The Lamb rotary engine shown by Hiscox has a hollow ring piston inside an annular chamber. A crank carries the ring centre around the shaft axis, while a slot in the ring passes over a fixed partition between the ports. The ring therefore orbits and rocks. Use the calculator to explore this geometry and watch the slot move along the partition.
Lamb Rotary Engine Interactive Calculator
Set shell radius, crank eccentricity, ring thickness and an illustrative shaft speed. The animation keeps the ring tangent to the circular chamber walls while its chamfered slot follows the fixed partition.
Equation Used
R is the outer chamber radius, e the crank radius and t the ring wall thickness. The fixed inner chamber radius is rᵢ−e. The slot centre follows the vertical partition at distance ℓ from the moving ring centre. Illustrative dimensions and a clearance at the chamfered slot are used; packing, port timing, steam pressure, torque, power and leakage are not calculated. Shaft motion is displayed eight times slower than the selected speed. Zero speed stops the mechanism and leaves revolution time undefined.
An orbiting ring and a stationary partition
The outer shell and inner circular wall are fixed. The piston is a ring between them, carried by a crank pin offset from the common shaft axis. As that pin goes around, the ring moves around the chamber and changes the spaces between its inner and outer surfaces and the stationary walls.
The partition extends from the inner wall to the outer wall. The ring has a chamfered opening that straddles it. Keeping this opening on the partition makes the ring rock back and forth while its centre orbits. A light marker attached to the ring makes that rocking visible.
The blue crank is shown in front of the chamber section. Thin spokes represent an end plate connecting the ring to its crank-pin bearing; they occupy a different axial plane from the stationary inner wall. The drawing separates these layers so the crank connection remains visible.
Geometry of the illustrated arrangement
Let the fixed shaft centre be O=(0,0). For crank angle θ, the ring centre is C=(e cos θ,e sin θ). Choose piston outer radius rₒ=R−e. Its circular outer boundary then remains internally tangent to the shell. With piston inner radius rᵢ=rₒ−t, a fixed inner wall of radius rᵢ−e is tangent to the piston's inner boundary.
The slot reference point lies at the middle of the ring wall, a distance ℓ=(rₒ+rᵢ)/2 from C, and on the vertical line x=0. Its height is y=e sin θ+√(ℓ²−e² cos²θ). The ring angle follows the line from C to this point.
The slot height ranges from ℓ−e to ℓ+e, giving a full travel of 2e. The maximum ring rock from vertical is arcsin(e/ℓ). Revolution time is 60/n seconds for n>0. The selected ranges keep the inner fixed wall positive and ℓ greater than e.
Example with a 100 mm outer chamber radius
For R=100 mm, eccentricity 20% and wall thickness 10%, the crank radius is e=20 mm and wall thickness t=10 mm. The piston outer and inner radii are 80 and 70 mm. The fixed inner wall radius is 50 mm.
The slot reference radius is ℓ=75 mm. Its height varies from 55 to 95 mm, a 40 mm travel. Maximum ring rock is arcsin(20/75), approximately 15.47 degrees. At 60 rpm, the real-time revolution period is 1 second; the explanatory animation takes 8 seconds.
A historical rotary-engine concept
Hiscox illustrates this arrangement as the Lamb rotary engine in figure 328. Reuleaux discusses the corresponding annular-piston machine on pages 349–350 and plate XV, figure 1 of The Kinematics of Machinery. It demonstrates how a crank and a sliding partition connection can create moving chamber spaces without an ordinary reciprocating cylinder.
The model is useful for studying the distinction between an orbit and a rotation, and for seeing why a sliding slot must also accommodate angular motion. Its chosen dimensions are examples for that study, not dimensions of a particular surviving engine.
Sealing and admission need more than geometry
The ring contacts the outer wall on one side and the inner wall on the opposite side. Near the partition, its slot both slides and changes angle. Reuleaux identifies the sealing difficulty at that connection and notes that the proposed additional closing piece was not clearly described.
The animation shows clearance at the slot. Steam-tight packing and admission or exhaust timing are outside this geometric model. Reuleaux notes that the low position of the piston can allow communication between ports unless valve gear prevents it.
Port colours identify the two connections only. They are not pressure contours. Wall contact, end-face sealing, thermal expansion and lubrication would all affect a physical machine; no efficiency, output rating or working pressure follows from the geometry shown here.
Frequently asked questions
Does the ring turn once per crank revolution?
No. Its centre travels around the shaft, but the slot constrains the ring to rock back and forth. The crank completes full turns while the ring keeps its opening toward the partition.
What keeps the piston against the chamber walls?
In the ideal geometry, the piston outer radius plus crank eccentricity equals the shell radius. Its inner radius minus eccentricity equals the fixed inner wall radius.
Why is there a gap at the partition?
The chamfered slot must allow the ring to slide and rock relative to the fixed plate. The drawing includes clearance and does not model a pressure seal or packing design.
What does the slot-travel result mean?
It is the vertical travel of the selected reference point at the middle of the ring wall. The full travel is twice the crank eccentricity.
Can I use the speed slider as an operating recommendation?
No. It controls an ideal motion example. The display runs at one eighth of the selected speed; no inertial load, wear, power or suitable operating range is calculated.
Why is revolution time blank at zero speed?
A stationary shaft does not complete a revolution in a finite time. Geometry results remain available while the mechanism is stopped.
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