Two meshing spur gears carry crank-wrists that drive a linked traverse bar. Explore the changing linkage positions and calculate opposite-direction gear speeds, configuration repeat time and mesh tooth-passage rate.
Dual Spur-Gear Crank-Wrist Timing Calculator
Enter integer tooth counts and driver speed. The worksheet reports the exact opposite-direction speed ratio, driven speed, crank-configuration repeat and mesh tooth-passage rate. The connected animation uses declared drawing proportions because the historical plate supplies no dimensions.
Equation Used
- Both external spur gears are ideal and remain in mesh without backlash.
- Each gear carries one crank-wrist and the two connecting links remain rigid.
- The output joint is constrained to a horizontal guide in the declared reconstruction.
- Gear module, pressure angle, tooth strength, bearing loads, link dimensions and historical scale are not specified or rated.
The tooth counts set the opposite-direction speed ratio. Their greatest common divisor determines how many driver revolutions bring both crank-wrists back to their initial phases.
Two meshing gears drive two crank-wrists
Brown's movement 122 shows two external spur gears carrying offset crank-wrists. Each wrist drives one end of a connected floating member, and its central joint is associated with the horizontal traverse bar. Because the gears rotate oppositely and their crank phases advance according to tooth count, the linkage gives a non-simple alternating traverse.
The animation is a dimensionally declared reconstruction of that visible topology. Brown supplies no link lengths, tooth counts or guide details.
Historical motion-conversion study
Use the calculator to calculate gear timing and repeat period of a selected tooth-count pair. Applying this linkage to a machine requires a complete dimensional synthesis, interference check, bearing and tooth-load analysis, lubrication plan and guarding assessment.
External-gear timing
Timing example
With a 24-tooth driver, 36-tooth driven gear and 60 rpm input, the driven gear turns oppositely at 40 rpm. The two crank phases return together after 3 driver revolutions, or 3.00 seconds, and 1,440 teeth pass the mesh per minute.
What gear timing can determine
The gear ratio and configuration repeat follow from tooth counts. Traverse stroke and the detailed output motion also depend on crank offsets, connecting links and guide geometry. The diagram uses illustrative proportions; those dimensions are not historical measurements or machine design specifications.
Variable-traverse questions
Is this a barrel cam or reverse-helix traverse?
No. The historical drawing shows two meshing spur gears with crank-wrists and links.
Does the timing calculation predict traverse stroke?
No. Stroke depends on the missing crank, link, guide and attachment dimensions.
Why does the animation have declared dimensions?
They illustrate how the gears and links connect. The proportions are chosen for the diagram and are not dimensions supplied by Brown.
Variable-traverse references
- Five Hundred and Seven Mechanical Movements, movement 122: two spur gears with crank-wrists produce a variable alternating traverse of the horizontal bar.
- Cornell University Library scan of Brown's mechanical movements: historical plate and wording for movement 122.
- Carnegie Mellon course resource, Making Automata Mechanisms: reproduces Brown's two-spur-gear crank-pin variable traverse as an automata mechanism.
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