Locus

LocusFour-bar coupler curves

Crank–rocker · full crankNotes Agents

Drag P to move the coupler point · drag A to set the crank · scroll to zoom · double-click to frame · space to pause

Atlas

Classic Grashof driver. The coupler traces a one-loop sextic.

Links

GroundO₂O₄

CrankO₂A

CouplerAB

RockerO₄B

Along couplerp

Offsetq

Motion

Speed0.70 rad/s

Crank angle θ₂63.0°

Dynamics

Simulate 10-bar

Reduced Euler–Lagrange on the crank. Loop closure gives every bar pose; the Jacobian builds M(θ). Two torsion springs. Viscous damping at every revolute. No gravity.

Spring 1

k112.0

Neutral 63.0°

Spring 2

k28.0

Neutral 68.8°

Release Δθ₂30°

Mass density μ0.55

Joint damping c0.22

Constant force

Magnitude2.0

Direction-90°

Construction

Coupler curve10-bar cognates

Triple-joint split ε0.070

Replaces coincident P with P₁₂, P₁₃, P₂₃. Cayley parallelograms, coupler triangles, inertia and joint rates all use the split pins.

Joint circlesRadical axisJoint labelsHomogeneous coords

Projective readout

Class: Crank–rocker
Grashof s+l: 5.50 ≤ 7.00
θ₃ coupler: 24.3°
θ₄ rocker: 83.7°
Transmission: 59.5°
A: [0.68 : 1.34 : 1.00]
B: [4.33 : 2.98 : 1.00]
P: [2.03 : 4.19 : 1.00]
O₆ cognate: [2.43 : 1.85 : 1.00]
Roberts–Chebyshev: 10-bar · 3 four-bars · 1 sextic
Radical axis C₁ − C₂: 6.64x − 2.67y − 20.75 = 0

Joint A rides a circle about O₂; B rides a circle about O₄. Their common points are the pencil C₁ − λ C₂, reduced to the radical axis cut with C₁. P is the image of that pair under the rigid map of the coupler, so the locus is a sextic.