The Slotted Vibrating Bar to Horizontal Bar is a planar linkage that converts the angular oscillation of a slotted vibrating lever into the straight reciprocating motion of a horizontal bar through a sliding pin engaged in the slot. Franz Reuleaux catalogued the family in his 1875 Theoretische Kinematik des Getriebes as part of the slot-and-pin oscillating chain. The slotted arm rocks back and forth around a fixed pivot, the pin in the horizontal bar rides the slot, and the bar travels left and right along its guideway. You get clean reciprocating linear motion from a simple oscillating input — no cams, no cranks, no springs.
Slotted Vibrating Bar to Horizontal Bar Interactive Calculator
Vary pin radius, lever swing, cycle rate, and required clearance to see the horizontal bar stroke, travel speed, and clearance status.
Equation Used
The article stroke equation uses the horizontal projection of the follower pin radius. L_pin is the distance from the lever pivot to the pin center, theta_max is the lever half-swing, and S_out is the peak-to-peak horizontal bar travel. The speed output is derived from the same stroke by assuming the bar travels out and back once per cycle.
- Follower pin is at the effective radius L_pin from the lever pivot.
- theta_max is the half-angle of the lever oscillation from center.
- Stroke is peak-to-peak horizontal travel.
- Mean speed assumes one forward and one return stroke per cycle.
- Slot length, pin clearance, and guide stiffness are adequate to prevent end-stop impact or binding.
Inside the Slotted Vibrating Bar to Horizontal Bar
The Slotted Vibrating Bar to Horizontal Bar, also called the Vibrating slotted-arm to straight arm in older kinematics texts, runs on three moving parts: a slotted lever pivoted at one end, a horizontal bar constrained to slide on a linear guideway, and a follower pin fixed to the horizontal bar that rides inside the slot. When you rock the slotted lever through its arc — typically ±15° to ±30° in production builds — the slot sweeps the pin sideways. Because the pin is locked vertically to the horizontal bar's guideway, only the horizontal component of the slot's motion transfers. The bar reciprocates along its guide, and you get a near-linear output stroke from a rotational input.
The geometry matters more than people expect. If the slot length is shorter than the maximum horizontal projection of the pin's travel, the pin bottoms out at the slot ends and you'll hear a hard knock every cycle — usually accompanied by spalling on the slot end-stops within a few hundred thousand cycles. If the slot is too wide for the pin (typical clearance is 0.05 to 0.10 mm for a 6 mm pin in steel), backlash shows up as a dead band at stroke reversal, and the horizontal bar lags the lever by a measurable fraction of a millimeter. Pin wear is the dominant failure mode — the contact stress concentrates on a thin line where the pin meets the slot wall, and once the pin goes oval the output stroke shortens visibly.
The horizontal bar guideway tolerance is the other thing builders get wrong. A sloppy linear guide lets the bar wander vertically, which means the pin tilts in the slot, which means edge-loading on the slot wall. We size the guideway clearance at H7/g6 minimum for any build that needs to last past a million cycles.
Key Components
- Slotted Vibrating Lever: The driven oscillating arm, pivoted at one end, with a longitudinal slot machined along its length. Slot width typically matches the pin diameter +0.05 to +0.10 mm for a clean sliding fit. The lever oscillates through ±15° to ±30° depending on the required output stroke.
- Follower Pin: A hardened steel pin (often 58-62 HRC) fixed rigidly to the horizontal bar. It rides inside the slot and transfers motion. Pin diameter is sized for shear and contact stress — a 6 mm pin handles around 200 N peak side load before Hertzian contact fatigue becomes the limiter.
- Horizontal Bar: The output member, constrained to move only along the horizontal axis by its linear guideway. Travels back and forth as the pin is swept by the slot. Stroke length equals 2 × Lslot × sin(θmax) for small angles.
- Linear Guideway: Constrains the horizontal bar to a single translational degree of freedom. Tolerance class H7/g6 or better for million-cycle service. Loose guideways let the bar tilt, which edge-loads the pin and accelerates wear.
- Lever Pivot Bearing: A bushing or rolling-element bearing supporting the slotted lever's fixed pivot. Must handle reversing radial loads at the input torque. Bronze bushings work below 60 oscillations per minute; above that, needle bearings are the right call.
