Exercises: Motion transformation mechanisms

Explain the difference between a transmission mechanism and a motion transformation mechanism, giving an example of each: a bicycle chain versus the screw and nut mechanism in a tap. What is the input and output in each case (rotation or linear displacement)?

When turning a nut on a screw, the nut moves forward along the thread. Explain what transformation occurs (rotation into linear movement) and name two everyday objects that use the screw and nut mechanism, indicating what is achieved by this linear movement in each case.

The figure shows a slider-crank mechanism: a rotating wheel (crank), a hinged rod (connecting rod), and a part that can only slide between two guides (slider).

Explain what input motion goes into the mechanism and what output motion comes out (what the slider does while the crank turns full circles) and name a real-life machine where this transformation occurs.

A rack and pinion is a toothed wheel that meshes with a toothed bar. Explain what transformation it performs and match it with its use: (a) car steering, which converts the turning of the steering wheel into the side-to-side turning of the road wheels, and (b) a rack corkscrew, which converts the turning of the handle into the rising of the cork.

A cam is a pear-shaped component that, as it rotates, pushes a follower making it move up and down. Explain what transformation it performs and why the shape of the cam determines the exact motion of the follower. Give an example of a machine that uses cams (sewing machine, car engine).

A crankshaft is a shaft with bends, like several cranks in a row, which converts the reciprocating motion of the pistons into the rotation of the engine shaft. Explain how it is similar to a slider-crank mechanism and where it is found in a car: what input motion enters through the pistons and what output motion goes to the wheels?

An eccentric is a wheel whose axis of rotation is not at its centre: as it rotates, its edge pushes in a similar way to a cam. Explain how it is similar to and different from a cam, and why an electric sander uses an eccentric to vibrate (an off-centre rotating mass).

A ratchet is a mechanism with sloped teeth and a pawl that allows a shaft to rotate in one direction and blocks it in the other. Explain how it works using the example of a car handbrake or a socket wrench, and explain what would happen when pedalling a bicycle if the rear sprocket did not have a ratchet mechanism (the freewheel).

The figure shows a rotating cam with its follower resting on top; the motion of the follower is to be described.

Describe precisely what the follower does during one complete revolution of the cam (when it rises, when it falls, when it is at its highest point), explain what this motion depends on, and reason how it would change if the cam were more "pointed".

The figure shows a pinion with $12$ teeth meshed with a rack: for each tooth that passes, the rack advances $5\ \text{mm}$.

Calculate how many millimetres the rack advances when the pinion turns one complete revolution and how many revolutions are needed for it to advance $30\ \text{cm}$. Explain why this mechanism converts rotation into such precise displacement that it is used in 3D printers.

Identify the transformation mechanism in each device and explain the transformation it performs: (a) a car windscreen wiper (a motor rotates and the blades sweep from side to side), (b) an old pillar drill (turning a handle makes the drill bit move down in a straight line to drill), and (c) the pendulum of an antique clock moving the hands. Draw a diagram of one of them.

You can do it on paper and send a photo with your answer.

In a foot pump for inflating tyres, you push the plunger down and... nothing rotates. But in a combustion engine, it is the pistons that push and the shaft that rotates. Explain that the slider-crank mechanism works in both directions (from rotary to reciprocating and from reciprocating to rotary), giving an example of each direction of use.

A car jack lifts a tonne by turning a small handle: it is a screw and nut mechanism. Explain why it can lift so much weight (each turn advances very little: high force in exchange for a large rotational movement) and what practical advantage there is in the nut not "unscrewing" by itself under the weight of the car.

To operate an engine valve, either a cam or an eccentric can be used. Compare both solutions: which one allows you to design the exact movement of the valve (how much it rises and when) and which one is simpler to manufacture, and explain why cams won out in car engines.

A bicycle freewheel uses a ratchet mechanism: when pedalling forwards it drives the wheel, but if you stop pedalling, the wheel keeps turning without you. Explain how the ratchet achieves this (what it locks and what it frees) and what would happen on a "fixed-gear" bike, where the pedals and wheel are fixed together, when going down a hill.

You want a toy doll to wave (arm up and down) when wound up, which provides a rotational movement. Propose two different mechanisms capable of converting this rotation into the reciprocating motion of the arm (cam with follower and slider-crank with eccentric), draw both diagrams, and evaluate which one is easier to fit inside the toy.

You can do it on paper and send a photo with your answer.

A student builds a model windscreen wiper by directly connecting the shaft of a toy electric motor (which rotates at 3000 rpm with very low torque) to the crank of the wiper blades. When placing the blades on the dry windscreen and turning the motor on, the blades barely move for an instant, vibrate abruptly, and the motor stalls, heating up quickly.

1. Explain the two mechanical reasons why this direct assembly fails (think about the appropriate rotational speed for wiping and the torque required to overcome friction).

2. Propose which intermediate mechanism you must necessarily insert between the motor and the crank to solve both problems at the same time, and justify your choice.

In an industrial sewing machine, a single motor rotates a shaft that simultaneously drives the needle (reciprocating vertical movement) and the feed dogs located in the base (which push the fabric forward in small steps).

1. Following a breakdown, the needle starts breaking continuously because the feed dogs push the fabric backwards just as the needle is pierced through it. Describe in detail the correct synchronisation between both movements during a complete cycle (one revolution of the motor shaft): at what moments the fabric must advance and at what moments it must remain still.

