A yoke-bar reciprocator from a disk crank is a slider-crank variant where a crankpin on a rotating disk rides inside a transverse slot cut into a sliding bar — the yoke — converting rotation directly into pure sinusoidal linear motion. Because the crankpin is fully captive in the slot, the yoke moves as x = R × cos(θ) with no connecting rod and no angular swing. We use it where compact stroke control, true harmonic motion, and zero side-thrust on the slider matter — driving compressor pistons, test rigs, and metering pumps where 50-300 RPM operation is typical.
Yoke-bar Reciprocator From Disk Crank Interactive Calculator
Vary crank radius, crank angle, and speed to see yoke displacement, stroke, velocity, and acceleration for pure sinusoidal Scotch-yoke motion.
Equation Used
The disk crank pin has horizontal position R cos(theta). Because the yoke slot only permits linear guide motion, the yoke displacement is x = R cos(theta). Differentiating with constant angular speed gives velocity v = -R omega sin(theta) and acceleration a = -R omega^2 cos(theta).
- Crank angle theta is measured clockwise from the +R position.
- The yoke is rigid and constrained to pure linear sliding motion.
- Friction, clearance, pin compliance, and guide deflection are neglected.
- Speed is constant during the evaluated crank angle.
Inside the Yoke-bar Reciprocator From Disk Crank
The mechanism is sometimes called a Scotch yoke, and the geometry is brutally simple. A flat disk spins on a fixed axis. A hardened crankpin pressed into the disk at radius R engages a transverse slot machined into a bar — the yoke — which is constrained to slide along one axis by linear guides or gibs. As the disk rotates, the crankpin sweeps a circle, but the slot only cares about the horizontal component of the pin's position. The yoke therefore moves with displacement x = R × cos(θ), velocity v = -R × ω × sin(θ), and acceleration a = -R × ω² × cos(θ). Pure sinusoidal motion. No connecting-rod second-harmonic distortion like you get from a standard slider-crank.
The slot width is the spec everybody gets wrong. The crankpin diameter and the slot width must run a sliding fit on the order of H7/g6 — typically 20-40 µm clearance for a 12-20 mm pin. Open it up to 100 µm and you'll hear the pin hammering at top and bottom dead centre as the contact face flips. Tighten it under 10 µm and the pin galls inside an hour at 200 RPM because there's nowhere for the lubricant film to live. The slot faces themselves need to be ground parallel within 0.02 mm over the full slot length, otherwise the yoke develops a cocking moment that the linear guides have to absorb — and that's how you destroy a guide rail.
Failure modes are predictable. Slot wear shows up first as elongation in the direction of slider travel, since the pin pushes hardest at θ = 90° and 270°. You'll see asymmetric wear if the disk rotation is unidirectional. The crankpin bushing or needle bearing fails next — peak side load on that pin is F = m × R × ω², and at high RPM with a heavy yoke that number climbs fast. If you skip the bearing and run a hardened pin in a bronze-lined slot, plan to replace the slot insert every 2-5 million cycles depending on load.
Key Components
- Drive Disk: A balanced steel or cast-iron disk carrying the crankpin at radius R. Disk runout must be held under 0.05 mm TIR or you'll modulate the stroke length cycle-to-cycle. We typically size the disk diameter at 2.5 × R minimum to leave material around the pin bore.
- Crankpin: A hardened, ground pin (60 HRC, surface finish Ra ≤ 0.2 µm) press-fit into the disk. The pin engages the yoke slot through either a needle roller bearing or a bronze sliding bushing. Pin diameter sets the side-load capacity directly.
- Yoke Bar: The sliding output member with the transverse slot. Slot length must exceed 2R + pin diameter + 2 mm clearance, otherwise the pin bottoms out at top and bottom dead centre. Slot face hardness should match or exceed the pin/bushing for predictable wear.
