Mechanical systems

Linear, rotary, oscillating and reciprocating.

Both reverse. Reciprocating motion travels back and forth along a straight line; oscillating motion swings back and forth along an arc about a pivot.

Linear — a drawer or a lift. Rotary — a fan or a drill bit. Oscillating — a pendulum or a windscreen wiper. Reciprocating — a piston or a jigsaw blade.

Because a mechanism is defined by what it converts. "The handle" says nothing; "rotary motion applied by hand at the handle" tells you what has to come out the other end.

Changing the direction of a movement, altering the magnitude of a force by making the arms unequal, and making a part follow a particular path.

A fixed pivot is attached to the frame and cannot move; a moving pivot travels with the bars. Finding the fixed pivots first is how a linkage is read.

Reverse motion — one fixed pivot, the output moves the opposite way. Parallel motion — two fixed pivots with equal bars, the output stays parallel. Bell crank — a right-angled bar turning movement through 90°.

Because two equal bars stay parallel, so the tray translates without tilting. A single lever swings its far end through an arc and the contents slide off.

Input, process and output. The input and output are motions; the process is the mechanism that converts one into the other.

The type of motion, its speed, its direction, or the force it delivers.

Input: reciprocating motion from the hand. Process: a piston and washer in a cylinder with a one-way valve. Output: compressed air flowing one way into the tyre.

The system sensing its own output and correcting it — an engine governor closing a throttle as speed rises, or a thermostatic valve closing as a radiator warms.

MA = load ÷ effort — how many times a mechanism multiplies the force applied to it. On a lever it equals the effort arm divided by the load arm.

Distance. The effort end travels further than the load end, in the same ratio, because force × distance in equals force × distance out less friction.

When speed or reach matters more than force — tweezers, a fishing rod, a broom, the human forearm. All multiply movement and divide force.

Reduce friction with bearings and lubrication, stiffen members so movement is not lost in flexing, and shorten the chain so fewer joints add losses.

Gear-driven, belt-driven, cam, lever and linkage.

Gears — speed and force with no slip. Belt — speed across a gap, quietly. Cam — rotary into a timed rise and fall. Lever — force. Linkage — direction or path.

Driven divided by driver — teeth for gears, diameters for belts. Small driving large is slower and stronger; large driving small is faster and weaker.

Shafts far apart or not perfectly aligned, quiet running, lower cost, no lubrication needed, and a slip under overload that protects the motor.

Because each mechanism changes one thing. Chaining gives cheap standard parts, faults traceable to one stage, and ratios changeable by swapping a single component.

Efficiency, free play and wear. Efficiencies multiply: five stages at 95% each deliver about 77% of the input.

Write the motion at each junction first, then name the mechanism that converts each pair. One stage at a time: motion in, motion out, reason.

Belt — reduces motor speed. Gears — synchronise the two shafts. Crank — rotary into reciprocating for the needle. Cam — times the fabric feed. Linkage — clamps the presser foot.

Spur, bevel, rack and pinion, worm and wheel, ratchet and pawl, idler, and compound.

Teeth on the driven gear divided by teeth on the driver. A 10-tooth driver into a 40-tooth driven gear is 4:1 — a quarter the speed, about four times the torque.

The direction of the output, so it turns the same way as the input, and it bridges a gap between shafts. It does not change the overall ratio.

It gives a very large reduction in one step and cannot be back-driven, so the load holds wherever it stops.

A driver pulley on the input shaft, a driven pulley on the output shaft, a belt running in the grooves of both, and a tensioner or adjustable mounting.

Driven diameter divided by driver diameter. A 40 mm driver turning a 120 mm driven pulley is 3:1 — a third of the speed, about three times the torque.

It spans a gap with two parts, runs quietly with no lubrication, tolerates shafts slightly out of line, and slips under overload instead of shearing a tooth or stalling a motor.

Where two shafts must stay synchronised, because a belt slips and stretches. An engine camshaft, a sewing machine or a printer needs gears or a toothed timing belt.

A shaped disc turns on a shaft and a follower rides its edge. Where the profile is far from the shaft the follower rises; where it is close it drops. The profile is the motion.

Pear — a dwell then one rise. Circular and eccentric — one smooth rise, set by the offset. Triangular — three rises per turn. Oval — two. Snail — a gradual rise then a sudden drop, one direction only.

A stretch of constant radius on a cam profile, where the follower holds still while the shaft keeps turning. It is why a pear cam suits an engine valve.

The offset of the shaft from the centre of the disc, not the disc's diameter. Double the offset and the rise doubles.

By which of the fulcrum, load and effort sits between the other two. F, L, E in class order: fulcrum in the middle is first, load in the middle is second, effort in the middle is third.

Second class. The load sits between the fulcrum and the effort, so the effort arm is always longer — a wheelbarrow, nutcracker or bottle opener.

To multiply movement, speed and reach rather than force. A fishing rod, a broom and the human forearm all trade force away deliberately.

Effort arm divided by load arm, both measured from the fulcrum. Effort × effort arm = load × load arm is the same relationship written as moments.