A grooved cylinder converts rotation into repeated out-and-back follower motion. Explore its developed-surface diagram and calculate total follower travel, mean path speed and reversal rate from stroke, cycles per revolution and drum speed.
Grooved-Cylinder Travel and Cycle Calculator
Enter a declared one-way stroke, complete return cycles per drum revolution and drum speed. The worksheet reports exact follower path per revolution, mean path speed and cycle or reversal rates. It does not predict local velocity, acceleration, pressure angle or load.
Equation Used
- L is the declared one-way follower stroke.
- c is an integer number of complete out-and-back follower cycles per drum revolution.
- The follower remains engaged with a closed traverse groove and constrained to translate.
- Groove width, follower shape, reversal curve, local velocity and acceleration, pressure angle, friction, load, stress, wear, stiffness, vibration and safety are excluded.
Every complete return cycle covers twice the one-way stroke. Multiplying by cycles per revolution and drum speed gives mean path speed and event rates; the groove profile is needed for local velocity and acceleration.
A rotating traverse groove moves a constrained follower
Traverse-cam patents describe a cylindrical cam with intersecting oppositely directed spiral grooves. A follower rides the groove while a guide constrains it to translate, producing reciprocal motion as the cylinder rotates.
The animation unwraps one declared drum revolution into a flat trace so the closed path and connected carriage are visible. Its corners mark event boundaries only; real reversal geometry is curved and design-specific.
A declared traverse-motion study
Grooved cylindrical traverse cams are documented in winding machinery. This worksheet describes the connection and calculates total travel and event rates; it does not establish suitability for a particular winder, machine tool, feeder or production line.
Travel and event-rate equations
Mean path speed is total path divided by time. It is not the instantaneous speed through a reversal.
Declared two-cycle example
For L=120 mm, c=2 complete return cycles per revolution and N=100 rpm, the follower travels 480 mm per drum revolution, its mean path speed is 0.800 m/s, it completes 200 return cycles per minute and encounters 400 end reversals per minute.
Mean travel speed and end reversals
Total path divided by time gives mean speed, but it does not describe the motion at an end reversal. Local velocity and acceleration depend on the groove displacement law and follower geometry. A practical traverse cam needs suitable reversal curves, guidance through groove crossings and an assessment of the resulting loads.
Grooved-cylinder questions
Does the sharp unwrapped corner represent a machinable groove?
No. It is an event diagram; the real reversal must use a suitable profile.
Can mean path speed be used as peak follower speed?
No.
Does adding return cycles automatically produce a viable cam?
No. Pressure angle, groove crossings, follower guidance and reversal geometry must be engineered.
Traverse-cam references
- US3407262A, Winding Machine Traverse Cam and Follower: primary patent describing a cylindrical traverse cam with intersecting oppositely directed spiral grooves, a sliding follower and dedicated reversal-control geometry.
- US3086722A, Yarn Traverse Mechanism: primary patent documenting a driven cylinder with a helical cam groove and a guided follower assembly.
- Lu et al., Design and Implementation of Multi-Grooved Simultaneous Separation and Screening Equipment: designs follower motion and theoretical and actual cylindrical-cam groove profiles and analyzes pressure angle rather than inferring reversal dynamics from stroke and rpm alone.
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