The Eccentric Cone Change-velocity (form 2) is a cam mechanism in which a tilted truncated cone rotates against an axial follower, producing an output velocity that varies sinusoidally within a single input revolution. It solves the problem of generating a smoothly accelerating-then-decelerating output motion from a constant-speed input shaft without using gears or linkages. The follower rides on the cone's slanted face, so its axial position depends on both rotation angle and cone tilt. You get a compact, single-piece change-velocity drive used in winders, dosing pumps, and traverse mechanisms.
How the Eccentric Cone Change-velocity (form 2) Works
The mechanism is a truncated cone mounted on a shaft so its axis sits at a small angle — typically 3° to 12° — relative to the rotating axis of the input shaft. A spring-loaded follower rides on the cone's flat end face, and as the cone spins, the contact point traces a circle on a tilted plane. The follower's axial position varies as a sine of the input angle, so output velocity peaks at the 90° and 270° crank positions and goes to zero at the 0° and 180° dead points. That's the form 2 distinction — the follower contacts the end face of the cone, not the slanted side surface like form 1.
The tilted cone face is what generates the change-velocity behaviour. If you machine the tilt angle wrong by even half a degree on a 60 mm cone face, the peak follower velocity shifts by about 8% and the dwell symmetry breaks — you'll see one stroke direction running faster than the other, which on a traverse drive shows up as uneven pitch on the wound package. Surface finish on the contact face has to hold Ra below 0.4 µm, otherwise the follower chatters at the velocity peaks where contact force is lowest.
The most common failure mode is follower lift-off near top-dead-centre. When the input speed climbs past the design point, the follower's required deceleration exceeds what the return spring can deliver, and the follower bounces. You hear it as a tick at twice the input frequency. Fix is either a stiffer spring, a lower running speed, or — if the geometry allows — a positive-drive yoke that captures both faces of the cone.
Key Components
- Truncated Cone (tilted): The rotating element. Tilt angle α typically sits between 3° and 12° — below 3° the velocity variation is too small to be useful, above 12° the contact stress at the follower tip rises sharply. The cone face must be flat to within 0.02 mm across its full diameter.
- Axial Follower: Slides along a guide bushing parallel to the input shaft. Tip is usually a hardened roller or a ground hemispherical button. Side load on the follower stem must stay under 5% of the spring preload, otherwise the bushing wears oval and the follower develops a ±0.1 mm radial wobble.
- Return Spring: Holds the follower against the cone face throughout the revolution. Preload sized so contact force never drops below roughly 1.5× the follower mass × peak acceleration. Undersizing the spring is the single most common cause of velocity-peak chatter.
- Follower Guide Bushing: Bronze or PTFE-lined sleeve that constrains follower motion to pure axial translation. Internal bore tolerance H7 with the follower stem at h6 — any looser and the follower tips under side load, any tighter and thermal growth jams it.
- Input Shaft and Cone Mount: Carries the cone with the tilt fixed by a precision-ground washer or a machined-in shoulder. The mount must repeat the tilt angle within ±0.1° on reassembly, otherwise the velocity profile shifts on every service interval.
Where the Eccentric Cone Change-velocity (form 2) Is Used
You see the eccentric cone change-velocity (form 2) wherever a designer needs a smooth, non-uniform axial output from a constant-speed input — and where space won't allow a four-bar linkage or a planetary differential. It shows up most often in textile traversing, fluid dosing, and small-batch material handling. The mechanism is cheap to make, has only one moving contact pair, and the velocity profile is fully defined by the cone geometry, which means once you've cut the part right, the output is repeatable for the life of the cone.
- Textile Winding: Yarn traverse modulator on cone winders similar to the Savio Polar/E series, where the cone's variable-rate output prevents ribbon winding by softening the stroke endpoints.
- Pharmaceutical Dosing: Low-volume reagent pump heads on benchtop fillers like the Watson-Marlow Flexicon PF7, where the change-velocity profile gives gentle aspiration and faster delivery.
- Wire and Cable Manufacture: Layer-winding traverse on bunching machines such as the Niehoff D-series, used to vary stroke speed at lay reversal points and reduce wire stress.
