Crank phase and cylinder-axis angle affect when pistons reach their stroke limits. This calculator compares equally stepped crank phases and illustrates the resulting piston motion. It does not calculate an angle that guarantees constant torque or dynamic balance.
Crank Equalizing Angle Interactive Calculator
Compare crank-throw phases and the piston positions they produce. Change the count, first phase and repeated spacing; inspect their relative positions.
Equation Used
- Two to six crank throws with one repeated phase increment.
- Angles wrap modulo 360 degrees.
- Parallel cylinder axes and equal illustrative crank and rod lengths.
- No torque, pressure, firing-cycle or balance model.
Geometric phase comparison only. Cylinder-bank angle, pressure, firing order and dynamic balance are not calculated.
Crank phase versus cylinder angle
Crank phase is the angular position of a throw about the shaft. Cylinder-axis angle describes where a cylinder points relative to that shaft. They are distinct quantities: changing either can change piston timing.
Hiscox’s historical examples of crank equalizing angle include steam-driven air compressors with different cylinder-axis and crank relationships. A simple 360/n rule is an equal-spacing construction, not a complete analysis of those pressure-driven machines.
The upper end view shows the selected throw phases. The separate sections below use parallel cylinder axes and equal example link lengths so the effect of crank phase is visible. Each connecting rod remains attached to its crank pin and guided piston throughout rotation.
Comparing a crank layout
Use this tool to inspect how a repeated phase increment places two to six throws around a shaft. It can reveal coincident phases or a difference from equal spacing. Actual engines and compressors also depend on cylinder arrangement, working cycle and pressure histories.
Phase arithmetic
The equal-spacing reference is 360/n degrees for n distinct positions around one revolution. With first throw A₁ and repeated spacing s, throw k is wrap(A₁+(k−1)s), where wrap returns an angle from zero up to but excluding 360 degrees.
The displayed spacing difference is |s−360/n|. It compares the selected increment with the reference, not every circular gap or a torque error. Some increments repeat an earlier phase before all throws have been placed.
The piston illustration uses the slider-crank length constraint. For illustrative crank radius r, rod length L and throw angle θ, piston position along a vertical guide is r sinθ + √(L²−r²cos²θ). The same shaft rotation is added to every setup angle.
Three-throw example
For three throws, a first angle of zero and spacing of 120 degrees produce setup phases of 0, 120 and 240 degrees. The selected spacing difference is zero.
Changing spacing to 180 degrees produces 0, 180 and 0 degrees. Two throws now coincide, even though there are three separate cylinder stations. The illustration and phase list show that duplication.
Limits of equal spacing
Equal crank spacing is a geometric property. Torque uniformity requires a force-versus-angle model; balance requires moving masses, cylinder directions and shaft-plane positions. The calculator compares crank phases and piston positions; it does not predict torque variation.
The station drawings use equal illustrative crank and rod lengths and a slowed common cycle. The upper view overlays different axial crank stations for comparison; it is not a drawing of several connecting rods occupying one plane.
Crank-phase questions
Does zero spacing difference mean the machine is balanced?
No. It only means the selected step equals 360/n degrees.
Are these firing angles?
No. They are crank-throw phases. Firing sequence also depends on the engine cycle and cylinder arrangement.
Why can two phase markers overlap?
The repeated increment can return to an earlier angle modulo 360 degrees. Separate throws can therefore occupy the same phase.
Does changing the first angle change relative spacing?
No. It rotates the whole layout while preserving the differences between throws.
Reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, 1901 edition, printed pages 175–176, figures 654–657, for historical crank equalizing-angle arrangements in air compression. Use the phase arithmetic to compare layouts; pressure and torque behavior require a separate force analysis.
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