Epicycloid vs. Hypocycloid: Know the Difference

By Shumaila Saeed || Updated on December 25, 2023

An epicycloid is a curve traced by a point on a circle rolling outside another circle, whereas a hypocycloid is traced by a point on a circle rolling inside another circle.

Epicycloid vs. Hypocycloid

Key Differences

An epicycloid is formed when a circle rolls around the outside of another circle, with the tracing point on the circumference of the rolling circle. On the other hand, a hypocycloid is generated when a circle rolls inside another circle, with the tracing point also on the circumference of the rolling circle.

Dec 07, 2023

In an epicycloid, the resulting curve is more extended and convoluted, often with cusps pointing outward. In contrast, a hypocycloid typically has inward-pointing cusps, creating a star-like shape when the rolling circle is significantly smaller than the fixed circle.

Dec 07, 2023

The mathematical complexity of an epicycloid increases with the size of the rolling circle relative to the fixed one. For hypocycloids, the complexity is influenced by the ratio of the diameters of the inner and outer circles.

Dec 07, 2023

Epicycloids can have varying appearances based on the ratio of the diameters of the two circles, from elongated loops to flower-like patterns. Hypocycloids can range from simple ellipses to complex star shapes, again depending on the diameter ratio.

Dec 07, 2023

Epicycloids have applications in gear design, particularly in systems where non-standard gear tooth profiles are beneficial. Hypocycloids are also used in gear systems, especially in mechanisms like rotary engines where compact and efficient gear shapes are necessary.

Dec 07, 2023

ADVERTISEMENT

Comparison Chart

Rolling Motion

Outside another circle

Inside another circle

Dec 07, 2023

Curve Shape

Extended, convoluted curves

Star-like shapes with inward cusps

Dec 07, 2023

Cusp Direction

Outward pointing

Inward pointing

Dec 07, 2023

Appearance

Varies from elongated loops to flower-like

Ranges from simple ellipses to complex stars

Dec 07, 2023

Applications

Gear design with non-standard tooth profiles

Compact and efficient gear systems

Dec 07, 2023

ADVERTISEMENT

Epicycloid and Hypocycloid Definitions

Epicycloid

Curve traced by a point on the rim of a circle rolling outside another circle.

The epicycloid drawn by the rolling gear was intricate.

Nov 27, 2023

Hypocycloid

Curve formed by a point on a circle rolling inside another circle.

The children's toy created a perfect hypocycloid.

Nov 27, 2023

Epicycloid

Used in gear design for creating specific tooth profiles.

Engineers used an epicycloid curve for the new gear's design.

Nov 27, 2023

Hypocycloid

Varies from simple ellipses to complex shapes.

The hypocycloid shifted from an ellipse to a more intricate pattern.

Nov 27, 2023

Epicycloid

Appears in various forms, from loops to flower-like shapes.

The epicycloid resembled a series of interconnected flowers.

Nov 27, 2023

ADVERTISEMENT

Hypocycloid

Used in compact and efficient gear mechanisms.

The rotary engine's design incorporated a hypocycloid.

Nov 27, 2023

Epicycloid

A mathematical curve with cusp points facing outward.

The epicycloid in the diagram had several outward-facing cusps.

Nov 27, 2023

Hypocycloid

Dependent on the ratio of inner to outer circle diameters.

Adjusting the diameters resulted in a different hypocycloid shape.

Nov 27, 2023

Epicycloid

A complex curve depending on the diameter ratio of the involved circles.

Changing the circle sizes altered the epicycloid's shape.

Nov 27, 2023

Hypocycloid

Characterized by inward-pointing cusps, often star-like.

The hypocycloid in the machinery looked like a star.

Nov 27, 2023

Epicycloid

The curve described by a point on the circumference of a circle as the circle rolls on the outside of the circumference of a second, fixed circle.

Oct 19, 2023

Hypocycloid

The plane locus of a point fixed on a circle that rolls on the inside circumference of a fixed circle.

Oct 19, 2023

Epicycloid

(geometry) The locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle. Category:en:Curves

Oct 19, 2023

Hypocycloid

(geometry) The locus of a point on the circumference of a circle that rolls without slipping inside the circumference of another circle. Category:en:Curves

Oct 19, 2023

Epicycloid

A curve traced by a point in the circumference of a circle which rolls on the convex side of a fixed circle.

