This page illustrates the phase relationship between two crank radii. Its calculator reports angle-to-arc conversion and an ideal sine factor; it does not model a complete linkage or guarantee passage through dead centre.
Helping Crank Over Center Interactive Calculator
Explore a nominal phase and symmetric tolerance band, convert angular half-band to crank-pin arc length, and compare the minimum ideal sine factor at the two band endpoints.
Equation Used
- Two crank radii share an angular reference and nominal phase separation.
- The arc conversion uses the entered radius and angular half-band only.
- The ideal sine factor assumes the same applied force and crank radius for comparison.
- No connecting-rod geometry, load, force direction, inertia, friction, stiffness, clearance, strength, balance or startup dynamics model.
Ideal geometry only. The percentage assumes equal force and equal crank radius and is not available torque, starting reliability or a manufacturing-tolerance recommendation. A complete linkage, load and dynamic model is required for design.
Ideal phase relationship
A crank's moment arm for a force direction can include a sine term. If one crank is at a reference dead-centre angle, a second idealized crank separated by phase φ has a normalized sine factor |sin φ|, reaching one at 90°.
That statement alone does not describe a real helping linkage. The input force directions, crank radii, connecting rods, constraints and loads determine actual torque and whether a mechanism can pass through a singular position.
Use as a geometry check only
Phased cranks appear in many mechanisms, but this calculator does not identify or validate a particular machine arrangement. Use it to inspect phase and arc relationships, then analyze the actual linkage, loads and dynamics separately.
Angle-to-arc and ideal sine-factor equations
For radius r and phase half-tolerance δφ in radians, the crank-pin arc half-band is s=rδφ; the full symmetric arc band is 2s and the full phase band is 2δφ.
The percentage tile is 100 times the smaller of |sin(φ-δφ)| and |sin(φ+δφ)|. It is normalized geometry under equal-radius, equal-force assumptions—not torque capacity.
Transparent example
At r=120 mm, nominal phase 90° and tolerance ±2°, the arc half-band is 120×2π/180≈4.19 mm, total arc band is 8.38 mm and phase band is 4°. The endpoint sine factor is sin(88°)≈99.94%.
This does not show how much torque a machine has or whether it will start from every position.
Scope and limitations
A design needs the full linkage geometry, applied-force directions, individual crank radii, required load torque over the cycle, inertia, speed, friction, compliance, clearances, balance, strength and failure consequences. Phase near 90° maximizes this isolated sine factor but is not automatically an optimal or safe mechanism design.
Questions
Does 100% mean the helping crank supplies all required torque?
No. It means only that the isolated sine factor equals one under equal-force and equal-radius assumptions.
Is the arc band a machining tolerance?
No. It is the geometric arc corresponding to the entered angular band. Allowable manufacturing error requires a system tolerance analysis.
Does this calculator include flywheel energy?
No. It has no speed, inertia or energy inputs.
Calculation basis
The calculation uses the circle-arc identity s = rδφ, with δφ in radians, and the normalized moment-arm factor |sin φ|. Within the available 50° to 130° endpoint range, the smallest sine factor over a phase band occurs at one of its endpoints.
The two fixed-size radii illustrate angular separation. Entering a different throw radius changes the arc-length outputs but does not resize the drawing. The tolerance input changes the numerical band and factor; no tolerance sector or complete helping linkage is drawn.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
