A grooved barrel cam converts rotation into a repeating linear stroke. A roller attached to a guided carriage follows the groove as the drum turns. This calculator converts rise, dwell and return angles into time at a chosen cam speed. Set the angle sum to 360° for one complete cycle with equal dwell at each end.
Grooved Cam Reciprocating Interactive Calculator
Vary cam RPM and rise/dwell/return angles to see the timing of each reciprocating stroke sector.
Equation Used
At constant shaft speed, sector time is proportional to its angle. The example uses 170° rise, 10° dwell at each end and 170° return, totaling 360°. Other sums are not a complete one-revolution schedule with the entered equal dwells. The animation shows the drum without a groove or follower until the sum is 360°; the individual timing results remain available.
- One cam revolution produces one complete reciprocating cycle.
- The same dwell angle is used at both stroke ends.
- Sector timing is based on angular position, not groove force or acceleration.
How the groove moves the carriage
A groove changes axial position around a rotating drum. A roller held at a fixed angular location follows that axial position, moving its carriage along a guide. The guide constrains the output to a straight line.
The two groove flanks can transmit load in opposite directions, so a return spring is not needed to produce the return motion. This does not mean an ordinary roller rolls without slip against both flanks at once. Clearance, contact reversal and bearing arrangement matter in a physical cam.
Parts and motion events
- Cam drum: carries the groove and rotates with the input shaft.
- Groove: specifies the output position for each cam angle.
- Roller and pin: transfer contact force to the carriage.
- Carriage guide: restrains unwanted motion.
A rise moves toward one end, a dwell holds that position, and the return brings the carriage back. Here the same entered dwell angle applies at both ends. A complete schedule requires rise + return + 2 × dwell = 360°.
Using a fixed motion schedule
A barrel cam can synchronize a guide or transfer carriage with a rotating machine shaft. The groove fixes when the output advances, pauses and returns. Changing shaft speed changes the time scale without changing the angle schedule.
Choose the motion law and physical geometry together. Timing alone does not establish follower force, acceptable contact pressure, available stroke or fatigue life. A different product cycle may require a different cam or an adjustable drive arrangement.
Sector time at constant speed
t = T × θ/360°
Angle sum = θrise + θreturn + 2θdwell
N is cam speed in rpm, T is the time for one revolution in milliseconds, and θ is the angle of one sector. Dwell Time is the time for one end dwell, so it must be counted twice when totaling the cycle.
The numerical outputs are timings, not velocities or forces. In the drawing a normalized rise follows s = [1 − cos(πu)]/2, where u goes from zero to one during the rise; return reverses that curve. No physical stroke or carriage mass is entered.
A half-cosine segment meets a dwell with zero velocity but nonzero endpoint acceleration. Thus acceleration changes abruptly at that boundary. A physical high-speed cam requires a suitable motion law and a separate dynamic/contact analysis.
Example: 200 rpm with two short dwells
Enter 200 rpm, 170° rise, 10° end dwell and 170° return.
- One revolution takes 60,000/200 = 300 ms.
- Rise time is 300 × 170/360 = 141.6667 ms.
- Each dwell lasts 300 × 10/360 = 8.3333 ms.
- Return time is also 141.6667 ms.
- The angle sum is 170 + 170 + 2 × 10 = 360°.
The two movement intervals and two dwells total 300 ms. At 100 rpm, every time doubles. At 300 rpm, every time becomes two thirds of its 200 rpm value.
If the return angle changes to 160° with the other inputs unchanged, the sum is only 350°. The numbers still describe individual sectors, but the schedule leaves 10° unassigned. Restore a 360° sum before interpreting the preview as the stated complete cycle.
Groove, open cam or crank?
| Arrangement | How it constrains motion | Design consideration |
|---|---|---|
| Grooved cam | Two flanks provide positive return. | Clearance, contact reversal and groove geometry need attention. |
| Open cam | A spring or external load maintains contact with the profile. | Contact must be maintained throughout the intended cycle. |
| Crank and slider | Links constrain the output through a repeating stroke. | Motion follows the chosen link lengths rather than an independently specified cam profile. |
Frequently asked questions
Is Dwell Time for both ends combined?
No. It is the time at one end. The calculator uses the same dwell angle at the other end, so total dwell time is twice the displayed value.
What if Angle Sum is not 360°?
The entered sectors do not form the stated one-revolution cycle. Below 360° there is unused angle; above 360° the schedule cannot fit. The groove and follower are hidden until the sum is 360°, while the timing results still describe the individual sectors.
Does the drawing use exactly the entered angles?
Yes, when the angle sum is 360°. The groove and follower use the same displacement law, with the entered dwell at each end. Other sums do not produce an animated cycle. Rotation is slowed to one twentieth of the entered speed; stroke and component sizes are illustrative.
Can I calculate stroke speed from these outputs?
Not without a physical stroke and a specified displacement law. This calculator reports elapsed time only.
Does positive return remove backlash?
No. Groove and bearing clearances can still allow lost motion. Positive return describes how the opposite flank drives the reverse movement.
Can both groove walls have pure rolling contact with one roller?
Not generally. An ordinary single roller cannot maintain compatible no-slip rolling at both opposing flanks at once. Contact arrangement and clearance require attention.
What changes when I double cam rpm?
All sector times halve. For the same physical displacement law, velocities double and accelerations quadruple, but this tool does not calculate contact stress or component life.
References and further reading
Carnegie Mellon mechanism tutorial: cams explains rise, dwell and return events, including simple harmonic follower motion.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
