Henry T. Brown's movement 122 shows two meshing spur gears with crank-wrists, two connecting links, a floating member and a horizontal traverse bar. Brown states that rotation produces a variable alternating traverse, but provides no dimensions or stroke equation.
Considering a separate actuator-driven traverse
The vector comparison below does not size an actuator or calculate traverse travel. A separate actuator-driven traverse needs its complete linkage geometry, timing, force and end positions defined before a drive can be selected.
For crank motion, review the throw radius and the changing angle between the actuator and driven link. Those two details decide whether the actuator is pushing efficiently or fighting the geometry.
A crank or cam may tolerate continuous rotation through a difficult part of the cycle, while a linear actuator has defined end positions and internal limits. That difference matters when the mechanism needs repeatability or must not drive into a hard stop.
- Map actuator stroke to the actual output travel before choosing a model.
- Check for binding, changing leverage, and peak load near the ends of travel.
- Decide whether timed motion is acceptable or position feedback is required.
For a FIRGELLI design review, calculate the load case with the FIRGELLI actuator force calculator and plan the switching or controller arrangement with the linear actuator wiring diagram generator. If an actuator or cylinder is already installed, the linear actuator replacement finder helps keep the comparison tied to real dimensions.
Two Crank-disks Variable Alternating Traverse Interactive Calculator
Enter three included angles for two ideal equal vectors of magnitude r. Results are dimensionless vector-resultant magnitudes only—not the stroke of Brown's undimensioned historical linkage.
Equation Used
- The numerical comparison uses two ideal coplanar vectors of equal magnitude r.
- The entered angle is the included angle from 0 to 180 degrees.
- The historical drawing is a topology sketch only and is not dimensioned or drawn to a validated scale.
- No mapping from the vector resultant to Brown movement 122 bar travel is asserted.
- Gear geometry, crank radii, link lengths, joint locations, assembly branch, velocity, acceleration, force, friction, backlash, strength and application performance are omitted.
Two Meshing Gears, Crank-wrists and a Linked Bar
Brown's movement 122 shows two meshing spur gears. A crank-wrist on each gear connects by a link to opposite ends of a floating member, whose intermediate joint carries a horizontal bar.
Rotation of the two meshing gears moves the linked horizontal bar in an alternating traverse. Its displacement depends on the complete gear, crank and link dimensions.
What This Calculator Represents
The three inputs compare the magnitude of the sum of two equal vectors at three included angles. That geometry ranges from 2r for parallel vectors to zero for opposite vectors.
To calculate movement 122 bar travel, the gear radii, crank throws, link lengths and assembly configuration must also be specified. The equal-vector comparison does not provide that travel.
Equal-vector Resultant Only
|u+v|² = r² + r² + 2r² cos(phi)
|u+v|/r = sqrt(2 + 2 cos(phi)) = 2 cos(phi/2)
The identity follows from vector addition and the law of cosines. It is not Brown movement 122's bar-stroke equation.
Worked Vector Comparison
At 0°, equal vectors add to 2.00r. At 90°, the resultant is sqrt(2)r, about 1.41r. At 180°, the vectors cancel to 0.00r. These are vector magnitudes, not traverse distances.
Model Boundary
- Mechanism arrangement: two meshing spur gears, two crank-wrists, two links, a floating member and horizontal bar.
- Calculated: only an equal-vector resultant magnitude.
- Not calculated: historical bar position, stroke, timing, velocity, acceleration, forces, gear ratio, interference, backlash, wear, operating adjustment or application suitability.
Frequently Asked Questions
Are the gears coaxial?
No. Brown shows two separate meshing spur gears.
Does phase set the historical traverse stroke?
The source does not establish that relationship.
What does the cosine result calculate?
It gives the magnitude of the sum of two equal vectors divided by their common length. It does not give the historical bar stroke.
Can I multiply the result by a crank radius to get bar stroke?
No; not for Brown movement 122 without a complete kinematic model.
Does the drawing animate the solved linkage?
No. The drawing identifies the gear, crank and link arrangement; it does not calculate the bar motion.
Can this size a traverse mechanism?
No.
References
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, movement 122: two spur gears, crank-wrists and variable alternating traverse of the horizontal bar.
- 507movements.com, Movement 122: accessible rendering of Brown's original topology and caption.
- MIT OpenCourseWare, Calculus of Several Variables, Lecture 2: dot product and law-of-cosines relation supporting the equal-vector comparison.
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