This partial calculator evaluates exact in-line slider-crank geometry from a selected crank radius and connecting-rod length. It reports stroke, rod ratio, maximum rod obliquity and its tangent; it does not predict steam-engine loads, guide wear, power, efficiency or service life.
Linear actuator checks for Steam Engine (form)
An actuator-driven version of steam engine (form) should be reviewed for stroke, linkage angle, and peak force. The mechanism may feel light through most of the travel and still bind or spike in force at one position.
For a slider-crank style layout, pay particular attention near the dead-center regions. The actuator may have good leverage through the middle of travel but see a sharp force rise where the linkage straightens.
If the application needs synchronized motion, feedback should be treated as a requirement rather than an accessory. Two open-loop actuators wired together can drift apart when friction, load, or mounting geometry differs between sides.
- Map actuator stroke to the actual output travel before choosing a model.
- Check for binding, changing leverage, and peak load near the ends of travel.
- Decide whether timed motion is acceptable or position feedback is required.
For a FIRGELLI design review, calculate the load case with the FIRGELLI actuator force calculator and plan the switching or controller arrangement with the linear actuator wiring diagram generator. If an actuator or cylinder is already installed, the linear actuator replacement finder helps keep the comparison tied to real dimensions.
Steam Engine Form - Selected Slider-Crank Geometry Ledger
Explore exact in-line slider-crank geometry from selected crank radius and rod length.
Equation Used
- The slider axis passes through the crank centre.
- Crank and connecting rod are rigid pin-jointed links.
- Selected rod length is greater than the maximum selected crank radius.
- The tangent output is geometric and is not a force percentage.
- Loads, dynamics, clearances, wear and safety are excluded.
The secondary figure is an exact normalized slider-crank chain, not a cylinder, crosshead or valve-gear design.
Selected slider-crank geometry ledger
For an in-line slider constrained to the crank centreline, the rod angle satisfies sin(phi)=(r/L)sin(theta). Its maximum magnitude is arcsin(r/L), the stroke is 2r and the rod ratio is L/r. The selected range enforces L greater than r.
What the calculator determines
Use it to inspect exact geometry for selected dimensions. It cannot establish a steam-engine form, crosshead side load, guide pressure, wear, balance or suitability.
Selected relationships
phi_max=arcsin(r/L); rod ratio=L/r; stroke=2r; geometric tangent=tan(phi_max).
Selected-input example
At r=50 mm and L=240 mm, rod ratio is 4.8, stroke is 100 mm, maximum rod obliquity is about 12.025 degrees and its tangent is about 0.213.
Not a load or wear model
Cylinder pressure, piston area, inertia, speed, mass, gravity, friction, clearances, lubrication, guide geometry, valve timing, strength and safety are excluded.
Questions
Is tan(phi) a side-load percentage?
No. It is a dimensionless geometric tangent only; force resolution additionally requires a defined rod force and load model.
Why must L exceed r?
The selected full-rotation in-line geometry requires the connecting rod to remain longer than the crank radius.
Does the diagram identify an engine form?
No. It shows only the selected slider-crank chain.
Authoritative references
- Penn State ME 581 slider-crank geometric equations — gives phi=asin(R sin(theta)/L).
- NASA LATDYN slider-crank example — identifies the crank, connecting rod, slider and one-axis slider constraint.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
