Planetary Mechanisms and Gear 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 discussed, leading to the derivation of the gear ratio for a planetary mechanism. The tutorial concludes with an example calculation, demonstrating the concepts covered.

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

• Simple gear drives are more complex.

• Planetary mechanisms do not use gear ratios.

• Planetary mechanisms have a simpler formula.

• Simple gear drives have a straightforward 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?

• Diameter

• Number of teeth

• Radius

• Module

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 does the linear velocity of an object moving in a circle equal?

• Radius minus angular velocity

• Angular velocity plus the radius

• Radius divided by angular velocity

• Angular velocity times the radius

In a simple two-gear mechanism, what does the gear ratio equal?

• Sum of the teeth of both gears

• Ratio of the larger gear's teeth to the smaller gear's teeth

• Difference in the number of teeth between the gears

• Ratio of the smaller gear's teeth to the larger gear's teeth

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

• Sun gear

• Ring gear

• Planet gear

• Carrier

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

• Equal to the wheel's center velocity

• Half of the wheel's center velocity

• Twice the wheel's center velocity

• Three times the wheel's center velocity

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

• 5

• 6

• 7

• 8