Henry T. Brown movement 119 converts uniform pinion rotation into reciprocating rectilinear motion of a bar carrying an oblong endless rack. The pinion works alternately against the upper and lower rack runs, and its shaft rises and falls in a fixed vertical slot as engagement passes around each end.
Reciprocating-rack Crank Substitute Interactive Calculator
Watch the rack move back and forth as the rotating pinion follows its upper and lower runs. Enter stroke and full-cycle rate to calculate cycle time, one-way time and mean speed, with a separate sinusoidal speed comparison.
Equation Used
- One full cycle contains one stroke in each horizontal direction.
- The illustrated pinion rotates uniformly and rolls without slip along the selected rack pitch path while its shaft remains in one fixed vertical slot.
- Entered stroke sets the physical offset readout while the drawing keeps fixed proportions. It does not specify pinion radius, rack-end radius or tooth proportions.
- No pinion speed, acceleration through reversal, tooth profile, backlash, load, force, stress, wear, lubrication, tolerance or safe-speed prediction.
An endless rack passes a pinion through a vertical guide
Brown's movement 119 combines three constrained motions. The oblong endless rack is rigidly attached to a horizontal bar, so the rack can translate left and right. The pinion shaft is held at one horizontal position by a vertical slot but may slide upward and downward. As the uniformly rotating pinion rolls along the upper straight run, the rack moves one way; around the end, the shaft changes height; along the lower straight run, the same pinion rotation moves the rack the other way.
The diagram shows an oblong pitch path with rounded ends, a pinion tangent to that path, a vertical guide and a marked contact point. Its proportions illustrate motion; Brown’s sketch does not provide the dimensions needed to manufacture the teeth or guides.
What the historical movement demonstrates
The arrangement is a compact kinematic example of converting continuous one-direction rotation into reciprocating translation without reversing the input shaft. It is useful for studying alternate engagement, guided shaft motion and geometric reversal. Selecting it for a real machine would require a separate design of teeth, guides, bearings, lubrication, inertia, loads and end transitions.
Timing relationships, not a tooth design
For selected stroke S and full-cycle rate N, cycle time is T=60/N and one-way time is t=30/N. Dividing stroke by one-way time gives the ideal mean one-way speed vmean=SN/30.
For comparison only, a sinusoidal crank-pin projection with amplitude S/2 and frequency N/60 has peak speed vsine,peak=Ï€SN/60. Brown's source does not supply the pinion radius, rack-end pitch radius or transition law needed to turn that comparison into an actual peak-speed prediction.
Worked timing example
At a selected 300 mm stroke and 90 full cycles per minute, one cycle takes 0.667 s and one-way travel takes 0.333 s. The ideal mean one-way speed is 900 mm/s. The separate sinusoidal reference peak is 1,413.7 mm/s. Those values describe the selected timing arithmetic; they do not determine tooth size, pinion RPM, force or safe operating speed.
What the timing results tell you
For a selected stroke and cycle rate, the calculator gives the time available for each traverse and its mean speed. These are useful comparisons when exploring motion requirements. The sinusoidal peak is a separate reference, not the peak speed of the illustrated rack.
The rack reverses without reversing pinion rotation, but the pinion shaft must slide through its guide and pass around each end. A working design needs the tooth profiles, clearances, guide and bearing loads, and acceleration through reversal. The timing results alone do not provide those dimensions or loads.
Brown movement 119 questions
Why does the pinion shaft move vertically?
The fixed slot holds the shaft at one horizontal position while allowing it to follow the upper run, rounded ends and lower run of the translating rack.
Does the drawing specify tooth dimensions?
No. It shows a schematic pitch path and pinion. Stroke and cycle rate do not determine tooth size, rack-end radius, pinion radius or clearances.
Is the mean speed maintained through the end transitions?
No. Mean one-way speed is stroke divided by one-way time. The rack slows and reverses at each end; its instantaneous speed depends on the rack and pinion geometry.
Is Sine reference peak the rack mechanism’s actual peak speed?
No. It is the peak speed of a separate sinusoidal motion with the same stroke and cycle rate. It is included for comparison and is not a prediction of this rack’s maximum velocity.
Why does changing stroke leave the drawing the same size?
The diagram keeps fixed proportions on screen. Stroke changes the physical offset readout and speed calculations. Cycle rate changes both the timing results and animation duration.
Is one full cycle a single stroke?
No. A full cycle includes one stroke in each direction. With equal time assigned to each direction, one-way time is half the cycle time. The cycle-rate slider does not specify a safe operating rate for a real machine.
Primary mechanism reference
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, movement 119 — oblong endless rack, uniformly rotating pinion and vertically guided pinion shaft.
- 507 Mechanical Movements, movement 119 transcription — searchable transcription and animated presentation of Brown's description.
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