Slider-Crank Mechanism Calculator
Calculate crank angle, slider displacement, connecting rod angle, and velocity in a slider-crank mechanism. Step-by-step solutions with SI units included.
crank-slider mechanism calculator:
Formula: Displacement \( (x) = r \cos \theta + \sqrt{l^2 - (r \sin \theta)^2} \)
where \( x \) = Displacement, \( r \) = Crank length, \( l \) = Rod length, \( \theta \) = Crank angle
Calculate slider displacement, crank and coupler angles, and velocities using this Slider-Crank Mechanism Calculator. Enter crank length, connecting rod length, crank angle, and optional crank angular velocity. Geometric and kinematic equations of the slider-crank motion in the engine pump, suspension are shown by step-by-step formulas.
slider-crank unit conversion Tool Formula:
It is a Slider-Crank Mechanism Calculator, which assists users in studying planar slider-crank linkages, which are common in engines, pumps, and piston-cylinder mechanisms. It computes crank angle (θ2), slider (x), and connecting rod angle (θ3), and linear or angular velocity at a given input angular velocity.
Users can input crank length, connecting rod length, crank angle, and optional angular velocity of the crank. The calculator applies the geometric loop-closure equation:
Formula: \( x = r cos \theta_{2} + \sqrt{I^{2} - (r sin \theta_{2})^{2}} \)
To calculate the slider position and the angle of the connecting rod. The solutions are given step-by-step so that a better understanding of the kinematics is considered. The tool works with SI units: meters ( m ) in the case of length, radians/degrees ( rad/degrees ) in the case of angles, and m/s or rad/s in the case of velocity. Other options are analysis of velocity, plotting the slides' motion, and the results, which can be printed. Perfect as a reference to mechanical engineering students, teachers, engineers, and designers of piston-crank systems.
⚡ Work & Installation Input to Output:
Input:
- Crank length (r), Connecting rod length (l)
- Crank angle θ2 (deg/rad)
- Optional crank angular velocity ω2
- Units: meters (m) for lengths, degrees/radians for angles, m/s or rad/s for velocities
Processing:
- Validate inputs (crank length < connecting rod length)
- Compute slider displacement: \( x = r cos \theta_{2} + \sqrt{I^{2} - (r sin \theta_{2})^{2}} \)
- Compute connecting rod angle: \( \theta_{3} = arcsin(\frac{\textrm{r sin}\theta_{2}}{\iota}) \)
- If ω2 provided, compute slider velocity v = r ω2 sin θ3 / sin(θ3 - θ2)
- Optional: compute angular velocity of connecting rod
Output:
- Slider position (x)
- Connecting rod angle (θ3)
- Slider velocity (v) and connecting rod angular velocity (if ω2 given)
- Step-by-step calculations
- Optional plots and printable results
Testing and Final Adjustments
Test common scenarios:
- r = 0.1 m, l = 0.4 m, θ2 = 30° → compute x and θ3
- Check slider motion for θ2 from 0° to 180°
- Validate velocities if ω2 = 10 rad/s
- Confirm step-by-step formulas and numeric results are consistent
- Edge cases: crank perpendicular or aligned with slider
- Validate unit conversions (m ↔ mm, deg ↔ rad)
- Ensure mobile/desktop UX: numeric keypad, field labels, and error messages
- Include preset examples (engine piston motion, pump mechanism)
- Optimize SEO metadata: "Slider-Crank Mechanism Calculator," "Slider Displacement," "Connecting Rod Angle," "Velocity Analysis," and schema markup
Frequently Asked Questions - Slider-Crank Mechanism Calculator:
What is a slider-crank mechanism?
A slider-crank mechanism converts rotational motion of a crank into linear motion of a slider.
How do I calculate slider displacement?
Use x = r cos θ2 + √(l² - (r sin θ2)²) with crank length, connecting rod length, and crank angle.
How do I calculate connecting rod angle?
θ3 = arcsin(r sin θ2 / l) gives the angle of the connecting rod relative to the slider.
Can I compute slider velocity?
Yes, if crank angular velocity ω2 is known, v = r ω2 sin θ3 / sin(θ3 - θ2).
What units are supported?
Lengths in meters, angles in degrees/radians, velocities in m/s or rad/s.
Can this calculator handle engine pistons?
Yes, it is suitable for engines, pumps, and other slider-crank applications.
Is step-by-step solution available?
Yes, formulas and substitutions are displayed step-by-step.
Who should use this calculator?
Mechanical engineering students, teachers, engineers, and designers of crank-slider systems.
Can it plot slider motion?
Yes, optional plotting of slider displacement over crank rotation is available.
Can I solve for crank angle given slider position?
Yes, inverse kinematics can be applied if needed, though this calculator primarily solves forward kinematics.
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