Gear Mechanisms and Ratios

This tutorial explains the gear ratio formulas for simple and planetary gear mechanisms. It begins with basic facts about meshing gears, including parameters like the number of teeth and module. The tutorial then describes the components of a planetary mechanism, such as the Sun gear, ring gear, planet gears, and carrier. Key equations connecting linear and angular velocities are reviewed. The tutorial explains the gear ratio for simple gear mechanisms and derives the formula for planetary mechanisms, concluding with a practical example.

What is the main difference between the gear ratio formulas for simple gear drives and planetary mechanisms?

• Both have equally complex formulas.

• Simple gear drives have a more complex formula.

• Planetary mechanisms have a simpler formula.

• Simple gear drives have a simpler formula.

Which two parameters fully define a gear?

• Module and radius

• Number of teeth and module

• Diameter and radius

• Number of teeth and diameter

For two gears to mesh, what must be the same?

• Number of teeth

• Radius

• Module

• Diameter

What is the outer gear with teeth pointing inwards called in a planetary mechanism?

• Carrier

• Planet gear

• Ring gear

• Sun gear

In a planetary mechanism, what is the platform on which the planet gears are mounted called?

• Carrier

• Planet gear

• Ring gear

• Sun gear

What is the relationship between linear velocity and angular velocity for an object moving in a circle?

• Linear velocity is the square of angular velocity.

• Linear velocity equals angular velocity times the radius.

• Linear velocity is half of angular velocity.

• Linear velocity is independent of angular velocity.

In a simple two-gear mechanism, the gear ratio is the ratio of what?

• The radii of the gears

• The number of teeth of the smaller gear to the larger gear

• The number of teeth of the larger gear to the smaller gear

• The diameters of the gears

In the most common scenario of a planetary mechanism, what is the input shaft connected to?

• Ring gear

• Planet gear

• Sun gear

• Carrier

What is the instantaneous velocity of the top point of a wheel rolling without slipping?

• Independent of the wheel center's velocity

• Twice the linear velocity of the wheel center

• Half of the linear velocity of the wheel center

• Equal to the linear velocity of the wheel center

In the example given, if Zr is 60 and Zs is 12, what is the gear ratio?

• 8

• 7

• 6

• 5