A pivoted follower is a cam follower mounted on a fixed pivot so it swings through an arc as the cam rotates beneath it, instead of sliding along a straight line. It solves the friction and side-load problem that translating followers suffer when the cam pushes them off-axis. As the cam profile rises and falls, the arm rotates about its pivot and converts that rise into a controlled angular displacement at the working end. You see the same geometry in engine rocker arms, sewing-machine thread takeups, and high-speed indexers running 1,200 cycles per minute.
Pivoted Follower Interactive Calculator
Vary cam lift, follower arm length, output radius, and pressure angle to see pivot swing, output travel, and side-force tendency.
Equation Used
The calculator uses the pivoted follower geometry shown in the article: cam lift h raises the roller tip on an arm of length L, creating angular swing theta. The output travel is the arc length at the chosen output radius R.
FIRGELLI Automations - Interactive Mechanism Calculators.
- Follower arm starts approximately horizontal at zero lift.
- Cam lift h is converted into vertical roller-tip rise.
- Arm is rigid and theta is calculated in radians before unit conversion.
- Pressure angle side-force factor is relative to the normal cam force component.
How the Pivoted Follower Actually Works
A pivoted follower is a rigid arm with a roller, flat face, or arc tip on one end and a fixed pivot bearing on the other. The cam rotates and pushes the contact tip; because the tip is constrained to a circular path around the pivot, the whole arm swings, and the working end of the arm — usually opposite the cam, sometimes at 90° — produces an oscillating output. The advantage over a translating (sliding) follower is that no linear guide carries the cam's side load. The pivot bearing absorbs it, and pivot bearings are far cheaper and longer-lived than precision linear bushings under the same lateral force.
The geometry has to be right or the mechanism punishes you. The pressure angle — the angle between the cam-surface normal at the contact point and the velocity direction of the follower tip — should stay below 30° on rise and below 35° on return for industrial cams. Push past 30° and the side force on the pivot bearing climbs sharply, lift accuracy drops, and the follower can chatter. The pivot-to-tip distance (the arm length L) and the pivot-to-cam-centre distance set this geometry directly. Get the layout wrong and you cannot fix it with a stiffer spring or harder cam material.
Common failure modes are roller skidding, pivot-bushing wear, and follower lift-off. Roller skidding happens when the spring or follower preload is too low for the cam acceleration — the roller stops rolling and starts sliding, flat-spotting in 50,000 cycles instead of lasting 50 million. Pivot-bushing wear shows up as backlash at the working end. Follower lift-off happens at high speed when inertia exceeds the closing force, and the result is the trademark clatter of an over-revved valve train.
Key Components
- Pivot Pin and Bushing: The fixed rotation axis. Typically a hardened steel pin, 6-20 mm diameter for industrial work, running in a bronze or needle-roller bushing. Radial clearance must be 0.02-0.05 mm — tighter and it galls under thermal expansion, looser and you get measurable backlash at the working end.
- Follower Arm: The rigid lever between the pivot and the cam contact. Stiffness matters more than weight; a 10% deflection under peak cam force translates directly into 10% lift error. Forged steel or aluminium with a stress-relieved web is standard for cycle rates above 600 RPM.
- Cam Contact Tip: Either a roller (lowest friction, best for high speed), a flat face (cheapest, used in older engines), or an arc tip ground to a specific radius. Roller diameter sets the minimum cam concave radius — the cam profile cannot have a concave curve sharper than the roller, or it will dig in.
- Return Spring or Closing Cam: Keeps the follower in contact with the cam during the return stroke. Spring-loaded designs are simpler but speed-limited; conjugate (dual-cam) designs use a second cam to force-close the follower, eliminating the spring and pushing usable speeds past 2,000 RPM.
- Output Linkage: Connects the swinging arm to the driven element — a valve stem, a needle bar, an indexing pawl. The connection point along the arm sets the mechanical advantage and the output stroke; moving the link 20% closer to the pivot cuts stroke 20% and raises output force the same amount.
Industries That Rely on the Pivoted Follower
Pivoted followers show up wherever a rotating cam needs to drive a precise oscillating motion, especially when side loads on a translating follower would force you into expensive linear guides. The arc-of-travel output is often a feature, not a bug — many machines actually need angular motion, and the pivoted follower delivers it directly without a second linkage stage.
- Internal Combustion Engines: Rocker arms in pushrod V8s like the Chevrolet small-block — the pushrod lifts one end of the rocker, the other end pushes the valve open, and the pivot is a stud-mounted ball or shaft.
