Gear Base Pitch
Calculate the base pitch of an involute gear, p_b = π·m·cos(φ), from the module m (mm) and the pressure angle φ (degrees). The base pitch is the distance between two homologous flanks of consecutive teeth, measured along the base circle (or, equivalently, along the line of action) — different from the circular pitch (π·m), measured on the pitch circle. The base pitch is a FUNDAMENTAL property of involute meshing for an elegant reason: for two meshes to transmit motion correctly, they must have the SAME base pitch — it is the conjugacy condition of involute profiles. Moreover, the base pitch appears directly in the CONTACT RATIO (the average number of teeth in simultaneous contact, found by dividing the line-of-action length by the base pitch): a contact ratio above 1 (ideally above 1.4) ensures there is always at least one tooth pair meshed, transmitting motion continuously and smoothly, without impacts. The base pitch is also the basis of checking gears 'over two pins' or by span measurement (W over teeth), classic dimensional-control methods. It is an essential parameter in gear geometry and metrology. Enter the module and the pressure angle.
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Passo de base da engrenagem
O passo de base de uma engrenagem evolvente é p_b = π·m·cos(φ), a partir do módulo m e do ângulo de pressão φ. É a distância entre dois flancos homólogos de dentes consecutivos, medida ao longo do círculo de base (ou, equivalentemente, ao longo da linha de ação) — diferente do passo circular (π·m), que é medido no círculo primitivo. O passo de base é uma propriedade fundamental do engrenamento evolvente por uma razão elegante: para que dois engrenamentos transmitam movimento corretamente, eles precisam ter o mesmo passo de base — é a condição de conjugação dos perfis evolventes. Além disso, o passo de base aparece diretamente no cálculo da razão de contato (a média de dentes em contato simultâneo, obtida dividindo o comprimento da linha de ação pelo passo de base): uma razão de contato maior que 1 (e idealmente acima de 1,4) garante que sempre haja pelo menos um par de dentes engrenado, transmitindo movimento de forma contínua e suave, sem impactos a cada troca de dente. O passo de base também é a base da verificação de engrenagens 'sobre dois pinos' ou pela medição W de dentes (span measurement, com micrômetro de pratos), métodos clássicos de controle dimensional. É um parâmetro essencial na geometria e na metrologia de engrenagens. Informe o módulo e o ângulo de pressão.
Related Tools
Gear Base Diameter
Calculate the base circle diameter of an involute gear, d_b = d·cos(φ), from the pitch diameter d (mm) and the pressure angle φ (degrees). The base circle is the circle from which the INVOLUTE tooth profile is generated — the standard profile of modern gears. The involute is the curve traced by the tip of a string unwinding from a cylinder: that cylinder is exactly the base circle. The entire active tooth profile (the part that actually transmits force) is ABOVE the base circle; below it there is no involute profile. The base diameter is fundamental in gear geometry because it defines the involute profile and, with it, key properties: the LINE OF ACTION (the line tangent to both base circles of the mesh, along which tooth contact travels, always in the same direction — why involute gears transmit uniform motion), the base pitch and the contact ratio. The relation d_b = d·cos(φ) shows that the pressure angle is the angle between the line of action and the tangent to the pitch circles. It is an essential parameter in designing and manufacturing (generating) involute gears. Enter the pitch diameter and the pressure angle.
Minimum Pinion Teeth
Calculate the minimum number of pinion teeth to avoid interference, z_min = 2 ÷ sin²(φ), from the pressure angle φ (degrees). Interference is a geometric problem occurring when gears with FEW teeth mesh: the pinion tooth flank (the part below the base circle, where the involute profile does not exist) collides with the larger gear's tooth tip, causing vibration, noise, rapid wear or jamming. To avoid it, the pinion needs a minimum tooth count depending on the pressure angle: LARGER pressure angles ('fatter' teeth at the root) allow pinions with FEWER teeth without interference. For the standard 20° pressure angle, the theoretical minimum is about 17-18 teeth; for 14.5° (old standard), about 32; for 25°, about 12. When a pinion with fewer than the minimum is needed (for a high gear ratio in little space), profile CORRECTION (profile shift, corrected teeth) or undercut (root relief) is used, avoiding interference at the cost of weakening the tooth. This calculation is fundamental in designing a gear pair's geometry. Enter the pressure angle.
Tooth Thickness at Pitch Circle
Calculate the tooth thickness measured at the pitch circle of a standard gear, s = (π·m) ÷ 2, from the module m (mm). In a standard (uncorrected) gear, the circular pitch (the distance from one tooth to the next, along the pitch circle) is p = π·m, and it splits equally between the TOOTH (the solid part) and the SPACE (the gap between teeth): half each, hence s = π·m/2. This equality between tooth thickness and space width is what lets two standard gears of the same module mesh perfectly, with one's tooth fitting the other's space with proper clearance. Tooth thickness is a fundamental parameter: it sets the tooth STRENGTH (thicker teeth resist bending more) and the mesh backlash. In CORRECTED gears (with profile shift, used to avoid interference in small pinions, adjust center distance or balance pinion-gear strength), the pitch-circle tooth thickness DIFFERS from π·m/2 — it increases in a positively corrected pinion (strengthening it) and decreases in the gear. Measuring tooth thickness (by the chordal method, with a gear-tooth caliper, or over pins) is a classic gear quality-control check. Enter the module.
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