- Linear Guides: Recirculating ball rails or hardened flat gibs constraining the yoke to single-axis motion. Guide spacing should straddle the slot — never put both guides on one side of the crankpin engagement, or the yoke will pitch under load.
- Crankshaft Bearings: The disk shaft runs in two spaced bearings. Span between bearings should be at least 1.5 × disk diameter to keep deflection under load below 0.01 mm at the crankpin radius.
Who Uses the Yoke-bar Reciprocator From Disk Crank
You see this mechanism wherever a machine needs reciprocating linear motion that is genuinely harmonic — meaning the velocity and acceleration profiles are clean sine and cosine curves with no second-harmonic component. That matters for vibration control, balanced inertia, and predictable seal life. It also wins on packaging because the yoke is shorter than a connecting-rod assembly delivering the same stroke.
- Refrigeration Compressors: Tecumseh and Embraco hermetic compressors have used Scotch-yoke pistons in select model lines because the pure sinusoidal piston motion reduces noise compared to a slider-crank running the same stroke.
- Oilfield Pumping: Gardner Denver duplex mud pump test rigs use yoke-driven plungers to deliver controlled sinusoidal flow profiles for valve and seal qualification.
- Automotive Seat Testing: Instron and MTS durability rigs drive seat-cushion fatigue test platens via yoke reciprocators when the spec calls for a verified sinusoidal displacement waveform.
- Naval Steam Engines: The Bourke engine and several early submarine torpedo engines used Scotch-yoke pistons to eliminate piston side-thrust and shorten the engine envelope inside hull constraints.
- Pharmaceutical Metering: Watson-Marlow and Quattroflow piston-style metering pumps adopt yoke drives where the dosing accuracy depends on a repeatable harmonic flow waveform rather than the asymmetric pulse of a slider-crank.
- Materials Testing: Zwick/Roell low-frequency fatigue rigs use disk-and-yoke drives at 0.5-5 Hz to apply pure cosine-displacement loading to specimens.
The Formula Behind the Yoke-bar Reciprocator From Disk Crank
The displacement of the yoke from disk rotation gives you stroke, peak velocity, and peak acceleration directly — and these three numbers determine whether your design lives or dies. At the low end of the typical 50-300 RPM operating range, peak acceleration is low enough that bearing loads are dominated by the working force on the slider. At the high end, inertia force on the yoke mass overtakes the working load and becomes the design driver. The sweet spot for most industrial yoke reciprocators sits between 100-200 RPM, where you get useful throughput without the crankpin side-load climbing into bearing-killing territory.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| x(θ) | Yoke displacement from centre at crank angle θ | m | in |
| R | Crankpin radius from disk centre (half the total stroke) | m | in |
| θ | Crank angle measured from horizontal | rad | deg |
| ω | Angular velocity of the disk | rad/s | rad/s |
| vmax | Peak linear velocity of the yoke (occurs at θ = 90°, 270°) | m/s | in/s |
| amax | Peak linear acceleration of the yoke (occurs at θ = 0°, 180°) | m/s² | in/s² |
| Fpin | Peak inertial side load on the crankpin from yoke mass | N | lbf |
| myoke | Combined mass of yoke and any rigidly attached slider/piston | kg | lb |
Worked Example: Yoke-bar Reciprocator From Disk Crank in a low-frequency soil shear test rig
You are sizing the disk-and-yoke drive that produces sinusoidal axial displacement on a Wille Geotechnik DSA-28 cyclic direct-shear apparatus being commissioned at a geotechnical lab in Trondheim. The rig must deliver a 25 mm peak-to-peak stroke (R = 12.5 mm) on a yoke-and-platen assembly weighing 4.2 kg, running at frequencies between 0.5 Hz (30 RPM) and 5 Hz (300 RPM), with a nominal test frequency of 2 Hz (120 RPM). You need peak velocity, peak acceleration, and peak crankpin side load at all three operating points before specifying the crankpin bearing.
