The selected rocking arm is the output rocker of a planar four-bar linkage. A continuously rotating input crank can drive the rocker through a bounded angular range when the link lengths and inversion permit full crank rotation.
Rocking Arm Interactive Calculator
Explore sampled open-branch position geometry for a selected planar crank-rocker four-bar.
Equation Used
- Links are rigid and coplanar and all joints are ideal revolutes.
- The open circle-intersection assembly branch is selected.
- Rocker extrema are sampled every 0.5° over one nominal crank revolution.
- The speed tile assumes sinusoidal rocker motion; exact velocity, acceleration, loads and feasibility margins are excluded.
The secondary figure uses the same link lengths, open assembly branch and selected input speed.
How the selected crank-rocker works
Two fixed pivots define the frame. The input crank connects through a floating coupler to the output rocker. At each crank angle, the moving joint is the selected circle intersection satisfying both coupler and rocker lengths.
The calculator uses the open assembly branch and samples one input revolution. It is an ideal planar position model with rigid links and revolute joints.
What this calculator demonstrates
Select frame, crank, coupler and rocker lengths plus constant input speed. The calculator reports sampled rocker swing, the straight-line chord between extreme rocker-tip positions, Grashof margin, and a clearly labeled sinusoidal tip-speed estimate.
It does not compute exact instantaneous velocity, acceleration, transmission angle, forces, torque, stress, bearing load, clearance, balance, vibration, wear, fatigue, dwell, timing under load or a safe design.
Sampled position range and bounded estimates
For each sampled crank angle α, the crank-pin point B is known. The rocker-coupler joint C is the selected intersection of a circle centered at B with radius c and a circle centered at the rocker pivot with radius L. The sampled swing is max(θ) − min(θ).
The displayed tip displacement is the chord 2L sin(Δθ/2), not arc length. Grashof margin is (p+q)−(s+l), where s and l are shortest and longest. The speed tile is only the sinusoidal estimate L(Δθ/2)ω; it is not the exact four-bar peak speed.
Default selected example
For d=450 mm, r=150 mm, c=300 mm and L=500 mm, the selected open branch is sampled every 0.5° over one crank revolution. The result is a numerical range for that ideal assembly.
The 200 rpm input affects only the separately labeled sinusoidal speed estimate; it does not change the position range.
Scope and correction boundary
CMU and University of Illinois references define four-bar crank, coupler, rocker and Grashof classification. Ohio University notes emphasize branch, change-point and rotatability qualifications.
The removed article supplied universal clearances, life, speed, transmission-angle, product and fault-diagnosis claims not derivable from these five inputs. A positive Grashof margin alone does not validate strength, manufacturability or a particular machine.
Questions
Is tip chord displacement the distance traveled along the arc?
No. It is the straight-line separation between the two extreme tip positions.
Is the speed output exact?
No. It assumes sinusoidal rocker motion with the sampled amplitude at the input frequency. Exact velocity requires differentiating the four-bar position solution.
Does positive Grashof margin guarantee this exact inversion is a crank-rocker?
No. The shortest-link location and assembly branch also matter, and equality is a change-point case.
Can this calculator size pins or a motor?
No. Loads, torque, inertia, acceleration, transmission angle, friction, material and duty cycle are excluded.
Technical references
- Carnegie Mellon University, Planar Linkages — four-bar definitions, crank-rocker inversion and Grashof classification.
- University of Illinois, Four-Bar Linkages — planar four-bar position geometry, validity and Grashof quantities.
- Ohio University, Kinematics and Dynamics of Machines — Grashof law, link rotatability, change points and branch jumping.
- JPL/DARTS, Analytical Four-Bar Kinematics — position and velocity relationships for a four-bar loop.
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