Real-World Applications of the Slotted Vibrating Bar to Horizontal Bar
The Slotted Vibrating Bar to Horizontal Bar shows up wherever a designer needs a simple oscillating input to drive a horizontal reciprocating output without resorting to a full slider-crank. The Vibrating slotted-arm to straight arm geometry is compact, tolerant of imprecise input timing, and cheap to fabricate from flat plate stock. You'll find it in textile machinery, paper handling, agricultural feeders, museum kinetic displays, and bench-top automation where build cost matters more than positional precision.
- Textile Machinery: Yarn guide reciprocators on Saurer Volkmann two-for-one twisters, where the slotted lever oscillates from a cam follower and drives a horizontal yarn guide bar across the package face.
- Bookbinding: Glue-roller wiper drives on Müller Martini Bolero perfect binders, using the slotted-arm geometry to traverse a doctor blade across the glue pot at 80 cycles per minute.
- Agricultural Equipment: Seed-cup reciprocators on John Deere 1775NT planters, converting the oscillation of a rocker arm into the lateral shake that meters seed delivery.
- Museum Kinetic Sculpture: Horizontal traverse drives in George Rhoads ball-machine sculptures at the Boston Museum of Science, where slow oscillating input drives a horizontal sweeper bar that redirects falling balls.
- Packaging Machinery: Tucker-blade drives on Bosch Pack 401 horizontal flow wrappers, where the slotted vibrating lever transmits cam motion to the horizontal tucker bar that folds film ends at 120 packs per minute.
- Printing Presses: Ink fountain agitator drives on Heidelberg GTO offset presses, where a slotted oscillating arm rocks a horizontal stirrer bar to keep ink viscosity uniform across the fountain length.
The Formula Behind the Slotted Vibrating Bar to Horizontal Bar
The output stroke of the horizontal bar is governed by the slot length, the pin's position along the slot, and the angular swing of the slotted lever. At the low end of the typical operating range — a small ±10° swing — you get a short, smooth stroke that barely loads the pin. At nominal ±20°, you hit the design sweet spot where the slot-to-pin contact stress stays below 400 MPa for a 6 mm hardened pin and the output stroke is large enough to be useful. Push past ±30° and the geometry's nonlinearity bites — the stroke per degree of input changes faster, the pin sees higher Hertzian contact stress at the slot ends, and you start wearing the slot into a dog-bone shape.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Sout | Total horizontal bar stroke (peak-to-peak) | mm | in |
| Lpin | Distance from lever pivot to follower pin centre | mm | in |
| θmax | Maximum half-angle of lever oscillation from centre | rad or ° | rad or ° |
Worked Example: Slotted Vibrating Bar to Horizontal Bar in a corrugated-board flute pacing bar
You are sizing the slotted vibrating arm that drives the horizontal pacing bar on a BHS Corrugated MF-A flute former at a packaging plant in Memphis Tennessee, where the bar reciprocates to stage 2.4 m wide medium webs into the corrugating roll nip at 22 cycles per minute. The pin sits 180 mm from the lever pivot, the slotted arm swings ±20° at nominal, and the pacing bar must clear the staging fence by no less than 60 mm and no more than 140 mm of stroke.
Given
- Lpin = 180 mm
- θmax (nominal) = 20 °
- θmax (low end) = 10 °
- θmax (high end) = 30 °
Solution
Step 1 — convert the nominal half-angle to its sine value, then compute the nominal peak-to-peak stroke:
That sits cleanly inside the 60-140 mm window — the pacing bar clears the staging fence with margin and isn't slamming into either end stop.
Step 2 — check the low end of the typical operating range at ±10° (the setting you'd use for a narrow 1.4 m web that needs less travel):
That's right at the 60 mm minimum clearance — any lower and the bar would foul the staging fence on a high-humidity day when the corrugated medium swells. Don't run below ±10° on this geometry.
Step 3 — check the high end at ±30°:
That blows past the 140 mm upper limit — the bar would overshoot the staging fence catch and either jam the next web or destroy the bar's end-of-stroke bumper. ±30° is mechanically achievable but operationally wrong for this machine.
Result
The nominal stroke is 123. 1 mm at ±20° — a comfortable middle of the operating window with 17 mm of safety margin to either limit. At ±10° you collapse to 62.5 mm, just barely above the fence-clearance floor; at ±30° you overshoot to 180 mm and crash the end-of-stroke. The sweet spot is clearly ±18° to ±22° for a 180 mm pin radius on this BHS line. If you measure an actual stroke shorter than 123 mm — say 110 mm — the most common causes are: (1) lever pivot bushing wear letting the lever droop and shifting the effective Lpin, (2) slot-to-pin clearance opened past 0.15 mm from wear, producing dead band at each reversal, or (3) the cam driving the slotted lever is timed off by a few degrees so the lever isn't reaching its full ±20° swing.