- Industrial Sewing: Thread takeup levers on Juki DDL-8700 lockstitch heads — a face cam swings the takeup through a 120° arc to pull thread up after each stitch.
- Packaging Machinery: Sealing-jaw oscillators on Bosch SVE 2520 vertical form-fill-seal baggers, where a barrel cam drives a pivoted follower that slams the jaws shut at 80 cycles/min.
- Printing Presses: Inking-roller oscillation on Heidelberg Speedmaster XL 106 sheetfed presses — a pivoted follower riding a swash cam traverses the form rollers axially to even out ink film.
- Textile Machinery: Heald-frame lift on Picanol OMNIplus 800 air-jet looms, where pivoted followers driven by a dobby cam raise and lower harness frames in time with the weft insertion.
- Automated Assembly: Pick-and-place arm tilt on Mikron G05 rotary index assembly platforms — a plate cam drives a pivoted follower that tilts the gripper through 90° per station.
The Formula Behind the Pivoted Follower
The core formula links cam lift h to follower angular displacement θ through the arm length L and the contact geometry. At the low end of the typical range, with small lifts (under 5 mm) on a long arm (over 100 mm), the relationship is nearly linear and easy to size by hand. At the high end — short arms under 40 mm with lifts above 10 mm — the small-angle approximation breaks down, the pressure angle climbs past 30°, and you have to compute the exact arc geometry or your output stroke will be off by 5-15%. The sweet spot for most industrial pivoted followers is an L/h ratio between 8 and 15, where geometry stays clean and pressure angles stay manageable.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| θ | Angular displacement of the follower arm about its pivot | rad | rad (or deg) |
| h | Cam lift at the contact point — radial rise of the cam profile | m | in |
| L | Arm length from pivot centre to contact tip | m | in |
| sout | Linear stroke at the output point on the arm | m | in |
| Lout | Distance from pivot to output linkage attachment | m | in |
Worked Example: Pivoted Follower in a glass-bottle labelling machine pivoted follower
Your team is sizing the pivoted follower that drives the label-press pad on a Krones Canmatic rotary labeller running 36,000 bottles per hour. The plate cam delivers 8 mm of nominal lift at the contact point. The follower arm is 120 mm from pivot to roller centre, and the label-press pad attaches 200 mm from the pivot on the opposite side. You need the press-pad stroke at nominal lift, plus the behaviour at the low and high ends of the cam's tolerance band (lift can drift between 6 mm and 11 mm across the cam's wear life).
Given
- hnom = 8 mm
- L = 120 mm
- Lout = 200 mm
- hlow = 6 mm
- hhigh = 11 mm
Solution
Step 1 — at nominal 8 mm lift, compute the follower angular displacement using the exact arc form:
Step 2 — convert that angular swing into linear stroke at the press pad, 200 mm out from the pivot:
This is the design-target stroke — enough to press the label firmly against the bottle without overtravel into the bottle wall. At the low end of the cam's wear band, hlow = 6 mm:
That is a 25% stroke loss. On a Canmatic, 10 mm is below the threshold where the press pad reliably contacts the label across the bottle's full curvature, and you'll see misaligned labels and edge lift on the trailing corner. At the high end, hhigh = 11 mm:
The pad is now overtravelling by nearly 5 mm relative to nominal. The follower spring compresses past its design preload, the roller starts skidding through the dwell, and within a few hundred thousand cycles you'll see flat-spotting on the roller and a measurable rise in noise.
Result
Nominal press-pad stroke is 13. 33 mm at 8 mm cam lift — the design value Krones intends for a 330 ml bottle's label window. Across the cam's wear and tolerance band, stroke ranges from 10.0 mm at 6 mm lift (labels misalign at the trailing edge) to 18.3 mm at 11 mm lift (roller skids, spring bottoms, noise rises). The sweet spot lives in a tight ±1 mm window around nominal. If you measure 11 mm of stroke instead of the predicted 13.3 mm, suspect three things in this order: pivot-bushing radial clearance opened past 0.05 mm and is eating angular travel as backlash; the follower arm has yielded slightly at the cam-side web, dropping effective L; or the cam itself has worn at the lift peak, which a quick dial-indicator check on the cam profile will confirm in under five minutes.
