A grooved face cam can make a fixed-pivot arm oscillate while the cam turns continuously. In this example, the closed groove is generated from the desired arm motion, so the follower pin and the track remain geometrically connected throughout the animation.
Endless-groove Disk and Vibrating Arm Interactive Calculator
Set the arm’s chord travel, length and follower size. The rotating groove is generated from that exact motion, keeping the pin on its track throughout each cycle.
Equation Used
- Fixed pivot-to-shaft spacing of 2.2 arm lengths.
- Sinusoidal rocker angle; no dwell.
- Rigid arm and ideal centreline follower.
- Diametral groove allowance; local curvature check only.
One sinusoidal oscillation per revolution. Playback slowed 10×. Local curvature does not certify production geometry.
A fixed-length arm follows a rotating groove
The cam shaft and arm pivot remain fixed to the mounting plate. The gold arm carries a pin that follows the groove in the disk. Its pivot-to-pin distance stays constant. The dashed green lines mark its two extreme positions.
This example prescribes a sinusoidal arm angle, then constructs the groove by viewing the moving pin in the rotating cam’s coordinates. The resulting groove and follower position satisfy the same geometric relationship.
The shaft spacing is 2.2 arm lengths. The disk grows to contain the resulting track. One disk revolution produces one complete oscillation. There is no programmed dwell in this example, and playback is slowed by a factor of ten for inspection.
Explore a cam-driven oscillating follower
The five controls are: pin travel, arm length, pin diameter, groove allowance and cam speed. Pin travel is the straight chord between the extreme pin positions. It is not the curved distance travelled around the arm pivot.
A grooved face cam can impose a selected motion on an oscillating follower. Different motion laws require different tracks. The displayed sinusoidal example is not a universal profile for textile, indexing or packaging machinery.
Hiscox shows a rockshaft arm driven by a groove in a faceplate as device 1032. That arrangement differs from the neighbouring device 1031, where the groove is carried by the moving arm. This calculator illustrates the former.
Synthesize the groove from the arm motion
For chord travel s and arm length L, the total swing is 2A=2 asin(s/(2L)). The prescribed arm angle is φ=A sin θ, where θ is the cam angle. With the cam shaft at O=(0,0) and the arm pivot at B=(2.2L,0), the pin centre is P=(2.2L−L cos φ,L sin φ).
The groove centreline in cam-fixed coordinates is Q(θ)=Rot(−θ)P(θ). Turning that curve through θ places its corresponding point exactly at the animated pin. The cycle rate is N/60 Hz, and the groove width is pin diameter plus the entered diametral allowance.
The smallest centreline curvature radius is sampled around this generated track using ρ=|Q′|³/|Q′×Q″|. This value describes the generated track and is separate from the follower pin’s radius.
Default 40 mm chord and 120 mm arm
A 40 mm chord with a 120 mm arm gives approximately 19.19° total swing. At 120 rpm, the actual motion rate is 2 Hz. An 8 mm pin with 0.08 mm diametral allowance gives an 8.08 mm groove width.
For this synthesized profile, the smallest centreline curvature radius is about 141.11 mm. This is a calculated local geometric property of the displayed track, not a recommended fillet radius or a machining specification.
Increasing the chord to 80 mm while reducing the arm to 50 mm makes the path much tighter. Its smallest centreline radius is about 2.46 mm, too tight for the available pin sizes and groove allowance. The diagram remains visible as a geometry preview and reports the tight-curvature condition.
Clearance and curvature are different checks
Diametral allowance determines how much wider the nominal groove is than the pin. The ideal animation puts the pin on the centreline; clearance-induced movement and the loaded groove wall are not solved.
A local curvature radius smaller than half the groove width causes an inner offset problem. The display flags that condition. A positive local margin alone does not certify a machinable or load-capable cam: global wall interference, pressure angle, contact stress, material, lubrication and cutter geometry still require a complete design.
Tolerances and service life depend on the manufactured cam, follower, loads and operating conditions. The calculation uses only its stated geometry and prescribed motion.
Grooved face-cam questions
Why does changing arm length change the groove?
The track is generated from the selected fixed-length arm motion. Its shape must change to keep the same requested chord travel.
Why is playback slower than the entered speed?
The demonstration runs at one tenth of the calculated rate so the follower engagement can be inspected.
Does the calculated curvature radius specify a cutter?
No. It is the smallest sampled radius of the centreline, before a complete wall, cutter and load analysis.
Does the groove provide a dwell?
Not in this sinusoidal example. A dwell would require a different motion law and groove.
References
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances — device 1032, printed page 259: a rocking arm driven by a groove in a faceplate.
- Carnegie Mellon University: Introduction to Mechanisms, Chapter 6 — Cams — grooved cams, oscillating followers and inverse-motion profile construction.
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