When to Use a Slotted Vibrating Bar to Horizontal Bar and When Not To
The Slotted Vibrating Bar to Horizontal Bar — sometimes catalogued as the Vibrating slotted-arm to straight arm — competes with two close alternatives whenever a designer needs oscillating input converted to horizontal linear output. A Scotch yoke gives you pure sinusoidal motion with no slot wear concern but needs continuous rotation at the input. A standard slider-crank gives the cleanest linear output for the smallest envelope but adds a connecting rod and two more pin joints. The choice comes down to input type, precision needed, and how long you need it to last.
| Property | Slotted Vibrating Bar to Horizontal Bar | Scotch Yoke | Slider-Crank |
|---|---|---|---|
| Typical operating speed | Up to 200 cycles/min before slot wear dominates | 500-1500 RPM continuous rotation input | 300-3000 RPM continuous rotation input |
| Output positional accuracy | ±0.2 mm typical due to slot/pin clearance | ±0.05 mm with precision yoke fit | ±0.02 mm with quality bearings |
| Input motion type required | Oscillating input only | Continuous rotary input only | Continuous rotary input only |
| Build cost (relative) | 1.0× baseline — flat-plate slot fabrication | 1.4× — yoke slot is a precision feature | 1.6× — connecting rod adds parts and joints |
| Service life before rebuild | 1-3 million cycles before slot oval | 10-20 million cycles | 20-50 million cycles |
| Best application fit | Slow-speed reciprocators driven from a cam or rocker | High-speed sinusoidal reciprocators (engines, pumps) | General-purpose reciprocating drives |
Frequently Asked Questions About Slotted Vibrating Bar to Horizontal Bar
Two things usually cause it. First, the follower pin's effective radius from the lever pivot may not be what you measured statically — under load, the slotted arm flexes slightly and the pin's swept arc shifts inward by a millimeter or two on a long lever. Second, if your linear guideway has any vertical play, the pin tilts in the slot under reversing load and the contact point migrates along the slot wall, eating effective stroke. Check the lever for spring with a dial indicator at full load, and re-shim the guideway to under 0.05 mm vertical clearance.
No — the input must oscillate. If you want continuous rotation as your prime mover, you need a crank-and-rocker or a cam-and-follower stage between the motor and the slotted lever to produce the oscillation. People try to coupling a motor straight to the lever pivot through a reversing drive and it never lasts: the reversal shock destroys the motor coupling within weeks. Use a Scotch yoke instead if you've got rotary input — that's exactly what the Scotch yoke is for.
For oscillation rates under about 60 cycles per minute, a plain hardened pin (58-62 HRC, ground finish to Ra 0.2 µm) running in a lubricated slot is cheaper and lasts adequately. Above 60 cycles per minute, the sliding velocity at the slot wall starts to generate enough heat to break down the lubricant film and you'll see galling within months. Switch to a needle-bearing roller follower above that threshold — it pays for itself inside the first year of service.
The pin's position along the slot at any lever angle is Lpin / cos(θ). At θmax = 20° the pin sits at Lpin / 0.9397 = 1.064 × Lpin from the pivot, so a 180 mm nominal pin radius means the slot must extend to at least 192 mm from the pivot. Add 10 mm of margin past that and you're safe. Bottoming out is what produces that hard knocking sound at end-of-stroke and chips the slot end inside a few hundred thousand cycles.
That pause is dwell from accumulated backlash. Slot-to-pin clearance plus guideway play plus pivot bushing slop all add up — when the lever reverses direction, the pin has to travel across all that combined clearance before it re-engages the opposite slot wall and the bar starts moving again. On a build that's been running a year or two, total dwell can hit 0.5 mm of bar travel at each reversal. Measure your slot width with a pin gauge and replace the pin if clearance has opened past 0.15 mm.
Yes — same mechanism, two names. Older kinematics references (Reuleaux, Kennedy, Hartenberg-Denavit) tend to call it the Vibrating slotted-arm to straight arm. Modern automation catalogues call it the Slotted Vibrating Bar to Horizontal Bar. Both describe a slotted oscillating lever transmitting motion through a slot-and-pin pair to a horizontally constrained output bar. If you're searching old textile-machinery patents you'll see the older term; in current packaging-machinery documentation you'll see the newer one.
References & Further Reading
- Wikipedia contributors. Linkage (mechanical). Wikipedia
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