BL2.ru
Boosty
ENRU

Plane mechanism online: instantaneous centre of velocity, point velocities and accelerations

Enter the mechanism dimensions, crank angle and angular velocity. The calculator draws the linkage, finds the instantaneous centre of the coupler, velocities and accelerations of A, B, C and angular velocities and accelerations of links, step by step. Drag the slider or play the animation.

O is the origin, φ is the crank angle from the x axis, counter-clockwise. ω, ε > 0 — counter-clockwise. C lies on the coupler at distance AC from A. The slider moves along y = e.
Calculate

Instantaneous centre of velocity

A body in plane motion has, at every instant, a point P with zero velocity. All points move as if rotating about P: v = ω·(distance to P), perpendicular to the line joining the point to P.

Finding it

  • Draw normals to the velocities of two points; P is their intersection.
  • Slider-crank coupler: v_A ⊥ OA, slider velocity along the guide.
  • Four-bar coupler: intersection of lines OA and O₂B.
  • Parallel normals — the link translates instantaneously (ω = 0).

Accelerations

Use a_B = a_A + a_BA^n + a_BA^τ with a_BA^n = ω²·AB towards A and a_BA^τ = ε·AB perpendicular to AB; project onto two axes to find ε_AB and the slider (or rocker) acceleration.

FAQ

How is the instantaneous centre found?
Intersect the normals to the velocities of two points of the link. Parallel normals mean instantaneous translation.
How is the coupler angular velocity found?
ω_AB = v_A / AP, with AP the distance from A to the instantaneous centre.
Can accelerations be found with the instantaneous centre?
No — it has zero velocity, not zero acceleration. Use the relative acceleration equation.
Why does it say the linkage cannot be assembled?
With these lengths the coupler cannot reach the guide or the rocker at this crank angle.
Is it suitable for coursework?
Yes, for crank–coupler–slider or rocker linkages. Check the diagram and write up the steps yourself.