grade 8 structures & mechanical systems and control
2.5 a set of three gears that mesh is provided with the gears correctly labelled.
2.5.1 explain what will happen to the direction the gears turn if the middle gear is removed and the two remaining gears mesh and turn.

2.5.2 in relation to the driver will the driven gear turn faster or slower?

2.6 study the gear train below. gear a is the driver gear.

2.6.1 what is gear b called in this system?
2.6.2 what influence does gear b have on the rotation of gear a and c?

2.6.3 gear a is small and rotates fast. describe the effect this has on gear b, with regard to velocity and force ratio.

2.6.4 if gear b is smaller than gear c, does c have mechanical advantage? explain you answer.

2.6.5 explain the most important difference between gear system f and the rest of the gears in the system.

Question

grade 8 structures & mechanical systems and control
2.5 a set of three gears that mesh is provided with the gears correctly labelled.
2.5.1 explain what will happen to the direction the gears turn if the middle gear is removed and the two remaining gears mesh and turn.

2.5.2 in relation to the driver will the driven gear turn faster or slower?

2.6 study the gear train below. gear a is the driver gear.

2.6.1 what is gear b called in this system?
2.6.2 what influence does gear b have on the rotation of gear a and c?

2.6.3 gear a is small and rotates fast. describe the effect this has on gear b, with regard to velocity and force ratio.

2.6.4 if gear b is smaller than gear c, does c have mechanical advantage? explain you answer.

2.6.5 explain the most important difference between gear system f and the rest of the gears in the system.

