This crossed-arm governor uses two ball arms that continue past their common crossing pivot. Their short upper extensions connect through a pair of links to a guided central stem. The lower arms pass through a slotted sector.
Adjust the arms, upper links, spread angle, ball masses and upward stem resistance to compare linkage geometry and ideal static balance. The arrangement is illustrated in Hiscox figure 297.
Crossed-arm Steam Engine Governor Interactive Calculator
Adjust the crossed levers and upper links. Exact geometry moves the guided stem; ideal equilibrium includes ball gravity and an explicitly applied upward stem resistance.
Equation Used
- Two equal ball masses and rigid crossed levers.
- Equal upper connecting links and an axially guided stem.
- Stem resistance acts upward; no inferred steam pressure.
- Illustrative bearing layers and ball sizes; no link mass, friction or engine dynamics.
Crossed-arm linkage with adjustable proportions. The slowed rotation shows the selected geometry; the calculation gives static equilibrium, not engine speed regulation.
Crossed levers convert ball spread into downward stem travel
Each ball arm is one rigid lever extending across the center pivot to an upper pin on the opposite side. As the balls spread, those upper pins separate and descend. Equal connecting links bring their motion back to the shaft axis, moving the stem downward.
The slotted sector is centered on the crossing pivot and guides the arms without changing their circular path. The illustration separates the lever layers in depth for visibility; bearings and clearances are schematic.
The animation rotates the assembly at a fixed selected spread angle for inspection. Its playback speed is deliberately slow, and does not represent the calculated operating rpm. Changing the angle input changes the balls and stem together.
Explore the geometry and an ideal resistance load
Ball-arm length sets the main scale. The upper-extension ratio and connecting-link ratio control the stem motion. The angle selects one position in the range. Ball mass and upward stem resistance determine the ideal speed needed to balance gravity and that resistance.
The upward stem force is a defined external resistance opposing the stem’s downward motion. It is not a pressure inferred from a steam valve, and the historical drawing does not supply such a load. Set it to zero to inspect the unloaded ideal governor.
Rigid-link closure and equilibrium
Use meters for lengths. Let b be the pivot-to-ball length, a the upper extension, l the upper connecting-link length, and θ the angle from downward vertical. The ball-center radius is ρ=b sinθ. The upper pins are at height a cosθ and radial offsets ±a sinθ.
z=a cosθ+√(l²−a² sin²θ)
The stem pin height above the crossing pivot is z. Its derivative is z′=−a sinθ−a² sinθ cosθ/√(l²−a² sin²θ). The downward travel shown is z(10°)−z(θ).
For two balls of mass m, gravity g and an upward stem resistance F, the generalized resisting force is 2mgb sinθ−Fz′. The centrifugal contribution is 2mω²b² sinθ cosθ.
ω²=(2mgb sinθ−Fz′)/(2mb² sinθ cosθ); rpm=60ω/(2π)
Centrifugal force per ball is mω²ρ. When F=0, the equation reduces to ω²=g/(b cosθ); ball mass cancels from equilibrium speed but still changes centrifugal force.
Compare changes that affect geometry and force differently
The default uses 250 mm ball arms, 62.5 mm upper extensions, 93.75 mm upper links, a 30° spread, two 2 kg balls and 10 N of upward stem resistance.
Changing only the stem resistance changes equilibrium speed and centrifugal force without changing the selected geometry. Increasing arm length scales the entire linkage, while increasing only the upper-extension ratio changes the stem travel relative to ball spread.
What the static calculation covers
Hiscox figure 297 identifies crossed extended arms, upper links and a slotted sector. The reference does not give manufacturing dimensions. This model uses adjustable, clearly defined proportions and ideal rigid links, with no friction or link mass.
The result is a static balance at one selected spread. It does not predict valve flow, hunting, settling time, speed regulation improvement, engine feedback or a safe operating speed. The graph of required speed across the angle range is not an engine transient.
Comparing actual speed regulation requires engine, valve and governor-response data beyond this static linkage model. Drawn ball size is illustrative and does not determine mass.
Crossed-arm governor questions
Why does the stem move down when the balls spread?
The opposite upper ends of the crossed levers move apart and downward. The two upper links close onto the guided stem, lowering its pin.
Is the animation running at the calculated rpm?
No. It is a slow rotating inspection view at the selected arm angle.
Why can mass leave the speed unchanged?
With zero external stem load, gravity and centrifugal action both scale with ball mass. Their ratio cancels. The force per ball still changes.
Does this show better regulation than a Watt governor?
No measured regulation comparison is supplied by this model. Its outputs are geometry and ideal equilibrium values.
Construction reference
Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 83, figure 297: crossed and extended governor arms, an upper link movement, and a slotted sector.
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