Slider-Crank Mechanism — Piston Kinematics & Dynamics

Crank Drive

Crank speed 1200 RPM

Rod ratio L / r 3.5

Crank radius r 50 mm

Slide offset e 0 mm

Piston State

Position s(θ)

0.0 mm

Crank angle θ

0.0°

Velocity

0.00 m/s

Acceleration

0.0 m/s²

Stroke 2r

100 mm

Rod length L

175 mm

How it works

A crank of radius r spins at constant angular speed ω about a fixed axis; its pin drives a rigid connecting rod of length L, whose other end is pinned to a piston constrained to slide along a straight line offset by e from the crank centre. This is the slider-crank mechanism at the heart of every piston engine and reciprocating pump.

With crank angle θ = ωt, exact piston position along the slide is:

s(θ) = r·cosθ + √(L² − (r·sinθ − e)²)

The panel differentiates this exact expression numerically (central differences in θ, scaled by ω) to report true instantaneous velocity ds/dt and acceleration d²s/dt² — the same quantities an engineer uses to size connecting-rod stresses and check for piston-slap at high RPM:

v = ω · ds/dθ
a = ω² · d²s/dθ²

Crank speed — sets ω directly; acceleration grows with ω², so doubling RPM quadruples inertial loads on the rod.
Rod ratio L/r — a short rod (low ratio) makes the piston's motion sharply asymmetric between the outward and return stroke; a long rod (high ratio) approaches simple harmonic motion.
Crank radius r — sets the stroke 2r, scaling the whole mechanism.
Slide offset e — a desaxé (offset) layout, used in real engines to reduce piston side-thrust on one stroke at the cost of a longer, asymmetric return.

Crank + connecting rod Piston & cylinder guide

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