A rotating eccentric disc slides transversely inside an elongated yoke, producing sinusoidal straight-line rod motion. The slot accommodates the vertical component of the disc-center orbit while guides constrain the rod horizontally.
Elongated-Yoke Eccentric Geometry Calculator
Enter eccentricity, disc diameter and shaft speed. The worksheet reports ideal rod stroke, minimum internal slot height for the transverse orbit, maximum rod speed and maximum rod acceleration. It does not predict dwell, clearance, bearing load or service limits.
Equation Used
- The eccentric center follows a circular orbit of radius e at constant angular speed.
- The yoke is perfectly constrained to horizontal translation and the disc slides without clearance in slot width.
- Minimum internal slot height spans disc diameter plus the full transverse center orbit.
- Friction, lubrication, contact stress, dynamic load, clearance, wear and strength are excluded.
Eccentricity sets half the rod stroke. Disc diameter and the transverse orbit determine the ideal minimum slot height, while shaft speed determines peak ideal velocity and acceleration.
An eccentric disc inside a transversely elongated yoke
The shaft drives a disc whose geometric center is offset by eccentricity e. The disc center follows a circle. Its horizontal component moves the guided yoke and rod; its vertical component is absorbed by sliding within the elongated slot.
The resulting ideal rod law is sinusoidal. The historical source identifies the elongated yoke as a way to avoid vibrating motion of the rod, not as a dwell generator.
Straight guided eccentric motion
The geometry is applicable where a rotary eccentric must drive a rod constrained to one line. Real valve or pump design must add bearing, lubrication, clearance, load and speed analysis.
Exact ideal kinematics
Geometry example
With 15 mm eccentricity and a 50 mm disc, ideal rod stroke is 30 mm and minimum internal slot height is 80 mm. At 120 rpm, maximum ideal rod speed is 188.5 mm/s and maximum ideal acceleration is 2369 mm/s².
Straight-line motion and the role of the slot
Movement 90 in Henry T. Brown's Mechanical Movements describes an elongated yoke replacing the circular eccentric strap so the rod can move in fixed guides. In this ideal close-fitting geometry the rod moves sinusoidally; it has zero velocity only momentarily at each reversal, without a finite dwell.
Elongated-yoke questions
Does the historical mechanism create dwell?
No dwell is established by the cited source or this ideal geometry.
Why is the slot elongated?
To absorb the transverse component of the eccentric disc center orbit while the rod stays in straight guides.
Is D+2e a manufacturing dimension?
No; it is an ideal minimum before clearance and tolerance.
Primary mechanism references
- Henry T. Brown, Five Hundred and Seven Mechanical Movements, movements 89–90: movement 90 substitutes an elongated yoke for the circular eccentric strap to avoid vibrating motion of the rod in fixed guides.
- Cornell University Library scan, Mechanical Movements: primary scan of the same movement description and plate.
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