This calculator applies lossless work conservation to an abstract machine: input force times input travel equals output force times output travel. It is a definition of ideal mechanical advantage, not a real machine performance prediction.
Ideal Machine Interactive Calculator
Explore the ideal reciprocal trade between force and travel at equal work.
Equation Used
- Steady quasistatic comparison with no stored or changing kinetic/potential energy beyond the modeled work transfer.
- Input and output forces are collinear with their respective entered displacements.
- Perfectly rigid, lossless mechanism with work in equal to work out.
- No geometry/topology, friction, compliance, mass/inertia, strength, stability, backlash, efficiency, power/time, duty or safety model.
Work is displayed in N·cm; divide by 100 for joules. Friction and other dissipative effects consume energy in a real machine. Accelerating masses or deforming elastic parts can also store energy, which may be released later.
Lossless work reciprocity
An ideal machine conserves work: Fin din=Fout dout. Increasing force therefore requires proportionally greater input travel relative to output travel.
The moving bar is an abstract illustration. Its movement is not scaled to the entered input and output travel, and it does not represent a calculated lever, gear, pulley or hydraulic mechanism.
Use as an ideal limit and unit check
The identity can verify force/travel reciprocity and provides an upper ideal bound. It cannot select or rate a real mechanism.
Force gain is not energy gain
Fout/Fin=din/dout. The work tiles are equal by construction. N·cm is a work unit: 100 N·cm=1 J. Over an interval with no net change in stored energy and no other energy input, losses make useful output work less than input work.
Worked force-travel example
For 100 N input moving 30 cm while the output moves 10 cm, ideal force ratio is 3:1 and ideal output force is 300 N. Input and output work are both 3,000 N·cm=30 J.
Scope and limitations
Real design requires an identified mechanism and geometry, force directions through motion, friction and efficiency, compliance and deflection, moving mass and acceleration, impact and stored energy, material/connection strength, wear/lubrication, backlash, travel limits, power/speed, controls, guarding and applicable safety factors.
Questions
Does ideal mechanical advantage create energy?
No. Force gain is exchanged for travel.
Is work out always equal to work in?
Only in this lossless ideal definition.
Can this size a real mechanism?
No. Geometry, losses and strength are absent.
References & Further Reading
- Wikipedia contributors. Mechanical advantage. Wikipedia
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