Examples#
This gallery walks through every public feature of
engineeringkit.mechanical_engineering, one breakthrough per script:
rigid-body dynamics, gears and belts, screws, bearings, bolts and springs,
linkages and robot arms, vibration, normal modes and absorbers, and the whirling
and balanced rotor.
Units, assumptions and numerical validation
gives the physical validity limits. Each script is self-contained and can be
run directly with python examples/mechanical_engineering/<section>/<script>.py.
Sections#
dynamics – Huygens’s moment of inertia, Coriolis’s work and kinetic energy and Lagrange’s equations.
transmission – Euler’s involute gear, the Euler-Eytelwein belt-friction law and Lewis’s gear-tooth bending.
machine_elements – Coulomb’s power screw, Petroff’s and Sommerfeld’s journal bearings, the L10 life of rolling bearings, Rötscher’s bolted-joint diagram and Wahl’s spring factor.
mechanisms – Reuleaux’s slider-crank, Grashof’s condition, Freudenstein’s synthesis, Denavit-Hartenberg kinematics and Aronhold and Kennedy’s instant centres.
vibration – Rayleigh’s free and forced vibration, Frahm’s absorber, Holzer’s torsional method, Bernoulli’s normal modes and Dunkerley’s whirling shafts.
rotordynamics – the Jeffcott rotor and its critical speed, and Dalby’s balancing of rotating masses.
Dynamics#
Moments of inertia, work, kinetic energy and power, and Lagrange’s equations.
Huygens’s compound pendulum and the parallel-axis theorem (1673)
Machine elements#
Power screws, journal bearings, rolling bearings, bolted joints and helical springs.
Reynolds and Sommerfeld: hydrodynamic lubrication (1886-1904)
Lundberg and Palmgren’s rolling-bearing life (1947)
Wahl’s curvature factor for helical springs (1929)
Mechanisms#
Slider-cranks, four-bar linkages and their velocities and accelerations, and serial robot arms.
Reuleaux’s kinematics of machinery: the slider-crank (1875)
Freudenstein’s equation for four-bar synthesis (1954)
Aronhold and Kennedy’s theorem of three centres (1872-1886)
Rotordynamics#
Unbalanced rotors, critical speeds and balancing.
Transmission#
Gear trains, gear-tooth strength and belt drives.
Vibration#
Free and forced vibration, normal modes, frequency bounds, vibration absorbers and torsional modes.
Frahm’s vibration absorber and Den Hartog’s tuning (1909)
Rayleigh’s Theory of Sound: forced vibration and resonance (1877)
Daniel Bernoulli’s superposition of normal modes (1753)
Dunkerley’s whirling shafts and Rayleigh’s bound (1894)