2. Justify why a rack and pinion mechanism driven by a motor that continuously reverses its direction of rotation is not used for the needle's movement, and why a crank-slider or a cam driven by a continuously rotating motor is used instead.

Design a mechanical toy: when turning a handle, a cardboard bird moves up and down over its nest. Choose the mechanism (cam, eccentric, or slider-crank), draw the complete diagram showing the handle and the bird, justify your choice over the other options, and explain how you would make the bird rise slowly and drop suddenly.

You can do it on paper and send a photo with your answer.

Observe how a winged corkscrew (with two arms) works:

1. When turning the top butterfly handle, the worm screws vertically into the cork and, at the same time, the two lateral arms rise on their own. Identify the mechanism that couples the central shaft to the arms to achieve this transformation.

2. When we push the arms down with our hands to extract the cork, each arm acts as a lever. Draw or explain the position of the fulcrum, the effort (applied force), and the load (resistance), and identify, with reasoning, which class of lever it corresponds to.

3. If you were to redesign the corkscrew by making the arms twice as long, what effect would it have on the force you must apply with your hands to pull out the cork? Justify whether this would entail any practical disadvantage in the use of the tool.

A team is designing a hoist to lift pallets of bricks on a construction site and is hesitating between two systems to reduce the motor's speed and drive the cable drum:

• Option A: A spur gear train.

• Option B: A worm and worm wheel (worm gear) reduction unit.

• If a sudden power cut occurs while the load is suspended at a height of 10 metres, predict with reasoning what will happen to the load in Option A and in Option B based on the reversibility of each mechanism.

• In a petrol car engine, the crank-slider mechanism connects the piston to the crankshaft. Explain why in this case it is essential that the mechanism is completely reversible, analysing what happens when starting the car with the key compared to when the engine is already running autonomously.

A workshop press operates using a lead screw (screw-nut) mechanism with a thread pitch of $p = 2\ \text{mm}$, driven by a crank with a radius of $r = 14\ \text{cm}$.

1. If you need the end of the press to advance $7\ \text{cm}$ to clamp a workpiece, calculate how many complete turns the crank must make.

2. When completing one full turn, your hand covers the perimeter of the circle ($L = 2 \cdot \pi \cdot r$, take $\pi \approx 3,14$). If you apply a force of $10\ \text{N}$ at the end of the crank and we neglect friction (input work equals useful work: $F_{\text{hand}} \cdot L = F_{\text{press}} \cdot p$), calculate the compressive force exerted by the press on the workpiece.

3. If the lead screw were replaced with one having a pitch of $4\ \text{mm}$, justify how the number of turns required to clamp across the same distance and the force you would need to apply to achieve the same clamping force would change.

In a domestic roller blind, the strap winds around a pulley with a diameter of $D_1 = 16\ \text{cm}$, which is attached to the same cylindrical shaft with a diameter of $D_2 = 8\ \text{cm}$ around which the blind rolls.

1. If you pull the strap and the shaft completes 4 full turns, calculate the length of strap you have pulled out and the height the blind has been raised (take $\pi \approx 3,14$).

2. For a very heavy wooden blind, a user finds it requires too much effort to pull the strap. Two modifications are proposed to them:

3. Proposal A: Replace the strap pulley with one that has a diameter of $24\ \text{cm}$.

4. Proposal B: Replace the strap pulley with one that has a diameter of $10\ \text{cm}$.

Justify which of the two proposals reduces the force the user must exert and explain what associated drawback it will have regarding the length of strap needed to raise the blind completely.

A student proposes simplifying a car engine by replacing the camshaft that opens and closes the valves with an auxiliary crankshaft and connecting rods identical to the one for the pistons, arguing that "both mechanisms serve to transform circular motion into reciprocating rectilinear motion, so they are interchangeable".

1. Refute their proposal: analyse what type of motion a connecting rod-crank mechanism necessarily describes (smoothness, symmetry) and why this motion is not suitable for an engine valve, which needs to open very quickly, remain fully open for a specific time, and snap shut.

2. Explain how a cam allows this problem to be solved and which part of its geometry you would design to control the time the valve remains open without altering the engine speed.

3. Why do you think the opposite is not done: using cams to drive the engine's main pistons? Justify your answer considering the extreme forces of combustion and mechanical reversibility.

Topic challenge. Have you noticed the mechanisms that make your daily tasks easier? Your mission is to carry out a mechanical audit at home and propose a technical optimization.

1. Real data collection: Locate in your home one transmission mechanism (e.g. chainrings and sprockets of a bicycle) and one motion transformation mechanism (e.g. winged corkscrew with rack and pinion, or garlic press with lever and plunger). Count the teeth ($Z_1$ of the driving element and $Z_2$ of the driven one) or measure the diameters ($d_1$ of the driving element and $d_2$ of the driven one) and displacements in centimeters with a ruler.

2. Digital calculation: In LibreOffice Calc, design a table with the measurements obtained. Calculate the transmission ratio ($i = Z_1 / Z_2$ or $i = d_1 / d_2$), specifying whether the system is a reduction or multiplying system ($i < 1$ or $i > 1$, for example $i = 0,4$). Also describe the type of input and output motion of the second mechanism.

3. Technical proposal: Write a brief report proposing a specific modification (altering the number of teeth or the length of the lever arm) to halve the force the user needs to apply.

Assessment criteria:

• Rigor in obtaining real measurements and correct algebraic calculation of $i$.

• Accurate identification of input and output motions in the transformation.

• Physical justification and technical consistency of the improvement proposal.

• Structured presentation of data in LibreOffice Calc.