A slider-crank reversing mechanism converts continuous rotary input from a crank into back-and-forth linear motion of a slider, automatically reversing direction at each end of the stroke. You see it in every internal combustion engine piston, but in reverse — and in metal shaper machines like the South Bend 7-inch shaper, where it drives the cutting ram. The crank rotates one way, the slider has no choice but to reciprocate, swapping direction twice per revolution. That's the value: zero clutches, zero shifters, mechanical reversal built into the geometry.
Slider-crank Reversing Interactive Calculator
Vary connecting rod ratio and crank angle to see normalized slider position, travel, stroke, and reversal behavior.
Equation Used
The calculator uses the standard in-line slider-crank position equation normalized by crank radius R. With R = 1, the slider stroke is always 2R, while the connecting rod ratio L/R changes the detailed position curve between TDC and BDC.
- In-line slider-crank with no offset between crank center and slider guide.
- Crank radius is normalized to R = 1, so distances are reported as multiples of R.
- Rigid links and ideal pin joints with no clearance, runout, or elastic deflection.
- Theta increases clockwise from TDC at 0 deg to BDC at 180 deg.
How the Slider-crank Reversing Actually Works
The slider-crank is four parts pretending to be three: a rotating crank, a connecting rod, a slider running in a fixed guide, and the ground frame holding it all in line. As the crank turns through a full 360°, the wrist pin (where the connecting rod meets the slider) traces a path that's bounded — it can only travel along the slider's guide axis. That's the entire trick. Continuous rotation in, forced reciprocation out, with direction reversal happening automatically at top dead centre (TDC) and bottom dead centre (BDC).
The slider's motion isn't pure sine. Because the connecting rod is finite length, the slider accelerates harder on the crank-side half of the stroke than on the far side. We call this the connecting rod ratio — L/R, where L is rod length and R is crank radius. A typical engine sits around L/R = 3.5 to 4. Drop below 3 and the second-order acceleration term gets ugly… you'll feel vibration and the slider will hammer the guide bushings. Push above 5 and the linkage gets long and floppy with no real benefit.
If your stroke is wrong by more than ±0.5 mm on a precision build, the most common cause is crank-pin runout or a bent connecting rod — not assembly error. The reversal points are where wear shows up first, because slider velocity hits zero there and side-load from the connecting rod angle peaks. You'll hear it as a tick at each end of travel before you measure it.
Key Components
- Crank: The rotating member, fixed to the input shaft. Crank radius R sets exactly half the stroke length — stroke = 2R. Crank-pin runout must stay under 0.05 mm for smooth running on machine-tool builds; above that you'll feel the slider chatter at the reversal points.
- Connecting Rod: Links the crank pin to the slider wrist pin. Its length L controls how closely slider motion approximates a pure sinusoid. Aim for L/R between 3.5 and 4.5; running L/R below 3 doubles the secondary acceleration term and beats up the slider guide.
- Slider (Crosshead or Piston): Constrained to translate along a single axis by the guide. Carries the output load. Side clearance in the guide should be 0.02 to 0.05 mm on a 25 mm slider — tighter and it galls under thermal expansion, looser and the slider knocks at TDC and BDC.
- Slider Guide (Frame): The fixed prismatic pair. Hardened and ground for any application above 100 cycles per minute. Parallelism to the crank rotation axis must be within 0.1 mm over the full stroke length, or you'll see uneven wear stripes within 200 hours of running.
- Pivot Bearings: Two are needed: crank-pin bearing and wrist-pin bearing. Needle rollers for high-speed engine work, bronze bushings for slow industrial reversers. Radial play above 0.08 mm at the wrist pin shows up as audible knock at each stroke reversal.
Where the Slider-crank Reversing Is Used
The slider-crank is everywhere because it's the simplest mechanism that turns rotation into reversing linear motion without any external trigger, sensor, or control logic. Every reversal is geometric — it cannot fail to reverse as long as the crank keeps turning. That makes it the default choice for any machine that needs an output that goes out, comes back, out, comes back, all day, with no fuss. The catch is that velocity isn't constant across the stroke, so it's a poor fit when you need uniform feed rate or constant cutting speed across the work.
- Machine Tools: Cutting ram drive on metal shaper machines such as the South Bend 7-inch shaper and Atlas-Craftsman 7B — crank rotates continuously while the ram reciprocates the cutting tool across the workpiece.
