Mechanical Engineering
From questions to insights, 30online scientific tool. No registration required, free calculation and export.
Linkage Kinematics
calculates the trajectory, speed and assembly range of four-rod and additional two-link branches.
ideal rigid plane hinge; the six-rod mode is a fixed-fulcrum two-link branch chain driven by four-rod coupling points. Non-dynamic/collision solver.
Involute Gear Lab
Generates involute contours and closed DXF of spur external gears.
standard involute tooth surface, tooth root adopts simplified radial/arc connection, tool envelope is not simulated; used for design preview, CAD and manufacturing review are required before production.
Beam & Vibration
View deflections, bending moments, and foundation natural frequencies under concentrated loads.
Euler–Bernoulli homogeneous rectangular beam with small deflection; simply supported central load or cantilever end load; no shear deformation. Analytical solution of
Linear Spring
calculates the restoring force and elastic potential energy of linear springs.
Ideal linear spring with small deformation.
Damped Oscillator
calculates the displacement and energy attenuation of an underdamped system.
linear mass-spring-damping model, 0≤ζ<1, initial velocity is zero.
Circular Shaft Torsion
calculates the shear stress and torsion angle of a solid circular shaft.
Uniform solid circular shaft, linear elasticity, small torsion.
Euler Buckling
estimates elastic buckling critical load based on effective length.
Ideal straight and slender rod, small deflection, linear elasticity; actual design needs correction of defects and specifications.
Shaft Power
Transmission conversion between power, speed and efficiency.
Steady state rotation, no energy storage transient.
Bearing L10 Life
Estimate L10 life based on rated load and equivalent dynamic load.
ISO 281 basic life model; does not include lubrication, contamination, temperature and reliability corrections.
Mohr Circle
Find the principal stress, maximum in-plane shear stress and rotated section stress.
Two-dimensional symmetric stress tensor; the maximum in-plane shear stress is not necessarily the three-dimensional absolute maximum.
Axial Stress
σ=F/A: Calculate the axial normal stress based on the input, and provide local sensitivity curves and data export.
Uniform axial load, neglecting stress concentration.
Axial Extension
δ=FL/(EA): Calculate the axial elongation of the rod based on the input, and provide local sensitivity curves and data export.
Linear elastic constant cross-section members.
Average Shear Stress
τ=V/A: Calculate the average shear stress based on the input, and provide local sensitivity curves and data export.
is the average stress and does not represent the cross-section peak value.
Circular Second Moment
I=πd⁴/64: Calculate the moment of inertia of the solid circle section based on the input, and provide local sensitivity curves and data export.
The second moment of section about the centroid diameter axis.
Rectangular Second Moment
I=bh³/12: Calculate the moment of inertia of the rectangular section based on the input, and provide local sensitivity curves and data export.
The centroid axis is parallel to the width direction.
Polar Second Moment
J=πd⁴/32: Calculate the solid circular polar moment of inertia based on the input, and provide local sensitivity curves and data export.
Polar second moment at the centroid of circular section.
Bending Stress
σ=My/I: Calculate the beam bending normal stress according to the input, and provide local sensitivity curves and data export.
Assumption of small linear elastic deformation of slender beam.
Shaft Torsional Stress
τ=16T/(πd³): Calculate the torsional shear stress of the circular axis based on the input, and provide local sensitivity curves and data export.
Maximum linear elastic shear stress on the surface of a solid circular shaft.
Cantilever Tip Deflection
δ=FL³/(3EI): Calculate the end-load deflection of the cantilever beam based on the input, and provide local sensitivity curves and data export.
Slender beam with constant cross-section, linear elasticity, small deflection.
Simply Supported Deflection
δ=FL³/(48EI): Calculate the mid-span deflection of a simply supported beam based on the input, and provide local sensitivity curves and data export.
mid-span concentration, ideal simply supported boundary.
Thin Cylinder Hoop Stress
σh=pr/t: Calculate the hoop stress of a thin-walled cylinder based on the input, and provide local sensitivity curves and data export.
thin wall t/r≤0.1; does not include joint efficiency, corrosion allowance and design specification coefficients.
Constrained Thermal Stress
σ=EαΔT: Calculates fully constrained thermal stress based on input, providing local sensitivity curves and data export.
One-dimensional fully constrained, compressive stress is generated by heating; plasticity and temperature-dependent modulus are ignored.
Series Spring Stiffness
keq=k₁k₂/(k₁+k₂): Calculate the double spring series stiffness based on the input, and provide local sensitivity curves and data export.
Ideal linear massless spring in series.
Parallel Spring Stiffness
keq=k₁+k₂: Calculate the parallel stiffness of double springs based on the input, and provide local sensitivity curves and data export.
Two springs bear the same displacement.
Critical Damping
cc=2√(km): Calculate critical damping coefficient based on input, provide local sensitivity curve and data export.
linear single degree of freedom viscous damping system.
Damped Natural Frequency
fd=√(k/m)√(1−ζ²)/(2π): Calculate the damping natural frequency based on the input, and provide local sensitivity curves and data export.
is only used in underdamped linear systems.
Capstan Tension Ratio
Ttight/Tslack=e^(μθ): Calculate the belt friction tension ratio based on the input, and provide local sensitivity curves and data export.
Critical sliding state of flexible belt, ignoring bending stiffness and centrifugal force.
Flywheel Energy
E=Iω²/2: Calculate flywheel energy storage based on input, provide local sensitivity curve and data export.
Rigid body constant moment of inertia; does not represent allowable speed.
Centrifugal Load
F=mrω²: Calculate centrifugal load based on input, provide local sensitivity curve and data export.
Radial inertia load magnitude for uniform circular motion.
Lead Screw Speed
v=p n/60: Calculate the linear speed of the screw according to the input, and provide local sensitivity curves and data export.
Lead is the axial displacement per revolution, which is not necessarily equal to the single-start pitch.
Understand the method and then start calculating
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