For the ideal topology shown, a pin constrained to a horizontal guide lies in a slot through a fixed lever pivot. With perpendicular pivot-to-guide offset h and lever angle θ measured from that normal, x=htanθ. A symmetric ±θmax swing therefore gives stroke S=2htanθmax.
Slotted Vibrating Lever · Ideal Horizontal Pin Kinematics
Explore exact ideal horizontal-pin stroke and mean round-trip speed for a pivoted slotted lever.
Equation Used
- The pin center remains on a fixed horizontal guide and the slot centerline passes through the lever pivot.
- h is the fixed perpendicular distance from pivot to guide centerline.
- The lever swings symmetrically between plus and minus θmax.
- Cycle rate is constant and mean speed is based on total out-and-back distance.
- Clearance, friction, loads, inertia, wear, strength and safety are excluded.
Required one-sided travel is measured from the centered position.
Closed pin, slot and guide geometry
The pin remains on the horizontal guide and on the centerline of the pivoted slot. The finite slot is drawn long enough to capture the full selected pin-radius path.
What the calculator determines
Select pivot-to-guide offset, half-swing, cycle rate and required one-sided travel. The calculator reports peak-to-peak stroke, half-stroke, mean round-trip speed and any one-sided travel shortfall.
Ideal geometric identities
x=htanθ; S=2htanθmax; mean round-trip speed=2Sn/60; shortfall=max(Creq−S/2,0).
Selected-input example
For h=180 mm, θmax=20° and n=22 cycles/min, stroke is about 131.0 mm, half-stroke is 65.5 mm and mean round-trip speed is about 96.1 mm/s.
Ideal kinematics only
The model does not determine pin diameter, slot width, guide length, connecting structure, loads, friction, acceleration, contact pressure, wear, strength or safe cycle rate.
Questions
Why compare clearance with half-stroke?
The selected requirement is explicitly one-sided travel from the centered position.
Is the reported speed instantaneous?
No. It is total out-and-back distance per minute divided by 60.
References & Further Reading
- Wikipedia contributors. Linkage (mechanical). Wikipedia
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