A cylindrical or barrel cam carries a groove around a rotating drum. A follower engaging that groove moves along a guide. This model uses one smooth rise and one smooth return per revolution, so the groove closes continuously.
Cylindrical Cam Interactive Calculator
Build a closed barrel-cam pitch path. Adjust drum diameter, stroke and rise angle; the remaining rotation returns the follower. Select a cam angle for the result tiles.
Equation Used
- One cycloidal rise and one cycloidal return per revolution, without dwell.
- Constant input speed, rigid geometry and an ideal guided follower.
- Rise occupies beta degrees; return occupies 360−beta degrees.
- Finite roller, cutter geometry, undercutting, backlash, load and contact stress are not solved.
Tiles use the selected cam angle. Animation readouts show the moving position. Negative velocity indicates return.
A closed groove drives a guided follower
The drum rotates about its vertical shaft. The roller center stays at one circumferential position while its blue carriage moves along the fixed guide. The groove therefore converts rotation into axial travel.
The animation projects the same three-dimensional pitch path used by the calculation. Hidden groove portions are dashed. The lower view unwraps the cylindrical surface into a displacement-versus-angle plot.
Explore motion and timing
Changing stroke changes the follower excursion. Changing drum diameter changes the developed groove slope. Increasing input speed increases axial velocity and reduces event time without changing the path.
Changing rise angle reallocates the revolution between rise and return. At least 30 degrees remains for each event in this calculator. A 360 degree rise alone would leave no finite return interval for a closed repeating groove.
Cycloidal rise and return
For normalized event progress u, define f(u)=u−sin(2πu)/(2π). Rise displacement is S f(u); return displacement is S[1−f(u)]. Rise progress is cam angle divided by rise angle beta. Return progress is the angle beyond beta divided by 360−beta.
The derivative with respect to cam angle in degrees is ±S[1−cos(2πu)] divided by that event’s angle. Multiplying by 6N gives signed axial velocity in mm/s for speed N in rpm.
The developed cylindrical surface has circumferential distance R times angle in radians. The local groove slope is atan(|ds/dθ|/R), using a radian derivative and R=D/2. Rise time is beta/(6N). At zero speed, time is reported as stopped.
The chosen motion law gives zero velocity and acceleration at both reversals. It does not calculate contact force, a cutter offset or a safe operating speed.
A 50 mm drum with 25 mm stroke
With 180 degrees for rise and 60 rpm input speed, the rise takes 0.5 seconds and the return takes 0.5 seconds. At 90 degrees the follower is halfway up: travel 12.5 mm, axial velocity 100 mm/s and developed groove slope about 32.48 degrees.
At 270 degrees it is halfway down. Travel is again 12.5 mm but velocity is −100 mm/s. At 0, 180 and 360 degrees the axial velocity is zero.
Pitch path versus a finished cam
A real roller has finite diameter, and the machined groove must be generated around its contact geometry with suitable clearance. The illustrated width is not a manufacturing dimension. Tight curvature, interference, backlash, lubrication and contact stresses require additional design work.
The smooth rise joins the return at the top of the stroke, and the return joins the next rise at the bottom. The follower therefore repeats its motion without a jump in position or velocity.
Barrel-cam questions
Why do the tiles stay at the selected angle while the picture moves?
The tiles are a repeatable calculation at your selected angle. Live travel and velocity are shown inside the animation.
Can the rise occupy the whole revolution?
Not for this one-rise, one-return closed groove. A full-revolution rise would need a different return mechanism or another cycle.
Does a large slope automatically mean a usable design?
No. The value describes geometry only. Roller loading, guide reactions, curvature and strength still need checking.
What happens at zero speed?
The drum holds the selected angle, axial velocity is zero and rise time reads stopped.
Reference
Carnegie Mellon University, Introduction to Mechanisms, chapter 6, describes barrel grooves, guided followers, pitch curves and motion events. The stated cycloidal motion law defines follower position and its derivative defines velocity.
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