A series of cams slides along a rotating shaft so that a different throw acts on the same roller lever. Brown’s movement 150 uses this arrangement to change valve movement. The calculator models the selected cam and the resulting valve-rod travel.
Cams of Varying Throw Interactive Calculator
Choose one of three cam throws, set the maximum throw, and adjust the valve-rod attachment on the lever. Shaft speed changes rod speed; the lower inset shows which cam is aligned with the follower.
Equation Used
- Three illustrative circular cams provide one-quarter, one-half and full maximum throw.
- Cam body radius 30 mm; roller radius 6 mm; lever length 80 mm; fixed pivot at (80, 36) mm relative to shaft.
- Connecting rod length 70 mm. Output pin is the entered fraction of the pivot-to-roller arm.
- Maintained roller contact and rigid links are assumed; force, clearance, valve ports and steam-flow dynamics are not solved.
- Main drawing is the selected cam end view; inset shows axial selection. Playback is 20 times slower than entered shaft speed.
Sliding the cam set along the shaft selects the throw acting on the roller lever. The circular-cam example calculates connected lever and valve-rod motion over a revolution, including travel and peak speed. Steam demand and piston-stroke cutoff require additional valve and engine information.
Selecting a different cam throw
Brown’s movement 150 places a series of cams on a shaft so that they can move lengthwise. Selecting a larger or smaller throw changes the movement of the roller lever and its attached valve rod.
The main animation shows one selected cam in end view. A roller at the end of a rigid lever follows it, and a pin partway along the lever drives the valve rod through a connecting rod. The lower inset shows the cam series shifting along the shaft to align another cam with the follower.
This model uses circular eccentric cams as an explicit illustration. Their throws are one-quarter, one-half and all of the selected maximum. These proportions and dimensions are not claimed as Brown’s original construction dimensions.
A historical valve-motion arrangement
The reference identifies this as valve motion for expansive working. It establishes the selectable-cam arrangement and its effect on valve movement; it does not provide a general formula for fuel savings or steam use.
A particular engine’s admission and cutoff depend on valve ports, valve displacement, phase and piston motion. This page focuses on the mechanical cam-to-rod movement.
Calculating the connected motion
Each circular cam’s center is offset from the shaft by e, giving a throw of 2e. At every shaft angle, the roller center must lie one cam radius plus one roller radius from the cam center. It must also remain one fixed lever length from the pivot. Intersecting these two circles gives the roller position on the continuous upper assembly branch.
The valve-rod pin lies at the selected fraction of the lever. A fixed-length connecting rod joins that pin to a slider constrained to move vertically. These constraints give the valve-rod position over one full shaft revolution.
Travel is the difference between highest and lowest rod positions. Peak speed is found from the position derivative multiplied by shaft angular speed. Values are sampled over the full turn. Neither cam lift nor the fraction of a revolution is automatically a percentage of piston stroke or steam consumption.
Comparing the three cams
With a 12 mm maximum throw, the available cams have 3 mm, 6 mm and 12 mm throws. Selecting another cam changes the eccentricity in the end view and the calculated valve-rod travel.
Moving the valve-rod attachment closer to the fixed lever pivot reduces its travel. Doubling shaft speed doubles peak rod speed while leaving cam throw, total rod travel and lever swing unchanged.
What the calculation does not determine
The connected geometry establishes movement, assuming maintained roller contact. It does not establish the load needed to keep contact, bearing stress, spring force or an allowable operating speed.
A valve’s opening interval cannot be inferred from throw alone. Port dimensions and valve timing must be added before estimating admission, piston-stroke cutoff or steam demand. The results here describe mechanical travel and speed.
Questions about selecting cams
Why does the lower inset shift sideways?
It shows the cam series sliding along the shaft to bring a different cam under the follower, as described in Brown’s movement 150.
Does the lever stretch as the cam turns?
No. Roller position is solved with a fixed lever length and maintained cam contact. The connecting rod also keeps its length.
Can cam throw determine steam consumption?
Cam throw alone cannot determine it. The model contains no valve-port, pressure or cylinder calculation.
Why does shaft speed not change rod travel?
The geometry sets travel. Shaft speed changes how quickly the same path is traversed.
Primary drawing and description
Henry T. Brown, Five Hundred and Seven Mechanical Movements, movement 150, pages 40–41, Cornell University Library scan. The series slides lengthwise so a cam of greater or lesser throw acts on the lever carrying the valve rod.
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