Slider Crank Lab piston displacement, velocity & acceleration, live
x from outer dead centre · θ from ODC, direction of rotation
Crank R m
Rod L m
Speed n rev/s
θ °
Mechanism · drag the crank pin
x = 0 (ODC) R L O
Velocity diagram · o–a–b
o a b
Drawn to scale from the fixed point o: oa is the crank-pin velocity, ab the velocity of the piston relative to the pin (⊥ connecting rod), and their closure ob is the piston velocity — as in the lecture's vector-diagram method.
x, v, a over one revolution
— x (m) — v (m/s) — a (m/s²)
At θ = °
Binomial approximation
Equations (approx., R/L < 0.25)
x ≈ R(1−cosθ) + R²sin²θ/2L
v ≈ ωR(sinθ + R·sin2θ/2L)
a ≈ ω²R(cosθ + R·cos2θ/L)
Solid curves are exact; dashed are the binomial approximation from the lecture.
Extremes over one revolution
Drag the blue crank pin to set θ, or press Run to spin at n rev/s. Displacement is measured from the outer dead centre (crank and rod in line), as in the lecture. Try R = 0.2 m, L = 0.5 m, n = 50 rev/s, θ = 60° — the exam question.
Credit: WASTON44 · GitHub repo