A closed groove around a rotating drum can guide a follower through an outward and return traverse. This calculator studies the ideal case of one axial stroke per half-turn, with straight segments when the cylinder surface is unwrapped. It calculates speed, groove-centreline angle, reversal interval and the difference between entered groove width and pin diameter.
Heart-shaped Groove Interactive Calculator
Explore ideal closed drum-groove travel, lead angle, half-turn timing and the entered width difference. Outputs do not establish physical fit or operating limits.
Equation Used
- Ideal constant-pitch groove centreline with one outward and one return stroke per revolution.
- Stroke S occurs over half the drum circumference.
- Follower and groove widths are compared only as entered diameters/widths.
- No cusp blend, pressure angle, contact force, friction, acceleration, stress, lubrication, wear, life or safe-speed model.
Ideal groove-centreline kinematics only. Lead angle is based on one full axial stroke over half a drum revolution. Real reversal cusps require finite blends and dynamic/contact analysis.
A drum groove viewed as a flat map
Unwrap one drum circumference into a horizontal coordinate from zero to πD. In this ideal model the groove advances axially through stroke S over the first half-circumference and returns over the second. Joining the two ends of the map closes the track around the drum.
A guided follower moves axially as the drum rotates. The two sloping segments meet at the far-end turnaround; the map seam is the near-end turnaround. There is no crossing branch or multi-turn reversing screw in this particular model.
The centreline has sharp corners at both reversals. A real follower needs a finite turnaround profile and appropriate groove-contact geometry. The tool does not design those details or establish a clearance, speed or load rating.
The illustration is an unwrapped surface map, not a three-dimensional machining drawing. Its display speed is slowed for viewing and does not reproduce the entered drum speed in real time.
Using the traverse calculation
This idealized track is useful for comparing axial travel with rotational speed. It can help explain the timing of a guide that travels outward and back while its input continues rotating in one direction.
A winding application also depends on spool rotation, material diameter, tension, package geometry and the reversal motion. None of those inputs is present. The model does not identify the mechanism inside a named fishing reel, textile winder or cable winch.
Ideal unwrapped groove geometry
α = atan[2S/(πD)]
reversal interval = 30/N seconds
diametral difference = Wg − Df millimetres
S and D are in millimetres and N is revolutions per minute. The angle α is measured from the circumferential direction on the unwrapped surface. Each stroke spans πD/2 circumferential distance; it therefore has slope 2S/(πD).
The speed is the positive axial speed magnitude between ideal reversals. It is not a finite endpoint velocity or acceleration. The angle is a groove-centreline angle; the tool does not separately solve a contact pressure angle.
Wg − Df compares the two entered widths directly. Positive difference alone does not establish clearance through a curved turnaround or account for pin shape, tolerances, thermal expansion or deflection.
Example using the preset
Enter S = 100 mm, D = 50 mm, N = 300 rpm, follower diameter 6 mm and groove width 6.05 mm. The ideal speed is 1.00 m/s, the lead angle is approximately 51.9°, the reversal interval is 0.100 seconds, and the entered width difference is 0.05 mm.
For a separate 180 mm stroke and 60 mm drum at the same speed, v = 1.80 m/s and α = atan[360/(π × 60)] ≈ 62.4°. The reversal interval remains 0.100 seconds because it depends only on rpm.
These are numerical scenarios, not acceptable groove dimensions or operating settings. Increasing stroke increases speed and angle; increasing drum diameter decreases angle without changing speed or reversal interval.
What needs a complete design
A real groove requires a turnaround blend, follower geometry and constraints, material and surface specification, loads, lubrication and manufacturing tolerances. These determine contact and motion behavior beyond the ideal straight segments.
No universal life, hardness, blend radius, safe rpm or winding quality follows from the four outputs. In particular, a positive entered width difference and a finite lead angle do not certify that a follower can pass through the reversal.
Frequently asked questions
Why is there a factor of two in the lead angle?
One stroke spans half the circumference, πD/2. Its unwrapped slope is therefore S divided by πD/2.
Which direction is the lead angle measured from?
The circumferential direction on the unwrapped drum surface, not the drum axis.
Why does drum diameter not affect traverse speed?
The model prescribes the same axial stroke per half-turn regardless of diameter. Diameter changes the slope of that stroke on the unwrapped surface.
Does positive clearance prove the pin will run freely?
No. The output is only groove width minus follower diameter. Contact geometry and tolerances through the turnaround are not evaluated.
Is the reversal physically instantaneous?
Only in the ideal motion law. A real mechanism needs a finite interval for its velocity to change direction.
Does this represent a fishing-reel reversing worm?
It represents a single closed groove with one out-and-back stroke per revolution. A multi-turn reversing screw or a particular commercial reel needs its own track and follower model.
Reference
Carnegie Mellon University, Introduction to Mechanisms, chapter 6: Cams explains cam and follower arrangements and motion-law considerations. The equations here follow directly from the stated half-turn traverse geometry.
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