Transmission Mechanisms

Explain the difference between a machine and a mechanism using an example of each: consider that the machine is the complete device that performs a task for us (a bicycle, a blender) and the mechanism is each internal device that transmits or transforms motion (the chain, the gears).

Draw or describe a simple lever and label its three elements: the fulcrum, the effort applied (F), and the load to overcome (R). Using the example of a park seesaw, explain what happens when you move the fulcrum closer to or farther from the center.

There are three classes of lever depending on what is in the middle: the fulcrum (first class), the load (second class), or the effort (third class). Classify these objects and justify your answers by thinking about where each component is when using them: a pair of scissors, a wheelbarrow, and a pair of tweezers.

The figure shows a lever with its fulcrum, the applied effort, and the load, but the name of one of the measurements is missing.

Name all the elements of the lever in the figure (including the hidden one), state which class of lever it is, and explain, looking at the distances, whether you will apply a force greater than, less than, or equal to the weight of the load with this lever.

The principle of moments states that the effort is balanced when $F \times d_F = R \times d_R$. On a see-saw, a load of $40\ \text{N}$ is $1\ \text{m}$ from the fulcrum and you push at $2\ \text{m}$ from the fulcrum: calculate the force you must apply. Explain what you have gained (force) and what you have lost (distance) by moving further from the fulcrum.

A fixed pulley at the top of a flagpole allows a flag to be raised by pulling down on the rope. Explain what the fixed pulley changes (the direction of the force) and what it does not change (the amount of force required), and reason why it is still much more convenient than climbing up.

A movable pulley is attached to the load itself, so that the rope supports it with two segments. Explain why the required force is shared in this way (each segment "pulls" half) and what price is paid in return: how much rope must be pulled in to raise the load by one meter?

A block and tackle combines a fixed pulley with a movable one, so that the load hangs from two segments of rope. If the sack weighs $200\ \text{N}$, calculate what force must be applied by pulling the free end and how much rope must be pulled in to raise it by $2\ \text{m}$. State in your own words the "trade-off" made by any movable pulley: force in exchange for distance.

Two gears in mesh transmit rotation from one shaft to another. Explain two things that change when moving from one wheel to the other (the direction of rotation and the speed if they have a different number of teeth) and name two appliances in your home that contain gears.

The figure shows two meshed gears with their number of teeth and the speed of the first; that of the second is covered up.

Calculate the speed of the small gear using the gear ratio $i = \frac{n_{salida}}{n_{entrada}} = \frac{z_{entrada}}{z_{salida}}$, state which direction it rotates relative to the large gear, and explain why the small gear rotates faster.

Two friction wheels transmit rotation through direct contact, without teeth or a belt: one drives the other through friction. Explain in which direction the driven wheel rotates, what happens if the wheels are dirty or wet (it slips and does not transmit properly), and give an example where this slipping would be a problem and another where it acts as useful protection.

You need to design the reduction mechanism for a warehouse conveyor belt. The motor rotates at $1,200\ \text{rpm}$ clockwise, but the belt must rotate at exactly $200\ \text{rpm}$, also clockwise. In the workshop, you only have gears with $20$, $40$, and $60$ teeth, and shafts where you can mount one or two connected gears.

(a) Prove through calculations why it is impossible to achieve this exact reduction using a single pair of these gears.

(b) Design a compound gear train of two pairs of gears, choosing the appropriate gears to obtain exactly the required $200\ \text{rpm}$.

(c) Determine the direction of rotation of the output shaft in your design. Does it rotate in the clockwise direction required by the belt? If not, explain what mechanical element you would have to add to correct it without altering the final speed.

A bicycle transmits pedaling with a chainring, a chain, and a sprocket, rather than two meshed gears. Explain the advantage of using a chain to transfer rotation from one shaft to another that is far away, and why the chain does not slip like a slippery flat belt would.

Two pulleys connected by a belt: the driver pulley has a diameter of $10\ \text{cm}$ and rotates at $300\ \text{rpm}$, and the driven pulley has a diameter of $30\ \text{cm}$. Calculate the transmission ratio and the speed of the large pulley, and explain whether this system increases or reduces the speed (and what happens to the force on the output shaft as a result).

On a bicycle, the chainring has $44$ teeth and the sprocket has $11$. Calculate how many revolutions the wheel makes for each pedal revolution, and explain what you would change (chainring or sprocket) to climb a steep hill pedalling more easily, even if the wheel travels less distance per pedal stroke.

A worm drive consists of a worm screw that meshes with a gear wheel (worm wheel): each turn of the worm advances the worm wheel by just one tooth. If the worm wheel has $40$ teeth, calculate how many turns of the worm are needed for one complete revolution of the worm wheel, and explain why this mechanism provides a massive speed reduction and why the worm wheel cannot turn the worm (it is non-reversible).

Choose the transmission mechanism (lever, fixed pulley, block and tackle, belt and pulleys, gears, chain drive, or worm drive) for each requirement and justify your answer: (a) raising a piano to a first floor up the facade, (b) transmitting rotation from the motor to blender blades while greatly reducing speed, (c) changing only the direction of a force to hoist a sail, and (d) transmitting pedalling to the rear wheel.

Two workers must lift a $600\ \text{N}$ stone slab using a $2\ \text{m}$ long steel bar. They discuss two options:

• Option A (first-class lever): place the fulcrum at $0.4\ \text{m}$ from the stone and push down on the opposite end.

• Option B (second-class lever): rest one end on the ground, place the stone at $0.4\ \text{m}$ from the fulcrum, and pull up from the other end.

(a) Calculate the force that must be applied in each option.

(b) Justify which of the two configurations requires less effort based on comparing their lever arms.

(c) If a person can only exert a maximum of $100\ \text{N}$, is Option A valid? If it is not, calculate the maximum distance from the stone at which the fulcrum would have to be placed so as not to exceed those $100\ \text{N}$.

In a mechanical workshop, they want to install a manual winch to suspend $1,800\ \text{N}$ engines while they are being repaired. The technician is hesitating between two options for the crank's speed reducer:

• Option A: A simple gear train with two spur gears with $z_1 = 10$ and $z_2 = 50$.

• Option B: A $1$-start worm gear meshing with a $50$-tooth worm wheel.

(a) Calculate the transmission ratio of each option and predict with which of the two the mechanic will have to apply less force to the crank.

(b) If the mechanic releases the crank halfway through the lifting process to grab a tool, predict what will happen to the suspended engine in Option A and in Option B, justifying the mechanical concept involved.

(c) Based on the previous results, conclude which mechanism is ideal and reason what the drawback or "price to pay" (in time or number of turns) is when choosing the safer option.