Mechanical Engineering Glossary

The ratio of the number of teeth on the driven gear to the driver gear. Determines the mechanical advantage and speed reduction in a gear train.

The ratio of output power to input power, expressed as a percentage. Accounts for energy losses due to friction, heat, and other factors.

The force required to compress or extend a spring by one unit of length. Denoted as k, it is calculated as k = Gd⁴/(8D³n) for helical springs, where G is shear modulus, d is wire diameter, D is mean coil diameter, and n is active coils.

A material property that describes its resistance to shear deformation. Denoted as G, it relates shear stress to shear strain in the elastic region. For most metals, G ≈ E/(2(1+ν)) where E is elastic modulus and ν is Poisson's ratio.

A stress correction factor for helical springs that accounts for wire curvature and direct shear effects. Calculated as K = (4C-1)/(4C-4) + 0.615/C, where C is the spring index (D/d).

The tensile force in a belt, consisting of tight side tension (T₁) and slack side tension (T₂). The difference transmits power: P = (T₁ - T₂) × v. Initial tension is set to prevent slip under load.

The ratio of driven pulley diameter to driver pulley diameter, which determines speed change. Speed ratio = D₂/D₁ = N₁/N₂, where larger driven pulleys reduce speed and increase torque.

The total length of belt required for a drive system, calculated as L = 2C + π(D₁+D₂)/2 + (D₂-D₁)²/(4C), where C is center distance and D₁, D₂ are pulley diameters.

A rotational force that causes or tends to cause rotation, calculated as τ = F × r × sin(θ), where F is force, r is the lever arm length, and θ is the angle between them. Units: N·m, lb-ft, lb-in.

The perpendicular distance from the axis of rotation to the line of action of the force. Effective moment arm = r × sin(θ) when force is not perpendicular to the radial line.

A measure of an object's resistance to angular acceleration, analogous to mass for linear motion. Depends on mass distribution relative to the rotation axis. Units: kg·m², lb·ft².

The rate of change of angular velocity over time. Related to torque by Newton's second law for rotation: τ = I × α, where τ is torque, I is moment of inertia, and α is angular acceleration. Units: rad/s².