Rectilinear Vibrating Motion Mechanism: How It Works, Scotch Yoke Diagram, Formula and Uses

How the Scotch yoke works

The crank turns about a fixed center. Its offset pin moves up and down inside the vertical slot while pushing the yoke and attached slider horizontally. The guide prevents the slider from following the vertical part of the pin’s circular path.

The slider position follows the horizontal projection of the crank radius: x = e cos(θ). It moves from +e to −e and back during one crank revolution. It stops momentarily at each end of the stroke and reaches its greatest speed as it passes the middle position.

Comparing reciprocating motion

Use this example to compare the travel and rate of an ideal crank-driven slider. Increasing eccentricity increases both stroke and peak speed at a fixed RPM. Increasing RPM raises frequency and peak speed without changing the stroke.

The calculation can help define a desired motion before selecting hardware. It does not size a motor, pin, yoke or guide, or predict the performance of a complete feeder or vibrating machine.

Stroke, frequency and peak speed

Let e be eccentricity, theta the crank angle and f the rotational frequency. The displacement from the middle position is x = e cos(theta), the peak-to-peak stroke is S = 2e and f = rpm/60.

For ideal sinusoidal motion, peak speed is v_max = 2 pi f e. Use e in metres to obtain speed in m/s; the calculator converts the entered millimetres to metres.

Worked example

At 3 mm eccentricity and 1800 rpm, amplitude is 3 mm and peak-to-peak stroke is 6 mm. The slider position ranges from −3 to +3 mm. Frequency is 30 Hz and ideal peak slider speed is approximately 0.565 m/s. The animation runs more slowly so the movement is visible.

From motion to hardware

The equations assume a rigid crank, yoke and guide with the pin always engaged in the slot. Real clearance and deflection affect the motion, and sliding contact in the slot needs suitable materials and lubrication.

Check the moving mass, drive force, pin and guide loads, balance, stiffness and damping before choosing an operating speed. The two inputs here cannot predict resonance, wear, fatigue or bearing life.

The diagram is schematic, and playback is slowed and capped for viewing. Use the numerical results for travel, frequency and peak speed; do not time the animation to estimate machine speed.

Scotch-yoke motion questions

What is the difference between amplitude and stroke?

Amplitude is the largest displacement from the middle position and equals eccentricity e. Stroke is the full distance between the two extremes, so it equals 2e.

What changes when shaft speed increases?

Cycle frequency and peak slider speed increase in proportion to RPM. Amplitude and stroke stay unchanged because they depend on eccentricity.

Why does the animation run more slowly than the entered RPM?

Playback is slowed and capped so the mechanism remains visible. It illustrates the sequence of positions, not the real-time cycle rate. Use the frequency result for the calculated cycles per second.

What happens at zero shaft speed?

Cycle frequency and peak speed are zero, and the drawing holds at its starting position. Amplitude and stroke still describe the travel available if the crank were rotated.

Does this calculate feeder throughput?

No. It describes the motion of a crank-driven slider. Material transport depends on the feeder, track, parts, friction and motion of the complete machine.

Does the RPM input check resonance or bearing life?

No. Those checks require loads, moving mass, stiffness, damping, bearings and operating conditions. The entered RPM is a calculation input, not an approved operating speed.