Cams: two laws, the same lift
Compare a cycloidal rise with a 3-4-5 polynomial. Change lift, angle and speed, and explore why lower acceleration does not settle the choice.
Open notebook and compare curves →Mechanical engineering notebook
Understand motion. Check the numbers.
Gears, transmissions and cams explained through equations, diagrams and worked examples. A path from the mechanism on paper to a simulation in your browser.
Read · calculate · check
Put the concepts to work
Notebooks with explicit assumptions, equations, calculation activities and explained answers. Text, figures and examples remain available without JavaScript.
Planetary gears: results and sign conventions
Solve three configurations of the same assembly. Then enter two speeds and check carrier speed and the tooth geometry condition.
Open notebook and check speeds →Browser laboratory
All projects →Three ways to experiment
Engrenarium Web
Investigate planetary gear speeds. Compare what happens when the ring, sun or carrier is fixed.
CrucibleCam
Explore motion laws and cam profiles. Use SVAJ diagrams to investigate continuity between segments.
Interactive Powertrain
Follow engine rotation all the way to the wheels. Connect gear selection, differential action and vehicle speed on straights and turns.
Start with what you want to learn
26 articles in the library →Choose your path
Gears & gear trains
How teeth, shared shafts and mesh types determine speed and direction.
Planetary gears & transmissions
Learn to use speeds relative to the carrier before analysing multistage assemblies.
Cams & motion laws
Connect the displacement specification to velocity, acceleration and profile geometry.
Worked exampleSame teeth.
Same teeth.
Three behaviours.
A 24-tooth sun and a 72-tooth ring. Fixing a different member changes the result — and the direction of rotation.
Follow the calculation and check the results →1 200 → 300 rpm
Fixed ring, sun input and carrier output: a 4:1 reduction. The guide compares this result with a fixed sun and a fixed carrier, and shows how to detect sign errors.
Keep learning
Explore the library →Recent articles
Cams & motion
One cam rise, two laws: cycloidal and 3-4-5 polynomial calculations
Compare displacement, velocity, acceleration and jerk for a 30 mm rise. Change the inputs, check the equations and solve exercises.
Cams & motion
CrucibleCam for Windows: more tools for turning motion laws into designs
Discover CrucibleCam 1.5.0 for Windows: cam design, SVAJ analysis, automatic search, discontinuity correction and the features unlocked by PRO.
Planetary gears & transmissions
How to check planetary gear results: three worked cases
A 24-tooth sun and 72-tooth ring: calculate three configurations, check signs and solve an exercise with two inputs.
Reference shelf
Frequently asked questions
Frequently asked questions
FAQ — gears, cams and simulators
Short answers about the portal's teaching tools and the mechanical concepts explored in the articles.
What is Engrenarium and what is it for?
Engrenarium is a planetary gears web simulator with educational and technical purposes. It helps visualize epicyclic arrangements and discuss kinematic relationships between input, output, and carrier.
Do I need to install any programs to use Engrenarium?
There is a web version and a full version for Windows. The web version allows you to quickly learn about the resource; the desktop version can be used when you want to work with the tool outside of the browser.
What is CrucibleCam and what can I analyse with it?
CrucibleCam is a browser-based cam design tool. It assembles motion segments, generates the cam profile and lets you inspect displacement, velocity, acceleration and jerk diagrams, as well as pressure angle and curvature.
Which displacement curve should I choose for a cam?
There is no single best curve. The choice depends on the required rise or return, available cam angle, rotation speed and the acceptable velocity, acceleration and jerk. Continuity at the junctions between segments must also be checked.
What does CrucibleCam's discontinuity correction change?
The correction can redistribute the angular interval β or the displacement variation ΔL of the segments to make boundary conditions compatible. The designer must still verify whether the resulting motion, pressure angle and curvature are appropriate for the mechanism.
Does the portal depend only on the simulator?
No. In addition to the simulator, there are articles on gears, compound trains, differentials, cams and motion curves. Engrenarium complements these texts when visualizing a planetary gear train helps you understand the calculation.
Who was the content written for?
The material was organized for students, teachers and professionals who need clear explanations about mechanisms, gears and teaching support resources in mechanical engineering.
How to get in touch?
Use the email available in the contact section or on the page About for questions about the technical content, tools or institutional context of the portal.
Mechanisms glossary
Technical reference
Glossary of terms
Objective definitions of frequent terms in the study of gears, transmissions and mechanisms.
- Module (m)
- Dimensional parameter that relates the pitch diameter to the tooth count of a gear.
- Gear ratio
- Ratio between the angular velocity of the input element and that of the output element.
- Sun gear
- Central externally toothed gear on a planetary gear train.
- Planet gear
- Element that meshes with other members of the train and can rotate around its own axis and the central axis of the assembly.
- Ring gear
- Gear with internal teeth that surrounds the planetary system.
- Planet carrier
- Structural element that supports the axes of the planet gears and rotates around the central axis of the system.
- Pressure angle
- Geometric angle associated with the transmission of force between elements in contact, relevant in gears and in cams.
- Train value
- Constant obtained with fixed carrier, used to relate speeds in epicyclic gear trains.
- Cam
- Profiled mechanical element that imposes a prescribed motion on a follower through direct contact.
- Follower
- Element that remains in contact with the cam and converts its profile into translational or oscillating motion.
- Displacement curve
- Law that defines follower position as a function of cam angle during rise, return and dwell intervals.
- SVAJ
- Set of displacement, velocity, acceleration and jerk diagrams used to evaluate the smoothness of a cam motion law.
- Dwell
- Angular interval in which the follower remains at a constant displacement while the cam continues to rotate.
- Base circle
- Smallest circle tangent to the cam profile; its radius affects pressure angle, curvature and the overall size of the cam.
- Jerk
- Time derivative of acceleration. Abrupt jerk changes can increase vibration and dynamic loads in high-speed mechanisms.
Books and translations
Publications
Translated books linked to the author's work
The books below bring together classic mechanisms, devices and movement solutions. They speak to the site's themes because they show how pairs of gears, cams, levers, and transmissions appear in real-world applications.
Translation into Portuguese
507 Mechanical Movements: Mechanisms and Devices
Translated edition with illustrated mechanisms and descriptions of operation in various applications, useful as reference material for students and those interested in movement synthesis.
Blucher Publisher, 2019
Translation into Portuguese
1800 Mechanical Movements, Devices and Components
Translated reference work with a wide variety of mechanisms, devices and classic mechanical solutions, useful for consulting alternative transmission, guidance, control, and motion conversion.
Barbudenge, 2025