- Internal Combustion Engines: Used inverted in every Cummins ISX, Honda K20, and Briggs & Stratton small engine — combustion drives the piston, slider-crank converts that linear motion into shaft rotation.
- Reciprocating Compressors: Atlas Copco LE-series air compressors use a slider-crank to drive the piston in the compression cylinder at 1450 RPM.
- Sewing Machines: Needle bar drive in Juki DDL-8700 industrial lockstitch machines — crank-slider lifts and lowers the needle 4000 to 5500 times per minute.
- Punch Presses: Drive on small mechanical presses like the Bliss C-22 — flywheel-driven crank pushes the ram down through stock and back up automatically.
- Pumps: Reciprocating mud pumps such as the Gardner Denver PZ-series triplex pumps used in oilfield drilling — three slider-crank assemblies running 120° apart move drilling fluid downhole.
The Formula Behind the Slider-crank Reversing
The slider position equation tells you exactly where the slider sits at any crank angle θ, measured from TDC. This matters because it lets you predict velocity and acceleration profiles before you cut metal. At small crank angles (near TDC) the slider barely moves — the first 30° of crank rotation moves the slider only about 13% of the stroke. Near 90° crank angle you hit peak slider velocity. Past 180° (BDC) the motion mirrors back. The sweet spot for a balanced design is L/R ≈ 4, where peak acceleration sits around 1.25 × R × ω². Drop L/R toward 3 and that peak climbs past 1.33 × R × ω², which is when bushing life starts dropping fast.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| x | Slider position measured from crank centre, along the slider axis | m | in |
| R | Crank radius (half the stroke length) | m | in |
| L | Connecting rod length (pin centre to pin centre) | m | in |
| θ | Crank angle measured from TDC | rad | rad |
| ω | Crank angular velocity | rad/s | rad/s |
Worked Example: Slider-crank Reversing in a benchtop CNC peck-drill ram
You are sizing the slider-crank drive for a benchtop peck-drilling head being built into a small electronics-board depaneling rig at a contract assembler in Penang. The drill needs a 40 mm vertical stroke, runs at a nominal 90 RPM crank speed, and you want to predict slider velocity at mid-stroke to size the spindle motor and check that chip evacuation has time to clear between pecks. You have selected R = 20 mm and L = 80 mm (L/R = 4).
Given
- R = 20 mm
- L = 80 mm
- Stroke = 40 mm
- N (nominal) = 90 RPM
- θ (peak velocity) = ≈ 78 °
Solution
Step 1 — at nominal 90 RPM, convert crank speed to angular velocity:
Step 2 — peak slider velocity occurs near θ = 78° for L/R = 4. The standard approximation for peak velocity in a slider-crank is:
That's the nominal peak — about 212 mm/s at mid-stroke. The drill spindle sees this as the feed rate at the moment of deepest engagement, so chip load calculations need to use this number, not the average stroke speed.
Step 3 — at the low end of the practical operating range, 45 RPM (when you're pecking through fibreglass-reinforced PCB and want a slow controlled feed):
At 106 mm/s the drill enters the work gently — you can hear each peck individually and chip evacuation has plenty of time. Push to the high end at 180 RPM for fast pecking through soft FR1:
424 mm/s is theoretical — in practice above ~150 RPM the slider-crank's asymmetric acceleration starts loading the wrist pin hard at TDC, and on a benchtop build with bronze bushings you'll see audible knock and bushing wear within 50 hours. The sweet spot for this geometry is 80 to 120 RPM.
Result
Nominal peak slider velocity is 0. 212 m/s (212 mm/s) at 90 RPM. That's the speed the drill bit hits the PCB at mid-stroke, and it's the number to feed into your chip-load calculation — not the average. Across the operating range, slider peak velocity scales linearly with crank speed: 106 mm/s at 45 RPM feels controlled and slow, 212 mm/s at 90 RPM is the design sweet spot, and 424 mm/s at 180 RPM is where the geometry starts fighting you. If your measured peak velocity is more than 10% off prediction, check first for connecting rod length error — a rod made 2 mm short on an 80 mm spec changes L/R from 4 to 3.75 and shifts peak velocity timing by 3°. Second, look for crank-pin eccentricity from a worn keyway, which lets the effective R drift and shows up as stroke length not matching the spec. Third, on slow builds, slider-guide friction from misaligned guide rails will cap velocity below prediction without any geometric cause — check rail parallelism with a dial indicator before blaming the linkage.
