & Module

Circular Pitch (p)

Diametral Pitch (P)

Module (m) — Metric Standard

Pressure Angle

14.5, 20 & 25 Degree Systems

Effects on Gear Performance

Involute Tooth Profile

Why Involute Is Standard

Conjugate Action

Contact Ratio

Gear Manufacturing

Hobbing

Shaping & Grinding

3D Printing & Modern Methods

Gear Standards

AGMA, ISO, DIN & JIS

History of Gears

Case Studies

Python Calculations

Exercises & Self-Assessment

Gear Geometry Calculations

Pressure Angle Comparison

Manufacturing Method Selection

Reflective Questions

Gear Specification Document Generator

Conclusion & Next Steps

Next in the Series

Continue the Series

Part 4: Spur & Internal Gears

Part 5: Helical, Herringbone & Crossed Gears

Part 2: Pulleys, Belts & Rope Drives