Connecting rod and crank, and the crankshaft

Explain what motion transformation the connecting rod-crank system performs and give two examples of machines that use it, indicating for each the direction of transformation (from rotary to reciprocating or vice versa).

Name and describe the function of the three main parts of the connecting rod-crank system: the crank, the connecting rod, and the slider (piston).

The same mechanism can operate in both directions: in a car engine, the piston pushes to produce rotation, whereas in an air compressor, a motor rotates and the piston compresses. Explain what changes between the two cases (which element acts as input and which as output) and why the mechanism is said to be reversible.

In an engine, the piston moves up and down, but at two specific positions its velocity momentarily becomes zero: top dead centre and bottom dead centre. Explain in your own words why this happens, relating it to the position of the crank and connecting rod at those moments.

The stroke of a piston (the distance it travels between its two extreme positions) is equal to twice the crank radius. If the crank has a radius of $40\ \text{mm}$, calculate the piston stroke. What radius would a crank need to achieve a stroke of $120\ \text{mm}$?

The piston moves fastest at mid-stroke than near the dead centres. Explain why, relating it to how the circular motion of the crank is projected onto the straight line of the cylinder (the rotational component pushing the piston changes with the angle).

Explain what a crankshaft is and how it differs from a simple crank (number of crank webs/arms and outputs), giving an example of a machine that uses each.

An engine runs at $3000\ \text{rpm}$. (a) Calculate how many revolutions the crankshaft makes per second and, therefore, how many complete up-and-down cycles the piston performs each second. (b) Calculate how many times per second the piston passes through a dead centre (top or bottom). (c) Given this rapid rate of direction changes, reason why balancing and lubrication of the mechanism are so critical in an engine.

The single-cylinder displacement (or swept volume) of an engine is the volume swept by the piston: $V = \pi \cdot r^2 \cdot c$, where $r$ is the cylinder radius and $c$ is the stroke. Calculate the displacement of a cylinder with a diameter of $80\ \text{mm}$ and a stroke of $90\ \text{mm}$, expressing it in $\text{cm}^3$ (use $\pi \approx 3{,}1416$ and round the result).

An amateur inventor claims to have designed an in-line 4-cylinder engine for a tractor in which all pistons rise and fall at the exact same time (cranks at $0^\circ$), arguing that "by adding the forces of the 4 cylinders at the same instant, the engine torque will be four times greater and it will have much more pulling force." Technically refute his proposal by analyzing: (a) the balance of first-order reciprocating inertia forces and the generated vibrations; (b) the regularity of engine torque over the $720^\circ$ of the four-stroke cycle compared to a standard crankshaft (crankpins at $180^\circ$); and (c) the impact that his design would have on the mass and dimensions of the flywheel required to keep the engine from stalling at idle.

On a test bench, the instantaneous torque delivered to the crankshaft of a four-stroke in-line four-cylinder engine (firing order 1-3-4-2) rotating at $2400\ \text{rpm}$ is monitored. The complete cycle lasts $720^\circ$. It is observed that in the angular interval between $\theta = 360^\circ$ and $\theta = 540^\circ$, the torque on the crankshaft not only lacks the usual driving peak, but becomes significantly resistive (negative), causing a sharp drop in angular velocity before recovering. (a) Reasonably diagnose what fault this record describes and identify which specific cylinder is the cause. (b) Justify why the torque in that interval turns out to be negative instead of simply zero. (c) Predict what will happen to the engine's speed fluctuation coefficient and explain what abnormal dynamic stresses the crankshaft undergoes due to this inoperative cylinder.

A single-acting piston pump driven by an electric motor must be designed to pump out water at a rate of $1,8\ \text{m}^3/\text{h}$. Due to dimensional constraints of the casing, the piston stroke cannot exceed $120\ \text{mm}$. (a) Determine the maximum allowable crank radius. (b) If the mechanism is driven at $150\ \text{min}^{-1}$ (cycles per minute), calculate the minimum bore diameter that the cylinder must have (in $\text{mm}$) assuming ideal filling (volumetric efficiency of $100\ \%$). (c) The design team is hesitating between doubling the piston diameter or doubling the rotational speed to increase the flow rate to $3,6\ \text{m}^3/\text{h}$. Evaluate and justify both alternatives by analyzing the impact of each on inertia forces ($F_{\text{inertia}} \propto m \cdot \omega^2$), frictional wear, and hydraulic head losses.

An electric motor rotates at $1440\ \text{rpm}$ and must drive a reciprocating plunger pump at $48\ \text{cycles/min}$ through a speed reducer and a slider-crank mechanism. The pump requires a stroke of $120\ \text{mm}$, and the connecting rod length is $240\ \text{mm}$. (a) Calculate the crank radius and the required total transmission ratio $i = n_{\text{output}} / n_{\text{input}}$. (b) Knowing that in a single spur gear stage ratios smaller than $1/6$ are not recommended for reasons of size and interference, design a two-stage reducer with gear wheels having between $15$ and $90$ teeth that exactly provides the required speed. (c) In this slider-crank mechanism with $\lambda = r/L = 60/240 = 0,25$, kinematically justify why the plunger reaches its maximum velocity before the crank reaches $90^\circ$ from top dead center, and not exactly at mid-stroke.

Two four-stroke internal combustion engines with the same total displacement ($600\ \text{cm}^3$) and the same average power output at $3000\ \text{rpm}$ are compared: engine A is single-cylinder and engine B is twin-cylinder with firing intervals spaced at $360^\circ$. Both incorporate a flywheel to limit the angular velocity fluctuation to an allowable value. (a) Analyze the engine torque diagram versus crankshaft rotation angle ($0^\circ$ to $720^\circ$) in each case and justify why the single-cylinder engine presents a much larger fluctuating work (net driving area above the mean). (b) Based on the rotational kinetic energy expression ($E_c = \frac{1}{2} I \omega^2$), justify why the moment of inertia $I$ required for the flywheel of engine A is drastically higher than that of engine B. (c) If the lightweight flywheel from the twin-cylinder engine were installed by mistake on the single-cylinder engine, make a reasoned prediction of the machine's behavior at idle and when subjected to a sudden load at low revolutions.

To drive an industrial power hammer that must deliver 180 blows per minute with a vertical stroke of $100\ \text{mm}$, the use of a cam-follower mechanism is ruled out and a slider-crank mechanism is chosen instead. (a) Analyze the critical limitations that a cam would present in this specific application regarding the type of contact (Hertzian contact stresses), the risk of follower liftoff/bounce at that rate, and the surface failure mechanism. (b) Explain how the slider-crank mechanism takes advantage of the variation in the angle between the connecting rod and the crank to multiply the available force (mechanical advantage tending to infinity in the absence of friction) near bottom dead center, right at impact with the workpiece. (c) Conceptually design a kinematic modification if the process required a dwell or rest period at top dead center to feed the material without stopping the drive motor.