Oct 19, 2023

Hypocycloid

A curve traced by a point in the circumference of a circle which rolls on the concave side in the fixed circle. Cf. Epicycloid, and Trochoid.

Oct 19, 2023

Epicycloid

A line generated by a point on a circle rolling around another circle

Oct 19, 2023

Hypocycloid

A line generated by a point on a circle that rolls around inside another circle

Oct 19, 2023

Repeatedly Asked Queries

What about the cusps of a hypocycloid?

They point inward.

Dec 07, 2023

What defines a hypocycloid?

A curve traced by a point on a circle rolling inside another circle.

Dec 07, 2023

What is an epicycloid?

A curve traced by a point on a circle rolling outside another circle.

Dec 07, 2023

Can an epicycloid be simple in shape?

It tends to be more complex.

Dec 07, 2023

Is a hypocycloid always star-like?

Often, but it can also be an ellipse.

Dec 07, 2023

Are epicycloids used in gear design?

Yes, for non-standard tooth profiles.

Dec 07, 2023

What about hypocycloids in gears?

Used in compact and efficient gears.

Dec 07, 2023

How do the cusps of an epicycloid point?

Outward.

Dec 07, 2023

Does the size ratio affect hypocycloids?

Yes, it alters their shape too.

Dec 07, 2023

Can hypocycloids be seen in everyday objects?

Sometimes, in specific gears.

Dec 07, 2023

Do epicycloids vary with circle size ratio?

Yes, they change shape with the ratio.

Dec 07, 2023

Do children's toys use epicycloids?

Some drawing toys do.

Dec 07, 2023

What is a complex epicycloid example?

A curve with many loops or petals.

Dec 07, 2023

Can epicycloids be symmetric?

They often have symmetrical patterns.

Dec 07, 2023

What's a simple hypocycloid example?

A three-lobed curve.

Dec 07, 2023

Do epicycloids have practical applications?

Yes, in specific mechanical designs.

Dec 07, 2023

Are hypocycloids in children's toys?

Yes, in some spirograph toys.

Dec 07, 2023

Are hypocycloids always symmetrical?

Generally, but depends on the circle ratio.

Dec 07, 2023

Are epicycloids found in nature?

Not typically, they're more mathematical.

Dec 07, 2023

What's a unique use of hypocycloids?

In rotary engines for compact design.

Dec 07, 2023

Share this page

Link for your blog / website

HTML

Link to share via messenger

Titrant vs. Titrate

Epicycloid vs. Hypocycloid

Wallet vs. Purse

Epicycloid vs. Hypocycloid

About Author

Written by

Shumaila Saeed, an expert content creator with 6 years of experience, specializes in distilling complex topics into easily digestible comparisons, shining a light on the nuances that both inform and educate readers with clarity and accuracy.

Trending Comparisons

Duplicate vs. Replicate

Duplicate vs. Replicate

May 24, 2026

Duplicate means to create an exact copy, focusing on identicalness, while replicate emphasizes reproducing the essence or function, often in a scientific context.

Border vs. Boundary

Border vs. Boundary

December 11, 2025

A border is a line that marks the edges between countries, while a boundary delineates limits within countries, properties, or concepts.

Smarter vs. More Smart

Smarter vs. More Smart

September 25, 2025

"Smarter" is the comparative form of "smart," commonly used in English; "more smart" is a less standard comparative form used for emphasis or stylistic reasons.

Humans vs. Aliens

Humans vs. Aliens

July 9, 2025

Humans are Earth's native species, known for their cultural diversity and biological adaptability, whereas aliens, as hypothetical beings, are often imagined with advanced technology and diverse forms in science fiction.

Respective vs. Perspective

Respective vs. Perspective

May 17, 2026

Respective refers to relating to each person or thing mentioned separately, whereas perspective is one's viewpoint or angle on a subject.

Nightingale vs. Mockingbird

Nightingale vs. Mockingbird

April 21, 2026

Nightingales are known for their rich, melodious night songs, specializing in their own tunes, while mockingbirds mimic sounds from their surroundings, showcasing a wide repertoire of imitated songs.

Company vs. Factory

Company vs. Factory

May 8, 2026

A company is a business entity engaged in commercial, industrial, or professional activities, while a factory focuses on manufacturing goods through mass production.

