A half-yoke connection joins reciprocating pump piston rods around a centrally placed crankshaft. A curved member leaves space for the shaft, while a connecting rod links the moving assembly to the crankpin. Hiscox illustrates this arrangement in figures 507 and 508. The animation follows an ideal slider-crank example of that layout.
Half-Yoke Connection Interactive Calculator
Set crank radius, connecting-rod length, speed and a calculation angle. The numerical outputs use the selected angle; the animation advances from it at one fortieth of the entered RPM.
Equation Used
The piston rods share one straight line through the crankshaft center. The connecting rod has pin-to-pin length L, and r is crank radius. Angle θ is measured from the upper dead-center crank position; positive x is downward. ω = 2πN/60. Dimensions are an illustrative model, not measurements of Hiscox’s drawing. Valve timing, fluid flow, pressure, pin strength, clearances and mechanical loads are not calculated.
A curved connection leaves room for the crankshaft
The upper and lower piston rods move together. A rigid, bow-shaped half-yoke connects them along one side of the central shaft. A separate connecting rod pivots between the lower attachment and the crankpin. Turning the crank therefore moves both piston rods through the same displacement.
The shaft center and cylinder guides remain fixed. The crankpin travels in a circle; the connecting rod rocks as it transmits motion to the guided assembly. The open side of the half-yoke leaves room around the crank and shaft. The illustration shows these connections in one plane, with cylinder sections to make the shared piston motion visible.
The crank and reciprocating assembly can transmit motion in either direction. The drawing does not include the pump valves or specify whether a particular installation is engine-driven or driven by pressure on a piston.
Connecting reciprocating rods around a central shaft
Hiscox identifies this as a pump piston-rod connection with a central crank. The adjacent figure shows the crankshaft form. The arrangement is useful to understand when a continuous straight connection between the reciprocating members would occupy the shaft’s space.
The curved connection must retain its shape under load and remain clear of the rotating parts. Its section, attachments and supports require dimensions and loads from the actual machine. The historical illustration supplies the arrangement, not a rated capacity or manufacturing specification.
Slider-crank geometry with a common piston displacement
Place the shaft center at the origin and take downward as positive. At crank angle θ, the crankpin coordinates are (r sinθ, −r cosθ). The lower attachment lies on the vertical piston line. Its distance below the crankpin is h = √(L² − r²sin²θ), so its vertical position is −r cosθ + h.
At upper dead center, this position is L − r. Subtracting that value gives x = r − r cosθ + h − L. The maximum displacement is 2r. The upper piston has the same displacement because the half-yoke is rigid.
Differentiating x with respect to time gives the displayed velocity. Positive velocity means downward travel and negative velocity means upward travel. The rod angle β = asin(r sinθ/L) describes its tilt from vertical. The allowed inputs keep L greater than r, so the square root remains real throughout a revolution.
Example: a 30 mm crank and 150 mm connecting rod
With r = 30 mm, L = 150 mm, N = 60 RPM and θ = 90°, the full stroke is 60 mm. The vertical rod projection is √(150² − 30²) = 146.97 mm, giving piston displacement 26.97 mm. Downward velocity is 188.50 mm/s, and rod tilt is 11.54°.
At 0°, displacement and velocity are zero. At 180°, displacement is 60 mm and velocity is again zero. At 270°, displacement returns to 26.97 mm but velocity is −188.50 mm/s. Finite connecting-rod length makes the mid-quarter position differ from the 30 mm half-stroke value.
Separate motion geometry from pump performance
Increasing crank radius increases stroke. A longer connecting rod reduces its maximum tilt for the same crank radius. Increasing RPM raises velocity proportionally while leaving the geometric stroke unchanged.
Pump delivery also depends on piston areas, rod areas, valves, leakage and the fluid circuit. Joint loads depend on pressure and inertia, and the curved member carries bending as well as transmitted force. This calculator provides kinematics only; it does not select a pin, rate a pump or determine a safe running speed.
Frequently asked questions
What is the half-yoke doing?
It joins the reciprocating piston rods around one side of the central shaft so they share the same displacement.
Does the curved member rotate?
No. It translates with the piston rods. The crank rotates and the separate connecting rod changes angle.
What determines the full piston stroke?
For this in-line slider-crank example, the stroke is twice the crank radius.
Why is the position at 90° less than half the stroke?
The connecting rod is tilted, so its vertical projection is shorter than its pin-to-pin length. That finite-length effect changes the displacement.
Why can the displayed calculation angle differ from the animation?
The angle input sets the numerical calculation and the animation’s starting offset. Playback adds rotation at one fortieth of the entered RPM; Pause and the position control let you inspect it.
Can I calculate pin shear or pump pressure here?
No. The model contains geometry and speed, not material strength, pressure, piston area or joint loading.
Are these dimensions taken from the historical machine?
No. They define an illustrative slider-crank with the same connection arrangement. Hiscox’s small drawing does not provide these dimensions.
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