Choosing the Slider-crank Reversing: Pros and Cons
Slider-crank reversing is the default, but it isn't always the right call. Two real alternatives compete in this space: the Scotch yoke, which gives true sinusoidal motion, and the rack-and-pinion with a reversing gearbox, which gives constant velocity at the cost of complexity. Pick based on what your output needs to do, not on which is theoretically elegant.
| Property | Slider-Crank Reversing | Scotch Yoke | Rack-and-Pinion with Reversing Drive |
|---|---|---|---|
| Typical operating speed | Up to 6000 RPM in engine duty, 60-300 RPM in industrial reversers | Up to 1500 RPM, limited by yoke side-loading | Up to 200 RPM, limited by reversal shock |
| Slider motion profile | Asymmetric — faster on one half stroke than the other | Pure sinusoidal (symmetric) | Constant velocity with sharp reversal |
| Cost (small-machine build) | Low — 4 parts, standard bearings | Medium — yoke slot needs precision grinding | High — gearbox plus reversing clutch or servo |
| Reliability and lifespan | 20,000+ hours with standard bushings | 8,000-15,000 hours, yoke slot wears | Depends on reversing element — often the weak link |
| Stroke-to-package ratio | Stroke = 2R, needs roughly 4R+L envelope | Stroke = 2R, more compact than slider-crank | Stroke is unbounded by mechanism geometry |
| Best application fit | Engines, compressors, presses, shapers | Steam pumps, valve actuators, pure sinusoid needed | Linear stages needing constant feed rate |
Frequently Asked Questions About Slider-crank Reversing
Stroke is geometrically symmetric about the crank centreline only if the slider axis passes exactly through the crank rotation axis. If your slider guide is offset from the crank centre — even by 1-2 mm — you've built an offset slider-crank, which deliberately makes the forward and return strokes different lengths and times. This is sometimes called a quick-return mechanism.
Check guide-rail centring with the crank at 90° and 270°: the slider position at those two points should be identical. If they differ, your guide rail is offset and you need to shim it back to the crank centreline.
The full slider acceleration equation has two terms: a primary term (R × ω² × cos θ) and a secondary term ((R²/L) × ω² × cos 2θ). At TDC both terms add together, giving peak acceleration of approximately R × ω² × (1 + R/L). If you sized the bushings using only the primary term, you under-spec'd the wrist pin load by 25% on an L/R = 4 build.
The fix is either lengthen the connecting rod (raises L/R, shrinks the secondary term) or de-rate the maximum operating speed.
For a compressor under 5 kW, slider-crank wins on bearing life and cost. The Scotch yoke gives sinusoidal motion which is smoother in theory, but the yoke slot carries side-load directly across a sliding surface — it wears measurably within a few thousand hours, and replacing it means scrapping the yoke. The slider-crank distributes load across two rolling-element bearings that you can replace as service items.
Choose Scotch yoke only when you genuinely need sinusoidal motion (some valve and metering applications) or when package length matters more than service life.
Almost always thermal clearance. The slider guide and slider were ground at room temperature, but at running temperature the slider expands more than the guide (especially aluminium slider in a steel guide). If your cold clearance was at the loose end of spec — say 0.05 mm — running clearance can hit 0.1 mm or more, and the slider rocks slightly at each reversal where velocity goes through zero.
Measure clearance hot, not cold. Tighten cold clearance to 0.02-0.03 mm if you've got significant thermal differential between slider and guide materials.
Set R first from your stroke requirement (R = stroke / 2), then make L as long as the envelope allows up to L/R = 4.5. Going beyond 4.5 buys almost nothing — the secondary acceleration term is already small and you're just adding mass and column-buckling risk. Going below L/R = 3 is where things get bad fast: secondary acceleration grows non-linearly, side load on the slider guide climbs, and you'll see scuffing and bushing wear inside 500 hours on continuous duty.
If the envelope forces L/R below 3, switch to a Scotch yoke or redesign the package.
Textbook examples assume infinite connecting rod length (L/R → ∞), which makes the slider motion pure sinusoidal and puts peak velocity at exactly 90°. On any real build with finite L, the asymmetry shifts peak velocity to a crank angle below 90° on the way down and above 270° on the way up. For L/R = 4 the peak is around 78°; for L/R = 3 it shifts to about 73°.
This matters for instrumented machines where you trigger off crank angle — assuming 90° will put your trigger event 12° late at L/R = 4. Use the exact derivative of the position equation, or look it up against your actual L/R.
References & Further Reading
- Wikipedia contributors. Slider-crank linkage. Wikipedia
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