A rotating crank carries a block that slides along a pivoted lever. The calculator finds the unequal times for that lever to swing between its extremes. A separate connecting rod drives the illustrated ram; the ram can reverse within a lever swing, so the reported ratio is not its stroke-time ratio.
Lever motion and ram motion
A connecting rod can introduce a ram turning point between the lever extremes. Read the reported ratio as lever timing; it does not establish actuator travel, load or ram cutting speed.
Inverted Slider-crank Chain Interactive Calculator
Enter crank radius, fixed-center distance, lever length and crank speed. The calculated timing is between the two extreme lever angles, not between the ram turning points.
Equation Used
- Fixed centers O and C with d greater than r throughout the input range.
- Uniform crank speed and ideal pin-in-slot contact.
- Rigid lever and connecting rod with a horizontal ideal ram guide.
- No clearance, interference, force, inertia, wear, lubrication or structural model.
The calculator derives timing from entered geometry; it does not reverse-solve geometry from a desired ratio.
Crank, sliding block and oscillating lever
The crank rotates about C and carries pin P at fixed radius r. A block at P slides along the slot line through lever pivot O, making the lever follow OP. The lever pin Q connects to a ram on a horizontal guide.
The drawn lever can be too short to contain the block at some entered dimensions. The connecting rod and guide also allow extra ram reversals. The calculator reports the lever’s tangent-position timing, not a complete quick-return machine’s cutting and return strokes.
Compare lever sweep timing
Changing r/d changes the angular sweep and the input intervals between lever extremes. Crank speed changes the cycle time, while lever length changes the attached ram geometry. The displayed ratio applies to the lever alone.
Tangent-position construction
For d greater than r, two tangents run from O to the crank circle. Their half-angle is α=asin(r/d). With uniform crank speed, the input rotates through 180°+2α during one lever sweep and 180°−2α during the other. The ratio of these angles is the lever sweep-time ratio; a complete revolution takes 60/n seconds.
The pin position is P=C+r[cosθ,sinθ]. The lever angle is ψ=atan2(Py−Oy,Px−Ox), and its rod pin is Q=O+L[cosψ,sinψ]. A fixed-length rod locates the illustrated ram at the right-hand intersection with its horizontal guide. Ram turning points depend on that extra geometry and need not coincide with the lever extremes.
Worked example
With r=60 mm and d=180 mm, α≈19.47° and lever sweep≈38.94°. The two crank intervals are 218.94° and 141.06°, giving a lever sweep-time ratio of 1.552:1. At 60 rpm, one complete cycle lasts one second. These values do not describe the turning-point intervals of the attached ram.
Limits of this illustration
The tangent calculation describes a slotted lever with its pivot outside the crank circle. A working ram drive also needs a slot long enough for the block, suitable guide and connecting-rod geometry, and checks for interference and extra turning points. Those requirements are not enforced across the illustrated input range. No cutting force, motor power or machine rating is calculated.
Frequently asked questions
What does the time ratio describe?
It compares the times for the slotted lever to swing between its two extreme angles at uniform crank speed. It is not the illustrated ram’s stroke-time ratio.
Why must d exceed r?
The lever pivot must lie outside the crank circle for two external tangents and a bounded oscillating lever.
Does changing lever length change the ratio?
No. The lever sweep ratio depends on r/d. Lever length changes the attached ram geometry and its turning points.
References
University of Babylon, Theory of Machines, quick-return mechanisms: labeled crank-and-slotted-lever construction and tangent-position timing relation.
Eugene S. Ferguson, Kinematics of Mechanisms from the Time of Watt: historical discussion and figures for Whitworth quick-return mechanisms.
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