A uniform-traverse heart cam illustrates an ideal motion law: the follower moves outward at constant speed during half a turn and returns at the same speed during the other half. The abrupt reversals are mathematical idealizations. A physical cam and follower must change direction over finite time, so this calculator describes displacement and nominal traverse speed rather than a buildable high-speed cam profile.
Heart-cam Uniform Traversing Interactive Calculator
Explore a selected-angle pose and ideal uniform-traverse equations. Endpoint dynamics and a manufactured roller-cam profile are not calculated.
Equation Used
The ideal heart-cam uses two mirror-image Archimedean spiral halves. Over the first half-turn the follower displacement x rises linearly from 0 to stroke S; over the second half-turn it falls linearly back to 0. Because the cam rotates at constant speed n, the traverse speed is constant and equals S*n/30.
- One full out-and-back traverse occurs per cam revolution.
- Ideal two-arc Archimedean heart cam with no dwell.
- Ideal point-follower law; roller geometry, smoothing and contact forces are not calculated.
- Reversal is treated as instantaneous at theta = 0 deg and 180 deg.
From cam angle to follower position
The model joins two linear displacement ramps. Position increases from zero to the entered stroke as angle advances from 0° to 180°, then decreases to zero by 360°. Adding the minimum radius gives the radial distance from the shaft centre to the ideal tracing point.
For an in-line radial point follower, these ramps correspond to two Archimedean spiral portions. A roller follower needs a profile constructed from its centre path and roller radius; the tool does not calculate that offset envelope or check undercutting.
The cam and ideal tracing point move together through the complete cycle. The angle input sets the starting offset; playback adds rotation at one fortieth of the entered RPM. Pause and the animation-position control let you inspect the moving pose. The numerical results below the picture continue to use the selected input angle. The small graph follows the animated displacement through one revolution. The thin follower line and fixed guide represent ideal geometry; return-contact forces and the dimensions of a physical blade are not modeled.
At each end of the ideal stroke, velocity changes sign abruptly. That discontinuity cannot describe the finite acceleration and forces of a real reversal. Spring force, contact stress, follower separation and practical speed limits need a defined smooth transition and a dynamic model.
Exploring uniform traverse
Uniform traverse is useful as a motion-planning concept when a guide or working element should cover distance at an even rate. The ideal law helps compare steady travel with the changing speed of a crank-driven motion.
Actual winding, feeding or spreading equipment also depends on the turnaround motion and its coordination with the process. This page does not identify the cam used in a particular commercial textile machine, predict package uniformity or prescribe a retrofit.
The calculated motion law
x = S(360 − θ)/180 for 180° < θ < 360°
r = rmin + x
speed = Sn/30
reversals per minute = 2n
S and rmin are in millimetres, n is revolutions per minute and θ is degrees. The calculator wraps 360° to 0°. Position is measured from the minimum-radius position, not from the shaft centre.
Sn/30 is the positive speed magnitude during either straight ramp. Signed velocity is positive on the outward ramp and negative on return. At the exact reversal angles, the ideal derivative is discontinuous; the displayed speed remains the nominal ramp speed rather than an instantaneous endpoint velocity.
There is one out-and-back cycle and two reversals per revolution. No acceleration, jerk, spring preload, roller-contact geometry or material strength is calculated.
Example using the preset
With S = 40 mm, n = 120 rpm, rmin = 20 mm and θ = 90°, x = 20 mm and r = 40 mm. The nominal ramp speed is 40 × 120/30 = 160 mm/s, and the reversal frequency is 240 per minute.
At 180°, position is 40 mm and radius 60 mm. At 270°, position and radius return to 20 mm and 40 mm; signed velocity is now negative, although the speed readout still shows 160 mm/s. At 360°, position is zero and radius 20 mm.
Increasing minimum radius by 10 mm adds 10 mm to every radius result without changing stroke, speed or reversal frequency. Doubling rpm doubles nominal speed and reversal frequency without changing the selected-angle position.
These values illustrate the equations. They do not establish an acceptable operating speed or a spring requirement.
Compare motion laws
| Motion law | Travel characteristic | Endpoint consideration |
|---|---|---|
| Ideal uniform traverse | Constant speed magnitude between reversals | Velocity jumps at each endpoint |
| Sinusoidal traverse | Speed varies throughout travel | Speed reaches zero before reversing |
| Designed smooth cam law | Specified travel and transition regions | Acceleration and jerk can be evaluated from the chosen law |
Motion law alone does not determine wear, allowable speed, manufacturing cost or service life. Those comparisons require the actual geometry, loading, materials and operating conditions.
Frequently asked questions
Is speed constant at the endpoints?
The ideal ramp speed is constant between reversals. At each endpoint its sign changes discontinuously, so there is no finite instantaneous acceleration in this ideal law.
Why does the speed readout stay positive on return?
It reports speed magnitude Sn/30, not signed velocity. Return velocity would have the opposite sign.
Why does minimum radius not change traverse speed?
It adds a constant offset to radius. It does not alter displacement change per degree or rotational speed.
Does this define a manufactured roller-cam surface?
No. The outline follows an ideal radial point-follower law. The highlighted point is not a roller; a roller follower needs its own offset-envelope construction.
Can I calculate a return spring from this tool?
No. A finite reversal motion, moving mass, external loads and spring dynamics are needed. None is included here.
Why can the animated angle differ from the selected input angle?
The selected angle sets the numerical results and the animation starting offset. Playback then adds rotation. The animated cam, tracing point and displacement graph use the same current angle.
Does this establish a textile machine setting?
No. No particular machine, fibre, yarn, package or operating limit is modeled.
Reference
Carnegie Mellon University, Introduction to Mechanisms, chapter 6: Cams discusses follower arrangements, motion laws and the abrupt velocity changes in ideal uniform motion.
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