- Glass Fiber Roving: Stroke modulator on roving winders modelled on Leistritz and Owens Corning lines, smoothing the bobbin edge build.
- Printing and Packaging: Ink-fountain ductor drives on small offset presses where a pulsed delivery curve is needed without resorting to a separate cam stack.
- Laboratory Instruments: Sample-stage oscillators on optical scanners where 10-30 µm axial dither is generated from a single low-RPM motor.
The Formula Behind the Eccentric Cone Change-velocity (form 2)
The output you usually need to predict is the peak axial velocity of the follower, because that's what sets bearing life on the follower stem and determines whether the return spring can keep contact at the velocity reversal points. At the low end of the typical operating range — 30 RPM input with a 5° cone tilt on a 50 mm radius — peak velocity sits in the millimetres-per-second region, slow enough that you can ignore inertia entirely. At the nominal range of 100-300 RPM the inertia of the follower starts mattering and you size the spring around it. At the high end, above 600 RPM, follower lift-off is the limiting factor regardless of how stiff your spring is. The formula below gives you the geometric peak velocity; what you do with it depends where in the range you're operating.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| vpeak | Peak axial follower velocity, occurring at 90° and 270° of input rotation | m/s | in/s |
| R | Radius from cone axis to the follower contact point on the cone end face | m | in |
| ω | Angular velocity of the input shaft | rad/s | rad/s |
| α | Tilt angle of the cone axis relative to the input shaft axis | degrees | degrees |
Worked Example: Eccentric Cone Change-velocity (form 2) in a benchtop electroplating barrel oscillator
You're designing a small electroplating barrel oscillator for a jewellery-finishing line — think of a benchtop unit similar to the Sterling Systems lab-scale plater. The barrel needs a gentle 12 mm axial dither to keep parts agitated in the plating bath, driven from a 1/8 hp gearmotor running at 180 RPM nominal, with the user able to dial input speed from 60 RPM up to 360 RPM. You've selected a cone with a 40 mm contact radius and a 6° tilt. You need to know the peak follower velocity across the speed range to size the return spring and the bath-side bellows seal.
Given
- R = 0.040 m
- α = 6 degrees
- Nnom = 180 RPM
- Nlow = 60 RPM
- Nhigh = 360 RPM
Solution
Step 1 — convert the nominal input speed from RPM to angular velocity in rad/s:
Step 2 — compute tan(α) for the 6° cone tilt:
Step 3 — peak follower velocity at nominal 180 RPM:
That's a brisk dither — fast enough that you can see individual strokes by eye but not so fast that the bellows seal flexes violently. Now the low end of the range, 60 RPM:
At 26 mm/s the barrel motion is slow and lazy — parts at the top of the load won't get the agitation kick they need to tumble down to the cathode contact, so plating uniformity drops on barrels above about 60% fill. The high end, 360 RPM:
That's the theoretical peak. In practice the follower's required deceleration at the velocity reversal points scales with the square of speed — quadrupling the input quadruples the deceleration demand on the spring — and a standard music-wire return spring sized for 180 RPM operation will lose contact above roughly 280 RPM, where you'll start to hear a metallic tick at 9 Hz from the follower hammering back onto the cone face.
Result
Peak follower velocity at the nominal 180 RPM design point is 79 mm/s. That's the sweet spot — barrel agitation is visibly active and the bellows seal flexes within its rated envelope. At the 60 RPM low end the velocity drops to 26 mm/s, which feels sluggish and produces poor plating uniformity at high barrel fill, and at the 360 RPM theoretical high end velocity reaches 159 mm/s but follower lift-off becomes the limit before you ever get there. If your measured peak velocity reads more than 10% below predicted, the most likely causes are: (1) cone tilt angle drifted because the precision shoulder washer wasn't seated flat on reassembly, (2) follower stem binding in the guide bushing from chemical attack on the PTFE lining causing 0.05 mm or more axial drag, or (3) spring sag below 80% of installed preload from heat-soak in the plating environment, which lets the follower partially lift even at the design speed.
