Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Analyze and calculate velocity ratios for epicyclic gear trains.
• Explain the function of different types of cams and followers.
• Understand the basics of designing a cam profile.
• Apply gear ratios in compound gear trains to solve for speed and torque.

Lesson summary

Advanced mechanisms and gear systems are fundamental to many machines and technologies that we rely on daily. From the gears in our cars to the mechanisms in agricultural machinery vital to South Africa's economy, understanding these systems allows us to design, maintain, and improve them.

Furthermore, many industries in South Africa, such as mining, automotive manufacturing, and agriculture, heavily rely on complex machinery that incorporates these advanced mechanisms. By grasping these concepts, you'll gain a valuable foundation for future studies and careers in engineering, manufacturing, and related fields, helping you contribute to South Africa's technological advancement.

Lesson notes

2.1 Epicyclic Gear Trains Epicyclic gear trains (also known as planetary gear trains) are gear systems where one or more gears (planet gears) revolve about another gear (sun gear). They are essential components in automatic transmissions, power tools, and robotics due to their high gear ratios and compact size.

Components: Sun Gear: The central gear.

Planet Gears: Gears that revolve around the sun gear.

Ring Gear (Annulus): A gear with internal teeth that meshes with the planet gears.

Carrier: Holds the planet gears and allows them to rotate.

Methods for Velocity Ratio Calculation: Tabular Method: Fix one element (usually the carrier). Give the arm (carrier) +1 revolution. Determine the revolutions of the other gears based on their gear ratios. Multiply the revolutions in step 2 by x to account for multiple rotations. Add y revolutions to all elements. This "unlocks" the fixed element and allows it to rotate. Set up an equation based on the given conditions (e.g., ring gear fixed). Solve for x and y. Calculate the velocity ratio using the final revolutions of the input and output shafts.

Relative Velocity Method: Define the absolute speeds of each component (Nsun, Nplanet, Nring, Ncarrier). Develop kinematic equations relating these speeds based on the geometry of the gear train. Use the equation relating the number of teeth and rotational speed of meshing gears (Ns Ts = Np * Tp where N is speed and T is number of teeth). Substitute known values and solve for the unknown velocity ratio (Ninput/Noutput).