A crank and connecting rod can convert rotary motion into constrained reciprocating slider motion. This page treats the ideal in-line, zero-offset geometry only.
Transmission Reciprocating Interactive Calculator
Vary crank radius, connecting-rod ratio, constant crank speed and crank angle from top dead center. The outputs are ideal geometry and cycle-average travel rate, not force or machine performance.
Equation Used
- Rigid crank and connecting rod with pin joints.
- The fixed crank axis lies on the slider axis; there is no offset.
- Crank radius and connecting-rod centre length define the geometry.
- The entered rpm is constant for the mean-speed calculation. The animation is slowed and its rate capped for viewing, so it does not display real-time RPM.
- No clearance, inertia, force, torque, friction, stress, vibration, balancing or bearing load is predicted.
In-Line Slider-Crank Geometry
The mechanism contains a crank rotating about a fixed axis, a rigid connecting rod and a slider constrained to the same axis as the crank centre. One complete crank revolution produces one complete out-and-back slider cycle.
The interactive drawing animates the cycle from the entered angle; the numerical displacement tile remains the exact result at the entered crank angle.
What the Calculator Represents
The calculator reports geometric stroke, connecting-rod centre length, slider displacement from top dead center and the cycle-average magnitude of slider speed. These quantities can describe an idealized reciprocating linkage, but they do not determine suitability for a compressor, engine, pump or other machine.
Displacement and Mean-Speed Equations
x = R(1 - cos theta) + L - sqrt(L^2 - R^2 sin^2 theta)
stroke = 2R
mean slider speed = 4RN/1000
Here R is crank radius in millimetres, lambda=L/R, theta is measured from top dead center, N is rpm, x is millimetres from top dead center, and mean speed is metres per minute.
Worked Geometry Example
With R=25 mm and L/R=5, the connecting-rod length is 125 mm and the stroke is 50 mm. At 90 degrees from top dead center, x is about 27.53 mm. At 300 rpm, the full-cycle mean slider speed is 30.0 m/min.
Model Boundary
- Calculated: exact rigid, zero-offset in-line slider-crank geometry.
- Timing input: constant rpm determines the mean-speed result; animation timing is slowed and capped for viewing.
- Not calculated: instantaneous velocity or acceleration, gas or process loads, inertia, side thrust, torque, bearing reactions, stress, fatigue, lubrication, clearance, deflection, vibration, balance or efficiency.
Frequently Asked Questions
Where is displacement zero?
At top dead center, where the crank and connecting rod place the slider farthest from the crank axis.
Why is stroke twice crank radius?
The two dead-center positions differ by the crank diameter, 2R.
Why does mean speed use 4R per revolution?
The slider travels one stroke out and one stroke back, for total distance 2(2R)=4R.
Does rod ratio change stroke?
No. It changes the displacement-versus-angle relationship, while geometric stroke remains 2R.
Does the calculator predict side thrust or torque?
No.
Can it size a real reciprocating machine?
No. Real design requires loads, materials, bearings, clearances, dynamics and safety factors.
References
- NASA report: slider-crank piston-displacement relation in crank angle, stroke and connecting-rod length.
- NASA LATDYN report: rigid slider-crank bodies, revolute joints and slider constraint.
- U.S. Patent 8,220,434: crank radius, connecting-rod length, top-dead-center datum and equivalent displacement equation.
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