A grooved heart-cam guides a follower outward and back as a disc rotates. An ideal profile formed from rising and falling Archimedean spirals gives constant-speed traverse between abrupt reversals. This calculator compares average speed, revolution time, nominal groove width and a selected fraction of stroke. It does not design the end transitions or predict acceleration.
Grooved Heart-cam Interactive Calculator
Enter stroke and cam speed for average traverse speed, roller size and clearance for nominal groove width, and a fraction for the selected stroke length.
Equation Used
One revolution covers an outward stroke and a return stroke, a total distance of 2S. Dividing by revolution time gives average speed magnitude, 2SN/60. It equals the speed between reversals only in the ideal constant-velocity model. Nominal groove width is roller diameter plus total clearance.
- One full out-and-back reciprocating cycle occurs per cam revolution.
- Stroke is completed once per half revolution in the ideal constant-velocity heart-cam model.
- Groove clearance is the total width increase over roller diameter.
- Selected Zone is stroke times the entered fraction. It does not define a velocity law or change the drawn profile.
How the heart-shaped path creates a stroke
For an in-line radial follower, groove-center radius sets follower position. A radius that increases linearly with cam angle gives constant outward velocity at constant rotation speed. A decreasing radius gives the return. Joining the two radial laws makes an ideal repeating heart-cam path.
The groove flanks can drive in opposite directions, avoiding the need for a spring to produce the return stroke. A physical roller still needs clearance, compatible wall geometry and a guide. A single roller generally cannot maintain pure rolling against both opposing flanks at once.
The ideal profile reverses velocity abruptly at the ends. A real moving mass cannot do this with finite force, so a working cam needs designed transition regions. Stroke and rpm alone do not define those regions.
Main parts
- Disc and drive shaft: rotate the groove.
- Groove: defines the intended follower-center path.
- Follower and carrier: transfer the motion to the load.
- Linear guide: constrains the output to the intended line.
Uniform traverse and reversal
A nearly uniform traverse can be useful for distributing material along a winding width or sweeping a guide through a repeatable path. The required deposition pattern also depends on the motion of the material and the behavior at each reversal.
A fixed cam ties the displacement pattern to shaft angle. Changing speed changes the time scale, while a different motion pattern generally needs different geometry. This tool does not establish which profile suits a particular machine.
Average motion and simple dimensions
vaverage = 2S/T = 2SN/60
w = d + c
Z = Sf/100
S is peak-to-peak stroke in mm, N is rpm, T is seconds per revolution, and average speed magnitude is in mm/s. The net displacement after a full cycle is zero, so average signed velocity is zero; the displayed value uses total distance traveled.
d is roller diameter, c is the total groove-width increase over that diameter, and w is nominal groove width, all in mm. Z is the selected portion of stroke when f is entered as a percentage. This percentage is a dimensional comparison, not a solved constant-speed interval.
The allowed clearance slider range is not a recommended manufacturing fit. Wall curvature, roller geometry, tolerance, temperature and loading need separate consideration. Acceleration cannot be obtained by substituting groove cusp radius into v²/r for this translating follower; the actual displacement law through each transition is required.
Example: 100 mm stroke at 60 rpm
Use a 100 mm stroke, 60 rpm, 12 mm roller, 0.030 mm total clearance and 80% Zone Fraction.
- Revolution time: 60/60 = 1 second.
- Total distance per cycle: 2 × 100 = 200 mm.
- Average speed magnitude: 200/1 = 200 mm/s.
- Nominal groove width: 12 + 0.030 = 12.030 mm.
- Selected Zone: 100 × 0.80 = 80 mm.
At 120 rpm the revolution time halves and average speed doubles to 400 mm/s. Groove width and selected zone length remain unchanged. Changing Zone Fraction to 60% gives 60 mm but does not change speed or the drawn groove.
Choosing a motion law
| Motion | Behavior | What to check |
|---|---|---|
| Ideal constant-speed out-and-back | Uniform speed magnitude between reversals. | Sharp velocity changes require transition design for a physical mechanism. |
| Sinusoidal reciprocation | Speed varies smoothly and reaches zero at stroke ends. | Whether the varying speed suits the process. |
| A designed cam or controlled-axis profile | Can allocate transition and working portions of the stroke. | Velocity, acceleration, jerk, loads and the capabilities of the drive. |
Frequently asked questions
Is Average Speed the peak speed?
No. It is total distance per revolution divided by revolution time. In a smooth profile the instantaneous speed varies and its peak may exceed this average.
Why is average velocity not zero?
The displayed quantity is speed magnitude based on distance traveled. The signed average velocity over the complete out-and-back cycle is zero.
Does Zone Fraction change the cam shape?
No. It only multiplies stroke to give Selected Zone in mm. The program does not design transition regions from that fraction.
Does Clearance mean a gap on each side?
It is the total width increase above roller diameter. The calculator simply adds that amount to the diameter; it does not allocate two separate side gaps.
Does the clearance slider give a recommended fit?
No. Its numeric range is an input range, not a fit recommendation. Actual groove geometry and operating conditions must be evaluated separately.
Can this predict cusp acceleration or follower life?
No. Neither a smooth transition law nor moving mass and contact geometry is entered. The ideal sharp reversal is not physically achievable at nonzero speed.
Does the animation run at the numerical rpm?
No. Playback is slowed and capped for illustration. The numerical average speed uses the entered rpm, while the drawn size is schematic.
Is one stroke twice the groove’s radial range?
For the in-line radial follower shown, stroke is the difference between maximum and minimum follower-center radius. Twice the stroke is the total distance traveled over one outward-and-return cycle.
References & Further Reading
- Wikipedia contributors. Cam. Wikipedia
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
