Understanding Planetary Gear Trains and Degrees of Freedom

Planetary gear trains, also known as epicyclic gear trains, are a type of gear train where one or more gears (the 'planet' gears) revolve around a central gear (the 'sun' gear). This configuration gives them unique characteristics compared to simple gear trains where all gear axes are fixed.

Key Characteristics of Planetary Gear Trains

• Moving Axes: A defining feature of planetary gear trains is that the axes of the planet gears are not fixed; they move relative to the frame, typically carried by an arm or carrier. This means option 3 ("They have a moving axis or axes") is a true statement.
• Orbiting Gears: As mentioned, the planet gears orbit around the central sun gear. This confirms that option 4 ("They have one or more gears orbiting about the central axis of the train") is also a true statement.

Degrees of Freedom (DOF) in Gear Trains

The degree of freedom of a mechanical system is the number of independent parameters that define its configuration. In the context of gear trains, it refers to the number of independent inputs (like the rotational speed of a shaft) required to determine the speed of all other shafts or components in the system.

• Simple Gear Trains: A simple gear train with fixed axes typically has one degree of freedom. If you know the speed of the input gear, you can determine the speed of all other gears based on the gear ratios.
• Planetary Gear Trains: Due to the moving axes of the planet gears and the presence of multiple relatively moving components (sun, planet, carrier, ring gear), a planetary gear train usually requires two independent inputs to define the motion of all its elements. For example, you might need to know the speed of the sun gear and the speed of the carrier to determine the speed of the ring gear or planet gears. Therefore, planetary gear trains are typically two-degree-of-freedom systems.

Analyzing the Given Statements

Let's evaluate each option based on our understanding of planetary gear trains:

• Statement 1: "They are a one-degree-of-freedom systems." As explained, planetary gear trains generally have two degrees of freedom, not one. Therefore, this statement is not true.
• Statement 2: "They are a two-degree-of-freedom systems." This aligns with our understanding; they typically have 2 DOF. This statement is true.
• Statement 3: "They have a moving axis or axes." This is a fundamental characteristic of planetary gear trains (the planet gear axes move with the carrier). This statement is true.
• Statement 4: "They have one or more gears orbiting about the central axis of the train." This describes the motion of the planet gears around the sun gear. This statement is true.

The question asks which statement is NOT true about Planetary gear trains. Based on our analysis, the statement that is not true is that they are one-degree-of-freedom systems.