When to Use a Eccentric Cone Change-velocity (form 2) and When Not To
The eccentric cone (form 2) competes with two other ways of generating change-velocity axial output from a rotating shaft: a barrel cam with a machined groove, and a Scotch yoke driven by an offset crank. Each one wins on different metrics. Pick based on stroke length, required RPM, and how much you can spend on the part itself.
| Property | Eccentric Cone (form 2) | Barrel Cam (grooved) | Scotch Yoke |
|---|---|---|---|
| Practical RPM ceiling | ~600 RPM (lift-off limited) | ~1200 RPM (positive drive) | ~3000 RPM (rolling contact) |
| Stroke length range | 1-30 mm typical | 5-150 mm | 10-300 mm |
| Velocity profile | Pure sinusoid | Arbitrary (groove cut) | Pure sinusoid |
| Part cost (small batch) | Low — single turned part | High — 5-axis machining | Medium — crank plus yoke |
| Follower bearing life at rated load | 8000-15000 hr | 20000+ hr | 30000+ hr |
| Tolerance sensitivity | Tilt angle ±0.1° | Groove width ±0.02 mm | Pin clearance ±0.01 mm |
| Best application fit | Low-cost dither and traverse | Programmable dwell motion | High-speed reciprocation |
Frequently Asked Questions About Eccentric Cone Change-velocity (form 2)
The form 2 cone produces a perfectly symmetric sinusoid only if the cone end face is flat and perpendicular to the cone's tilted axis. If the face has a slight conical error from the turning operation — even 0.05 mm dish across a 40 mm face — the follower sees a different effective radius on the up-stroke than on the down-stroke, and you get up to 10% velocity asymmetry.
Check by indicating the cone face on a surface plate with the part held in its operating mount. If TIR exceeds 0.02 mm, regrind or replace. The other common cause is the shaft bearing preload being uneven, letting the cone wobble half a degree off its nominal tilt during rotation.
You can, but the trade is bearing load. Peak contact force at the follower tip scales with both tilt angle and the square of speed. Doubling speed to compensate for a halved tilt quadruples the dynamic load on the follower bushing while the geometric Hertz stress only drops by a factor of about 1.4 from the lower angle.
Net result: smaller tilt plus higher RPM gives shorter follower bushing life. The rule of thumb is to pick the largest tilt angle that keeps your contact stress under the cone material's allowable, then run the lowest RPM that delivers your required cycle rate.
This is almost always follower bounce, not a geometric error. When the return spring is undersized, the follower lifts off near top-dead-centre and re-impacts the cone face slightly later in the rotation. The displacement transducer reads the impact spike as part of the velocity profile, inflating the measured peak.
Confirm by putting an accelerometer on the follower guide. If you see a sharp acceleration spike at twice the input frequency riding on top of the smooth sinusoid, you have lift-off. Increase spring preload by 25-30% and re-measure.
No — that's the fundamental limitation. The form 2 geometry produces a pure sinusoid because it's a tilted-plane projection, and a sinusoid has zero dwell. The follower only momentarily reaches zero velocity at the two endpoints.
If you need any dwell at all, switch to a barrel cam with a machined groove, where you cut a flat section into the groove for whatever angular range you want the follower to hold position. Trying to fake dwell on a cone with a soft follower or a damper just smears the velocity profile and adds repeatability error.
The cone's tilt angle is set by whatever feature mates against the cone hub — usually a precision-ground shoulder washer or a machined shaft shoulder. If chips, a burr, or even a fingerprint of grease sits between those mating faces during reassembly, you tilt the cone by an additional 0.1-0.3°, which shifts your peak velocity by 2-5% and breaks dwell symmetry.
Always wipe both mating faces with solvent, inspect under magnification for nicks, and reinstall in the same angular orientation each time. Mark the cone and shaft with a witness line so you index it consistently.
For strokes under about 5 mm, yes. Form 2 puts the contact point on a flat face, which lets you grind the face to a 0.2 µm Ra finish using ordinary surface-grinding equipment. Form 1's slanted side surface needs a profile grinder or a cylindrical grinder with a tilted workhead, which is harder to hold to fine finish.
For strokes above 15-20 mm form 1 wins because you can get the same stroke from a smaller-diameter cone — form 2 stroke equals 2R × tan(α), so big strokes force a big cone diameter and the package gets unwieldy.
References & Further Reading
- Wikipedia contributors. Cam. Wikipedia
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