Machine Kinematics
solved, then drawn
Concept

Pin in slot — where it appears

A joint that permits sliding along one line and free rotation about the pin, so it removes one freedom rather than two. It is the joint a Geneva mechanism's crank pin makes with its slot, and the freedom it leaves is what lets the pin enter and leave rather than staying engaged.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

A 3-stage stack at 35°. Every bar is the same length and every stage is at the same angle, which is a consequence of the solve rather than an assumption in the drawing: the pins at the crossings and the roller on the ground leave one freedom, and it has been used. The platform is at 1547 mm and the ram — the heavy line from the ground pin — is 428 mm long. Moving the ram one millimetre from here raises the platform 5.0 mm; at the bottom of the travel the same millimetre is worth 17.6 mm.

A roller is not a slider

A scissor lift has one degree of freedom, at every height and for any number of stages. Grübler's criterion agrees — if the rollers under it are counted as pins in slots. Count them as slider blocks, which is how every textbook draws a slider, and the same formula declares a machine holding a car in the air to be a structure with minus one.

applied · Mobility The wheel is the coupler — double wishbone. The suspension solved at 0 mm of bump, with the whole travel ghosted behind it. The two arms are the cranks and the upright between them is the coupler; the wheel is bolted to that coupler, so camber is the coupler's rotation and nothing else. Camber here is 0.00° and the contact patch has moved 0.0 mm across the road. The cross is the instantaneous centre of the upright, found from the solved velocity field; the roll centre is where the line from it to the contact patch crosses the car's centreline, and it is at 73 mm here.

The wheel is the coupler

A double wishbone is a four-bar standing on end whose coupler carries a wheel, so camber is coupler rotation and scrub is a coupler point's path. Both are computable, and the second one comes out with the opposite sign from the model every suspension book uses — by more than the whole scrub.

applied · Fourbar The fork and the roller, which is a Geneva pair. A lever escapement's fork with the balance's impulse pin inside it. The pin is on a roller of 0.150 against a fork of 1.00, and the slot points at the pin — which is the entire kinematic relation and is the same one a Geneva drive's pin and slot obey. The same eight lines answer both, and the check is that they reproduce the cams field's independently written Geneva solution to fourteen figures. The pin is in the fork for 44.4° of the balance's swing out of 540°, so the balance is left alone for 91.8% of the beat. Drag the balance.

Detached, and safe while detached

A lever escapement touches its balance for a twelfth of each beat and leaves it alone for the rest. What connects the two is a pin entering a radial slot — the same pair a film projector's Geneva drive is made of, solved by the same eight lines — and the sine rule then fixes the balance's lift angle at 44.4°, which is the number a Swiss lever is specified at.

timing · Intermittent

Named alongside it

The objects these essays reach for when they reach for this one.

ConstraintPrismaticBalanceBankingBeatCamberConstraint jacobianCouplerCoupler curveDegrees of freedomDetachedDraw

All concepts