The Dake square-piston engine contains two nested rectangular pistons working at right angles. The outer piston slides horizontally in its case; the inner piston moves vertically relative to that outer piston and connects directly to a rotating crankpin. The pistons translate rather than rock.
Dake Square Piston Engine Interactive Calculator
Explore the two perpendicular slides inside a Dake square-piston engine. Set crank radius and speed, then calculate a separate ideal pressure force for an entered working-face area.
Equation Used
- Rigid ideal perpendicular slides and a constant-speed shaft.
- Both slider strokes equal twice the crank radius.
- Net differential pressure acts uniformly on the entered effective face area.
- Calculated face force is not net shaft torque or indicated power.
The outer piston translates horizontally; the inner piston slides vertically relative to it. Both remain upright. The crankshaft rotates continuously.
Two slides, one rotating crankpin
Hiscox describes the Dake engine in movement 363 and relates its principle to Root’s square-piston engine, movement 362. The outer piston is a sliding frame. The inner piston slides within it. Their perpendicular motions resolve the circular crankpin path into horizontal and vertical components.
The animation removes the front cover. Bronze identifies the outer frame, blue the inner piston and gold the crank. The fixed shaft center remains in the middle of the case. Neither rectangular piston rotates. Steam ports and valve timing are outside this geometric model.
Explore the nested-slider geometry
Change crank radius to compare stroke and slider motion. Change shaft speed to compare peak velocity and acceleration. The illustration rescales to keep the mechanism visible; its housing dimensions and wall thicknesses are schematic.
For a measured working face, enter its effective area and the pressure difference across it. Their product gives an ideal force on that face. This separate pressure calculation does not prescribe the pressure sequence needed to operate the engine.
Crank coordinates and pressure force
For radius r and crank angle θ, x=r cos θ and y=r sin θ. The outer frame follows x. The inner piston shares x and moves by y within the frame. Each coordinate spans −r to +r, giving stroke 2r.
At constant shaft speed n, angular speed is ω=2πn/60. Each slider component has peak speed rω and peak acceleration rω². The displayed acceleration converts millimetres to metres. With pressure in kPa and area in mm², face force in newtons is ΔpA/1000.
A 25 mm crank at 60 rpm
Each slider has 50 mm total stroke. Angular speed is 2π rad/s, giving peak component speed 157.08 mm/s and peak component acceleration 0.987 m/s². At 400 kPa net pressure over 2500 mm², ideal force on the entered face is 1000 N.
The inner piston’s absolute path is circular. Its vertical motion relative to the outer frame is sinusoidal. These are different descriptions of the same constrained motion.
What this model does not predict
Actual torque depends on pressures acting on the separate working faces, their areas, valve timing and losses. Constant net pressure on one entered face is not a complete engine cycle model. The slider-motion and single-face force results do not determine shaft power.
A complete engine calculation would need the pressure history on each working face and the mechanical losses throughout the cycle. Valve cutoff, clearances, operating speed and service life depend on the specific engine.
Dake engine questions
Does the square piston rotate?
No. The two rectangular members translate; the crankshaft rotates.
How can the inner piston move vertically and follow a circle?
It slides vertically within a frame that is simultaneously translating horizontally.
What happens at zero speed?
Motion stops and calculated speed and acceleration are zero. Geometric stroke and the separate pressure-face force remain available.
Is the force output shaft torque?
No. It is pressure difference multiplied by a selected effective face area.
Original mechanism reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), printed page 98, movements 362 and 363. The text and illustration identify the nested pistons, perpendicular sliding motion and direct crankpin connection.
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