Choosing the Pivoted Follower: Pros and Cons
Pivoted followers are not the only way to convert cam lift to motion. Translating (sliding) followers and conjugate cam-and-rocker systems compete with them across speed, cost, and accuracy. Pick by the engineering dimension that drives your design.
| Property | Pivoted Follower | Translating Follower | Conjugate Cam Follower |
|---|---|---|---|
| Typical max speed (RPM) | 1,200-1,500 with spring close, 2,500+ force-closed | 600-900 limited by linear-guide friction | 3,000+ — desmodromic, no spring |
| Side-load handling | Excellent — pivot bearing absorbs side load | Poor — needs precision linear guide or bushing | Excellent — both cams constrain follower |
| Output motion type | Angular (arc) — direct rocker output | Linear (straight-line) | Angular or linear depending on layout |
| Position accuracy at output | ±0.05 mm typical at 200 mm arm | ±0.02 mm with ground guide | ±0.02 mm — no spring lift-off error |
| Cost per assembly (relative) | 1.0× (baseline) | 1.3-1.8× with precision guide | 2.5-3.5× — second cam, tighter tolerances |
| Maintenance interval (industrial) | 8,000-12,000 hr — pivot bushing relube | 2,000-4,000 hr — guide cleaning critical | 10,000+ hr — fully oil-bath enclosed |
| Best application fit | Valve trains, indexers, oscillating tools | Punch presses, low-speed feeders | High-speed packaging, racing engines |
Frequently Asked Questions About Pivoted Follower
You are seeing follower lift-off — the spring closing force can no longer accelerate the follower fast enough to track the cam's return ramp, so the roller leaves the cam surface near peak velocity and lands late. The arm bounces against the next cam segment instead of riding the profile, which truncates the effective lift seen at the output.
Quick diagnostic: put a dial indicator on the output and sweep RPM upward. If stroke is flat up to some critical RPM and then drops sharply with audible clatter, that is the lift-off threshold. Fix it by raising spring preload 15-25%, going to a stiffer spring, or moving to a conjugate (force-closed) cam if you need to run above ~1,500 RPM.
It is a force-vs-stroke trade. Output stroke scales linearly with Lout, and output force scales inversely. If you need 20 mm of stroke at 50 N, putting the link at 200 mm from the pivot gives you the stroke easily but cuts your available force. Move the link to 100 mm and you halve the stroke but double the force.
Rule of thumb — start with Lout set so that the required output stroke uses 60-70% of the available angular swing. That keeps you off the geometric limits where pressure angle climbs and gives headroom for cam wear without losing useful stroke.
Because the pivot bearing has to react every bit of side force the cam generates, and side force scales with tan(pressure angle). At 20° pressure angle you are reacting 36% of the cam's normal force as side load. At 35° it jumps to 70%. Past 40° the bearing load nearly equals the cam force itself, bushing wear accelerates, and the follower starts to chatter under transient loads.
Keep rise pressure angle below 30° and return below 35°. If your layout pushes past that, lengthen the arm, move the pivot further from the cam axis, or redesign the cam profile with a longer rise duration.
The most common cause is using the small-angle approximation θ ≈ h/L when you should be using the exact arc form θ = 2·arcsin(h/(2L)). For L/h ratios below 10 the difference is small but non-zero, and combined with manufacturing tolerance on L and h it can add up to 5-10%.
Second cause — the output point is not exactly perpendicular to the arm at mid-stroke. If your linkage geometry tilts the arm 5-10° off-vertical at mid-stroke, the projected linear stroke at the output is slightly longer than Lout × θ predicts. Re-measure with the arm at true mid-position before blaming the math.
Pick an arc tip when your cam has tight concave sections that no roller will fit into, when your speed is low enough (under 300 RPM typically) that sliding friction is acceptable, or when you need the cheapest possible follower for a high-volume disposable application. Arc tips are also more tolerant of contamination because there is no rolling element to skid or seize.
Roller followers win everywhere else. They handle higher speeds, higher contact stresses, and they extend cam life dramatically because the contact is rolling rather than sliding. The trade is roller cost, the minimum-radius constraint on cam concavities, and the need to keep spring preload high enough to prevent skidding.
The cam is fine — your wear is in the pivot bushing and roller bearing. A pivoted follower amplifies pivot clearance directly to the output: 0.05 mm radial play at the pivot becomes 0.083 mm of output drift at a 200/120 ratio, plus another 0.02-0.04 mm from roller-bearing internal clearance growing with mileage.
Diagnose by pulling the rocker and checking pivot-bushing radial clearance with a dial indicator before you touch the cam. Industrial spec is 0.02-0.05 mm; anything past 0.08 mm and the bushing is done. Replacing the bushing usually restores lash to within 0.02 mm of new-build values.
References & Further Reading
- Wikipedia contributors. Cam follower. Wikipedia
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