Given
- R = 0.0125 m
- myoke = 4.2 kg
- Nnom = 120 RPM
- Nlow = 30 RPM
- Nhigh = 300 RPM
Solution
Step 1 — convert the nominal 120 RPM into angular velocity:
Step 2 — peak velocity and peak acceleration at nominal:
Step 3 — peak crankpin inertial side load at nominal:
At 2 Hz the rig is well inside its sweet spot — 8.3 N on the crankpin bearing is a non-issue for any decent needle roller, and the platen tracks the cosine waveform cleanly enough that a Trondheim soil specimen sees a textbook sinusoidal shear cycle.
Step 4 — at the low end of the typical operating range, 30 RPM (0.5 Hz):
At 0.5 Hz inertia is essentially negligible — the only load on the pin is the soil reaction force coming back through the platen. The bearing selection at this end is governed entirely by the working load, not the dynamics.
Step 5 — at the high end, 300 RPM (5 Hz):
That's a 6.2× jump in pin load over nominal for only a 2.5× jump in speed — because inertial force scales with ω². At 5 Hz you'll start hearing slot-face chatter on any clearance above 60 µm, and a marginally undersized pin bearing that survived 2 Hz testing will fail within weeks.
Result
At nominal 2 Hz the yoke delivers 0. 157 m/s peak velocity, 1.97 m/s² peak acceleration, and an 8.3 N peak crankpin side load — comfortable territory where the rig will run for years on a standard needle bearing. The range is brutal though: pin load climbs from 0.52 N at 0.5 Hz to 51.8 N at 5 Hz, so the high end of the spec is what sizes the bearing, not the average duty cycle. If your measured displacement waveform looks distorted instead of pure cosine, check three things in this order: (1) yoke-slot clearance opened beyond 60 µm letting the pin lift off mid-cycle and slap on reversal, (2) linear guide preload lost on one side causing the yoke to yaw and clip the slot face at TDC, or (3) disk-shaft bearing radial play above 0.02 mm modulating R cycle-to-cycle and producing visible sidebands on a frequency-domain plot of the output position.
When to Use a Yoke-bar Reciprocator From Disk Crank and When Not To
The yoke reciprocator competes head-to-head with the conventional slider-crank and the cam-and-follower. Each one wins on a different axis. Pick the one that matches your dominant constraint — waveform purity, packaging, cost, or stroke flexibility.
| Property | Yoke-bar reciprocator (Scotch yoke) | Conventional slider-crank with connecting rod | Cam-and-follower reciprocator |
|---|---|---|---|
| Output waveform purity | Pure cosine, zero second-harmonic content | Asymmetric — second-harmonic distortion grows as L/R drops below 4 | Arbitrary — defined by cam profile |
| Typical operating speed | 50-300 RPM industrial; up to 1500 RPM in compressors | 100-6000 RPM (automotive engines reach 8000+) | 10-1200 RPM depending on follower dynamics |
| Side load on slider | Zero — yoke runs on its own guides | Significant piston side-thrust, scales with rod angle | Zero on slider; high contact stress at cam-follower interface |
| Stroke length flexibility | Fixed by R; change requires new disk | Fixed by R; change requires new crankshaft | Programmable via cam swap |
| Packaging length per unit stroke | Compact — roughly 2R + slot length | Long — needs 4-5R for the connecting rod | Compact but tall — needs follower clearance |
| Cost and manufacturability | Moderate — slot grinding is the cost driver | Low — mass-produced part ecosystem | High — cam profile machining and grinding |
| Typical lifespan to slot/bearing rebuild | 2-10 million cycles depending on lubrication | 10-100+ million cycles | 5-20 million cycles (cam wear limited) |
| Best application fit | Test rigs, metering pumps, low-noise compressors | IC engines, general reciprocating machinery | Indexing, dwell-required motion, custom profiles |
Frequently Asked Questions About Yoke-bar Reciprocator From Disk Crank
Pure sinusoidal motion of the yoke does not mean a vibration-free machine — the yoke mass still produces an unbalanced reciprocating inertia force F = m × R × ω² acting along the slider axis. A standard slider-crank can use a counterweight on the crank web to cancel roughly half this primary force. A Scotch yoke cannot, because there is no connecting-rod offset to exploit — a counterweight on the disk creates an equal and opposite rotating force in the perpendicular axis, which is just as bad.