Accepted Answer

### 2.5.1 # Brief Explanations: When two gears mesh directly (without a middle gear), adjacent meshing gears rotate in opposite directions. Initially, with three gears, the first and third rotate in the same direction (middle gear reverses direction). Removing the middle gear makes the two remaining gears mesh directly, so their rotation directions will be opposite. # Answer: The two remaining gears will turn in opposite directions (compared to the initial setup where the first and third turned the same way with the middle gear; now, direct meshing causes opposite rotation). ### 2.5.2 # Brief Explanations: The speed of a driven gear relative to the driver depends on the number of teeth (or gear size). If the driven gear has more teeth than the driver, it turns slower; fewer teeth, faster. When the middle gear (idler, doesn't change speed ratio) is removed, we compare the driver and the new driven gear. Typically, in a three - gear setup, the first and third gears: if the driver is, say, small and the original third is large, removing the middle (idler) and meshing driver and original third (now driven) – if the driven gear has more teeth than the driver, it turns slower; if less, faster. But generally, when two gears mesh, the smaller gear (driver) makes the larger gear (driven) turn slower (since more teeth mean each tooth on the driver moves a tooth on the driven, so a larger driven gear takes more driver rotations to complete one rotation). # Answer: If the driven gear has more teeth (is larger) than the driver, it will turn slower; if it has fewer teeth (is smaller), it will turn faster. (Commonly, in such setups, the driven gear after removing the middle gear is likely larger, so it turns slower relative to the driver.) ### 2.6.1 # Brief Explanations: Gear B is between gear A (driver) and gear C. A gear that is between a driver and another driven gear, used to transfer motion without changing the speed ratio (just direction, or to bridge the gap) is called an idler gear. # Answer: Gear B is called an idler gear. ### 2.6.2 # Brief Explanations: An idler gear (gear B) in a gear train only changes the direction of rotation of the gears it is between. It does not affect the speed (rotational velocity) of the gears. So, it will make gear A and gear C rotate in opposite directions (compared to if B was not there), but the rotational speed (number of rotations per unit time) of A and C relative to each other (the speed ratio) remains the same as if B was not present (since idler gears have the same number of teeth on both sides of the ratio calculation, so they cancel out in the speed ratio formula $ \text{Speed ratio}=\frac{\text{Number of teeth on driven}}{\text{Number of teeth on driver}} $). # Answer: Gear B (idler gear) changes the direction of rotation of gear A and gear C (makes them rotate in opposite directions relative to each other compared to direct meshing) but has no effect on their rotational speed (the speed ratio between A and C remains unchanged). ### 2.6.3 # Brief Explanations: 1. **Velocity (Rotational Speed)**: The speed ratio of two meshing gears is given by $ \text{Speed ratio}=\frac{\text{Number of teeth on driven (gear B)}}{\text{Number of teeth on driver (gear A)}} $. Since gear A is small (fewer teeth) and rotates fast, and gear B is larger (more teeth), the rotational speed of gear B will be slower than gear A. The formula for rotational speed relationship is $ N_A\times T_A = N_B\times T_B $ (where $ N $ is rotational speed, $ T $ is number of teeth), so $ N_B=\frac{N_A\times T_A}{T_B} $. Since $ T_B > T_A $, $ N_B < N_A $. 2. **Force Ratio**: The force (torque) ratio is the inverse of the speed ratio for meshing gears (from the principle of conservation of energy, $ \text{Power}_A=\text{Power}_B $, $ \text{Power}=\text{Torque}\times\text{Angular velocity} $, so $ \text{Torque ratio}=\frac{\text{Torque}_B}{\text{Torque}_A}=\frac{N_A}{N_B}=\frac{T_B}{T_A} $). Since $ T_B > T_A $, the force (torque) on gear B is greater than on gear A. So gear B has a higher force (torque) ratio (more torque) and lower rotational velocity than gear A. # Answer: - **Velocity**: Gear B will rotate slower than gear A. Using $ N_A\times T_A = N_B\times T_B $, as $ T_B > T_A $ (gear B is larger), $ N_B=\frac{N_A\times T_A}{T_B} $, so $ N_B < N_A $. - **Force Ratio**: Gear B will have a higher force (torque) ratio. The torque ratio $ \frac{\text{Torque}_B}{\text{Torque}_A}=\frac{T_B}{T_A} $, and since $ T_B > T_A $, $ \text{Torque}_B > \text{Torque}_A $, meaning gear B can exert more force (torque) than gear A. ### 2.6.4 # Brief Explanations: Mechanical advantage (MA) in gear systems related to torque is given by the ratio of the number of teeth of the driven gear to the number of teeth of the driving gear (for torque, $ \text{MA}=\frac{T_C}{T_B} $ when gear B drives gear C). If gear B is smaller (fewer teeth, $ T_B $) than gear C (more teeth, $ T_C $), then $ \text{MA}=\frac{T_C}{T_B}> 1 $. A mechanical advantage greater than 1 means that gear C has a mechanical advantage (it can exert more torque/force for the same input force from gear B, as $ \text{Torque}_C=\text{Torque}_B\times\frac{T_C}{T_B} $). # Answer: Yes, gear C has a mechanical advantage. The mechanical advantage for torque in gear systems is the ratio of the number of teeth of the driven gear (C) to the number of teeth of the driving gear (B), $ \text{MA}=\frac{T_C}{T_B} $. Since $ T_C > T_B $ (gear B is smaller than gear C), $ \text{MA}> 1 $, meaning gear C can exert more torque (force) than gear B applies to it, so it has a mechanical advantage. ### 2.6.5 # Brief Explanations: Gear system F appears to be a belt - and - pulley (or chain - and - sprocket - like, but in the diagram, it's a belt - driven system) while the rest are gear - to - gear (meshing gears) systems. The main difference is the type of power transmission: gear systems use direct meshing of teeth (positive drive, no slipping, constant speed ratio), while belt - driven systems (like F) use friction (or toothed belts) and can have slipping, and the speed ratio depends on the diameter of the pulleys (or sprockets) rather than the number of teeth (for non - toothed belts, it's a friction - based drive, while gears are a positive - engagement drive). Also, gear systems have gears with teeth meshing, while F uses a belt to connect pulleys (or gears with a belt, like a timing belt, but still different from direct gear meshing). # Answer: The most important difference is the type of power transmission: the rest of the gears use direct gear - to - gear meshing (positive mechanical engagement, no slipping, speed ratio based on number of teeth), while gear system F uses a belt (or similar) to transmit power (either friction - based or toothed - belt - based, with speed ratio based on pulley diameters, and potential for slipping in non - toothed belt systems, unlike gear meshing which has no slipping).

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2.5.1

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2.5.2