Disk-and-pin Lever Vibration Mechanism: How It Works, Parts, Diagram, and Calculator

A pin following a rotating face groove

The disk turns about a fixed shaft. A second fixed pivot supports the lever, whose pin remains at a constant distance L from that pivot. The groove constrains the pin as the disk rotates. A longer extension of the lever makes the output motion easy to see.

Brown provides a construction illustration, not a numerical groove profile. This calculator defines a sinusoidal rocking program β=A sinφ, with A=asin(e/L). The pin follows a circular arc around its pivot. Transforming that pin path into coordinates attached to the disk generates the closed groove. The displayed groove and follower are calculated from the same construction.

The lever pivot is placed at (0.65L,−L) relative to the disk center. The illustrated disk radius is 1.15L and pin diameter 0.05L. Those are explicit model proportions. The groove width equals pin diameter plus the entered clearance. The nominal pin runs on the groove centerline; load-dependent wall contact, impacts and elastic motion are not simulated.

What this study demonstrates

Use this model to explore how a face groove can program a lever motion and how amplitude, arm length and speed relate. It is an illustrative cam synthesis exercise, not a dimensioned replica of a historical machine or a rated vibration drive.

Contact load, pressure angle, curvature, lubrication, wear and the full mechanical installation must be considered separately when designing a physical cam.

Defined sinusoidal rocking program

Let q=e/L be the entered half transverse pin sweep divided by follower-arm length L. Half angular amplitude is A=asin(q), and total swing is 2A. For disk angle φ, the lever rocks by β=A sinφ. At n revolutions per minute, oscillation frequency is f=n/60 and peak angular speed is A×2πf radians per second. Transverse pin travel is 2L sinA=2Lq.

With screen-coordinate y positive downward, the pin position is F=(0.65L−L sinβ,−L+L cosβ). The groove centerline in disk-fixed coordinates is Q(φ)=Rot(−φ)F(φ). Rotating that groove by φ places its corresponding point exactly at the lever pin.

Clearance c changes groove width from pin diameter d to d+c. It does not change this prescribed nominal motion. Wear, contact loads and backlash dynamics require additional information.

Example: 100 mm follower arm

At L=100 mm, q=0.20 and n=600 rpm, A=11.537°. Total swing is 23.074°, transverse pin travel 40 mm, frequency 10 Hz and peak angular speed approximately 12.652 rad/s.

Doubling speed doubles frequency and peak angular speed while leaving the geometric swing unchanged. Doubling arm length doubles pin travel but leaves angular swing unchanged. Changing clearance changes the groove-width detail, not the nominal motion program.

A defined groove, not a universal vibration rating

This animation runs 100 times slower than the entered disk speed so the motion can be inspected. Display time is deliberately separated from the calculated frequency.

The source does not specify a sinusoidal law, pivot spacing or pin diameter; those are model choices stated here. The drawing pairs that arrangement with a groove calculated for the stated motion program.

A continuous groove path establishes the nominal motion. Physical cam design also requires checks of contact stress, curvature, clearance, balance and manufacturability.

Grooved-disk questions

Which part carries the pin?

The rocking lever. The groove is in the rotating disk.

Why does clearance not change swing?

The animation follows the nominal groove centerline. A real loose follower can contact different walls depending on force and inertia; that dynamic behavior is not solved.

Is the displayed speed real time?

No. Playback is slowed by a factor of 100 while the frequency output uses the entered rpm.

Is this Brown’s exact groove?

No. Brown establishes the mechanism arrangement. This calculator uses an explicit sinusoidal output program and derives a matching illustrative groove.