Brown movement 166 is a radial lost-motion mechanism: a crank pin alternately bears on the rounded ends of a slot in a connecting rod attached to a guided slide. While the pin crosses the slot without end contact, the slide remains at rest.
Slotted Connecting Rod · Lost-Motion Contact Model
Explore Brown movement 166 with a crank pin, radial lost-motion slot and guided output slide.
Equation Used
- The output slide pivot is constrained to a horizontal guide through the crank center.
- The slot is radial about the slide pivot with inner radius a=kR and travel L=2Rf.
- The pin and rod are rigid and clearance-free; rotation is uniform and positive.
- Impact, elasticity, friction, loads, wear, strength and production design are excluded.
Brown supplies the lost-motion topology and rest-at-end function but no dimensions; the inner-slot radius ratio is selected.
Crank pin, radial slot and guided slide
The crank pin follows the selected radius R. The connecting rod pivots at the output slide, and its radial slot extends from inner distance a=kR to outer distance b=a+2Rf. At every phase the model enforces a less than or equal to the pin-to-slide distance less than or equal to b. Contact with either rounded slot end moves the slide; free travel inside the slot leaves the slide fixed.
What the calculator determines
Select crank radius, lost-motion fraction, normalized inner-slot radius and speed. A periodic play-operator solution reports radial slot travel, guided-slide stroke, total rest share across both stroke ends and total rest time per revolution.
Contact-constrained lost-motion model
Slot travel L=2Rf; a=kR; b=a+L. With crank pin P and guided slide pivot B, feasibility requires a≤|P−B|≤b. The slide retains its position while feasible, moves to the inner-contact bound when |P−B| would fall below a, and moves to the outer-contact bound when it would exceed b.
Default selected-value example
For R=18 mm, f=0.4, k=2.6 and n=45 rpm, radial slot travel is 14.4 mm and the ideal guided-slide stroke is 21.6 mm. Rest share and rest time are evaluated from the complete periodic contact cycle.
Selected dimensions
Brown identifies the crank pin, slotted connecting rod, to-and-fro output and rest at both stroke ends, but gives no dimensions. The inner-slot radius ratio is therefore an explicit selected input, not a historical measurement. Clearance, impact, elasticity, loads, wear and manufacturing design remain excluded.
Questions
Why is the output at rest?
During free travel the crank pin remains between the two rounded slot ends, so neither end drives the rod and the guided slide retains its prior position.
Does a circle-chord formula give the rest time?
No. A chord c=2Rf subtends 2 asin(f), but the rest time here follows the pin-to-slide distance and contact at the two slot ends.
Are k=2.6 or the displayed proportions historical dimensions?
No. Brown supplies topology but not scale; k is a selected normalized dimension.
References
References & Further Reading
- Wikipedia contributors. Slider-crank linkage. Wikipedia
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