Segment levers and belt arrangements can transmit oscillatory motion, but their actual displacement law depends on geometry. The calculator applies an assumed sinusoidal displacement law to the entered stroke and cycle rate.
Vibratory Belt Motion via Segment Lever Interactive Calculator
Enter an initial reference stroke, a comparison stroke and a cyclic-speed reference. Results assume x=(S/2)sin(omega t) with one cycle per entered revolution—not a solved segment-lever or belt mechanism.
Equation Used
- Initial and comparison stroke are independent entered peak-to-peak values.
- The comparison displacement is ideal simple harmonic motion with amplitude S/2.
- Entered rpm is interpreted as one complete harmonic cycle per revolution.
- Standard gravity is 9.80665 m/s² for the acceleration conversion.
- Segment-lever geometry, belt wrap and elasticity, pulley ratio, slip, tension, force, torque, resonance, damping, structure, wear and safety are omitted.
Illustrated Topology, Assumed Motion Law
A segment lever can participate in a belt-motion transmission, but this page has no segment radius, lever length, pulley diameter or contact geometry. The drawing is therefore a topology cue. NASA TP-20220018746 supplies the separate simple-harmonic displacement, velocity and acceleration relations, while NASA Tech Brief 72-10476 documents a physical eccentric/Scotch-yoke harmonic drive.
What This Calculator Represents
The tool compares two entered full strokes and applies an ideal sinusoidal displacement law to the comparison stroke at a one-cycle-per-entered-revolution frequency.
Ideal Harmonic Reference
f=N/60
omega=2pi f
vmax=omega A
amax=omega²A
signed reduction=100(S0−S)/S0
The frequency conversion is an explicit assumption, not a derived motor-to-belt ratio.
Worked Assumption Example
For S0=8 mm, S=5 mm and N=1,400 rpm interpreted as cycles/min, signed reduction is 37.5%, ideal harmonic peak speed is about 0.37 m/s and ideal peak acceleration is about 5.5 g.
Model Boundary
- Calculated: entered-stroke comparison and ideal harmonic peak quantities.
- Illustrated: a generic rotating input, segment lever and vibrating belt cue.
- Not calculated: transmission geometry, actual belt displacement law, ratio, wrap, slip, tension, load, force, torque, resonance, damping, structure, wear or safety.
Frequently Asked Questions
Is entered motor rpm necessarily belt-cycle rpm?
No; one cycle per entered revolution is an explicit assumption.
Does the model solve segment-lever geometry?
No.
Why is amplitude half the stroke?
Stroke is defined as peak-to-peak travel for the ideal sinusoid.
Can signed reduction be negative?
Yes; that means the comparison stroke exceeds the initial stroke.
Are the peak values measured?
No.
Can this size a vibrating conveyor or belt drive?
No.
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