Closet vs. Dresser

Closet vs. Dresser

December 5, 2025

A closet is a tall, enclosed storage space usually built into a room's walls for hanging or storing clothes, while a dresser is a piece of furniture with drawers for keeping clothes and often has a flat top for items.

Metro vs. Train

Metro vs. Train

October 11, 2025

Metro refers to an urban railway system for cities, typically underground; a train is a set of rail vehicles on railways, used for long or short distances.

Treble vs. Bass

Treble vs. Bass

July 14, 2025

Treble refers to higher frequencies in sound, producing a sharp, clear tone, while Bass encompasses lower frequencies, giving a deep, resonant sound.

Strive vs. Thrive

Strive vs. Thrive

October 25, 2025

Strive involves making efforts towards a goal, while thrive denotes flourishing or prospering, often naturally.

Sentence vs. Utterance

Sentence vs. Utterance

June 27, 2025

A sentence is a grammatically complete series of words conveying a statement, question, exclamation, or command, while an utterance is any spoken word, phrase, or sound.

Royal Blue vs. Cobalt Blue

Royal Blue vs. Cobalt Blue

March 20, 2026

Royal Blue is a deep, vivid shade of blue with a hint of purple, symbolizing richness and sophistication, while Cobalt Blue is a slightly brighter blue with a hint of green, known for its striking vibrancy and clarity.

Sea Salt vs. Rock Salt

Sea Salt vs. Rock Salt

May 21, 2026

Sea salt is produced through the evaporation of seawater, offering a complex flavor profile, while rock salt is mined from salt deposits, known for its larger crystals and purity.

Infection vs. Disease

Infection vs. Disease

May 18, 2026

An infection is the invasion and multiplication of microorganisms in the body, while a disease is a condition disrupting normal body functions, often caused by infections, genetics, or environmental factors.

SIT vs. UAT

August 27, 2025

SIT (System Integration Testing) focuses on verifying interactions between modules, while UAT (User Acceptance Testing) ensures the system meets user requirements and expectations.

Saudi Arabia vs. UAE

Saudi Arabia vs. UAE

September 19, 2025

Saudi Arabia is largest country in the Middle East, known for its oil wealth and conservative Islamic culture, whereas UAE, federation of seven emirates, is renowned for its progressive cities like Dubai and Abu Dhabi, blending modernity with tradition.

Palm Tree vs. Coconut Tree

Palm Tree vs. Coconut Tree

May 22, 2026

Palm trees are a diverse group of plants that include many species, while coconut trees are a specific type of palm tree known for producing coconuts. Coconut trees are characterized by their tall, slender trunks and large, feather-like leaves.

NFC vs. AFC

May 12, 2026

NFC and AFC are conferences in the NFL, focusing on geographical division; NFC teams are historically from the older NFL, while AFC teams originated from the AFL.

Analyzation vs. Analysis

Analyzation vs. Analysis

July 4, 2025

"Analysis" is the correct term for the process of examining something in detail to understand it better or draw conclusions, while "analyzation" is a less common and often considered incorrect form of the word.

Cliff vs. Bluff

Cliff vs. Bluff

November 1, 2025

A cliff is a steep, high rock face, often along coastlines or mountains, while a bluff is a broad, rounded cliff often overlooking a river, valley, or other flat areas, with a steep face and a relatively flat top.

Extends keyword in Java vs. Implements keyword in Java

Extends keyword in Java vs. Implements keyword in Java

May 28, 2026

The extends keyword in Java is used for class inheritance, allowing a class to inherit from another class, whereas implements is used by a class to adhere to an interface, defining methods the class must implement.

Vinyl Flooring vs. Hybrid Flooring

Vinyl Flooring vs. Hybrid Flooring

April 29, 2026

Vinyl flooring offers affordability and water resistance, ideal for high-moisture areas; hybrid flooring combines the best of laminate and vinyl, providing durability and a more realistic wood look.

Falcon vs. Eagle

Falcon vs. Eagle

December 14, 2025

Falcons are smaller, faster birds known for their pointed wings and high-speed dives, while eagles are larger, possess broad wings, and showcase immense strength, especially in their talons.

Featured Comparisons

Helicopter vs. Chopper

Helicopter vs. Chopper

Hard Copy vs. Soft Copy

Hard Copy vs. Soft Copy

Fate vs. Destiny

Fate vs. Destiny

Coyote vs. Jackal

Coyote vs. Jackal

Cuddle vs. Snuggle

Cuddle vs. Snuggle