Cartwright’s geared parallel motion uses two equal gears and mirrored crank arms to drive equal connecting rods attached to a piston crosshead. The crank wheels turn in opposite directions, keeping the ideal piston assembly symmetric. The animation follows the arrangement illustrated in Brown’s movement 328 and Hiscox’s figure 287.
Cartwright's Parallel Motion Interactive Calculator
Adjust the two equal crank radii, the two equal connecting-rod lengths and crank speed. Watch the mirrored geared motion and calculate piston stroke, maximum rod tilt, mean piston speed and the speed of the lower flywheel shaft.
Equation Used
- Equal external crank wheels counter-rotate with mirrored crank-pin positions.
- Both connecting rods have length L and both cranks have radius r; L > r.
- The crosshead remains horizontal on the symmetric branch and the piston rod is aligned with the cylinder gland.
- Crank gear pitch radius is 1.5r; crosshead pin spacing equals crank-shaft spacing.
- Selected tooth counts are 40, 40 and 20, so the lower shaft turns at twice crank RPM.
- Playback is slowed by a factor of four. Tooth profiles, bearings and engine structure are simplified; no steam cycle, friction or wear calculation.
Equal meshing gears keep the two cranks mirrored. Equal rods connect them to the piston crosshead, giving a stroke of twice the crank radius on the symmetric branch. The calculator compares that stroke, rod inclination and speed; it does not calculate engine forces.
Two geared cranks drive one piston crosshead
The historical arrangement is a geared mechanism. Two equal external spur wheels mesh directly and rotate in opposite directions. Each carries a crank of equal radius, phased so their pins are mirror images about the piston centerline. Equal connecting rods run down to opposite ends of a crosshead attached to the piston rod.
Brown’s movement 328 and Hiscox’s figure 287 show this pair of cranks, a crosshead below them, and a third, smaller wheel driving the flywheel shaft. The equal and opposite rod inclinations distinguish this arrangement from a rocking-beam straight-line linkage.
The drawing shows the symmetric operating assembly with the piston rod centered through the cylinder gland. The gland guides the piston rod; the rods and crosshead lie in front of the gears and flywheel, as in the historical front view.
Exploring the historical engine arrangement
This page is a kinematic demonstration of the geared parallel motion illustrated in historical mechanism collections. Change the crank radius to change stroke; change rod length to change rod inclination and the piston’s position through the cycle. The two rods always retain their entered length.
The calculator does not infer piston side load, permissible steam pressure, maintenance interval or a safe operating speed. Reconstructing an actual historical engine requires its own dimensional drawings and structural assessment.
Exact geometry of the symmetric assembly
Let the crank centers be at (−a,0) and (+a,0), and the crosshead end pins at (−a,y) and (+a,y). For mirrored crank angles, the crank pins are (−a+r cos θ,r sin θ) and (+a−r cos θ,r sin θ). Each connecting rod therefore has horizontal component ±r cos θ and vertical component √(L²−r² cos² θ).
The crosshead coordinate is y = r sin θ + √(L²−r² cos² θ), measured downward from the crank centers. Its limits are L−r and L+r, giving stroke 2r. Rod inclination to vertical is α = asin(r cos θ/L), so the maximum magnitude is asin(r/L).
A piston travels two strokes per crank revolution, so mean speed is 4rN/60 in mm/s when r is in mm and N in rpm. The lower pinion in this teaching model has 20 teeth, half the 40 teeth on its driver, and therefore turns twice as fast. The actual historical tooth counts are not established by this illustration.
Read the default 75 mm crank example
With r = 75 mm, L = 300 mm and N = 20 rpm, piston stroke is 150 mm. Maximum rod tilt is asin(75/300) ≈ 14.48°. Mean piston speed is 4 × 75 × 20 / 60 = 100 mm/s. The selected 40:20 drive gives a flywheel speed of 40 rpm.
At θ = 90°, y = 375 mm; at θ = 270°, y = 225 mm. At θ = 0°, y = √(300²−75²) ≈ 290.47 mm. The connecting-rod geometry means piston position is not a pure sine wave, even with constant crank speed.
What gearing changes
The gear pair enforces equal and opposite crank rotation. Mirrored rod inclinations give an ideal symmetric force path, but real backlash, unequal rod lengths, bearing deflection and misalignment can disturb that symmetry.
Watt-style beam linkages and slide-bar crossheads use different joint arrangements. For the geared Cartwright assembly, crank radius sets stroke while rod length controls inclination and intermediate piston position.
Understanding the animation
Why do the crank wheels turn opposite ways?
They mesh as equal external gears, so their speeds have equal magnitude and opposite direction. The crank pins are mounted with mirrored phase.
Why is the piston stroke twice crank radius?
On the symmetric branch, the crosshead extremes occur at y = L−r and y = L+r. Their difference is 2r.
Does a longer rod change the stroke?
No. It reduces maximum rod inclination and changes the intermediate position law, while the same crank radius retains the same stroke.
Why does the flywheel turn faster?
The displayed lower pinion has 20 teeth and meshes with a 40-tooth crank wheel. That chosen 2:1 ratio doubles its speed. It is an illustrative tooth selection.
Can the model predict piston side load or wear?
No. It solves ideal geometry and speed only. Pressure, inertia, friction, clearance and structural flexibility are not entered.
References & Further Reading
- Henry T. Brown. Five Hundred and Seven Mechanical Movements, movement 328. Historical text and original illustration: equal geared crank wheels, equal connecting rods and piston crosshead.
- Gardner D. Hiscox. Mechanical Movements, Powers, Devices and Appliances, printed page 81, figure 287. Historical geared arrangement and third spur wheel driving the flywheel.
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