The fix is either a balance shaft running counter-rotating with a sliding mass, or a twin opposed-yoke layout where two yokes 180° apart cancel each other's primary inertia. If you only have one yoke and you've added a disk counterweight, remove it — you're trading one vibration axis for another.
Pick the yoke when waveform purity matters more than RPM ceiling. If your dosing accuracy or flow-pulse spec depends on a verified sinusoidal piston velocity — pharmaceutical metering, hydraulic pulsation testing, controlled-dispersion mixing — the yoke gives you that for free. A slider-crank with L/R = 4 distorts the velocity curve by roughly 12% at TDC, and getting that down means a longer connecting rod and a longer machine.
Pick the slider-crank when you need 1500+ RPM, when packaging length is not constrained, or when cost per unit dominates the decision. The connecting-rod ecosystem is mature and cheap. Slot-yoke parts are not.
Run the rig at 30% of normal speed and listen. Slot-clearance knock changes character with speed because it depends on the inertia reversal at TDC — at low RPM the knock fades and may disappear entirely below ~20% of nominal speed. Crankpin bearing knock is roughly speed-independent in character because the working load is still fully present.
Confirm with a dial indicator on the yoke at TDC: rock the disk through ±5° of TDC by hand and read backlash. If you see more than 80 µm of yoke movement before the disk starts turning, that's slot wear. If the yoke moves with the disk but you hear a click inside the disk hub, that's the pin bearing.
Asymmetric slot heating means asymmetric loading, and on a unidirectional yoke drive that's actually expected to a degree — the leading face of the slot takes the inertia load on one half of the cycle and the trailing face takes it on the other. But if the temperature delta between faces exceeds about 15°C in steady state, you have a problem.
The usual cause is a yoke that is not centred on its linear guides — the yoke is yawing slightly, so the pin contacts one slot face along its full length and the other only at one edge. Check guide-rail parallelism to the disk shaft axis to within 0.05 mm over the yoke length. The second possibility is a bent or canted crankpin, which loads the bushing on one end face only — pull the disk and check the pin perpendicularity to the disk face with a square.
For a rigid, well-machined yoke the deviation from x = R × cos(θ) should be under 0.1% of stroke, which on a 25 mm stroke is 25 µm. If you're seeing larger deviation in the measured waveform there are three real causes: yoke-slot clearance contributing a small flat region near TDC and BDC where the pin is briefly unloaded; flex in the yoke bar itself if it is undersized — a yoke deflecting 50 µm under inertia load adds visible distortion; and disk shaft runout, which adds a once-per-revolution sinusoid out of phase with the main motion.
The flat-spot signature near TDC and BDC is the most common and the most useful diagnostic — it tells you exactly how much slot clearance you have without disassembly.
You can — and it has been done — but you're now building a cam mechanism in disguise, and you've lost most of the reasons to choose a yoke in the first place. A curved slot turns the disk-and-yoke into a face cam where the crankpin is the follower. The motion is no longer pure cosine, manufacturing cost goes up significantly because the slot now needs profile grinding instead of straight slot grinding, and slot-face contact stress concentrates at the curvature changes.
If you need a custom waveform, build a proper cam-and-follower mechanism with a roller follower — it'll be cheaper to manufacture, easier to lubricate, and longer-lived than a curved-slot yoke trying to do the same job.
References & Further Reading
- Wikipedia contributors. Scotch yoke. Wikipedia
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