Involute profile and pressure angle<\/title>\n\n <link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n <link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin=\"\">\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=Inter:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\n\n <link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/katex.min.css\">\n <script defer=\"\" src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/katex.min.js\"><\/script>\n <script defer=\"\" src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/contrib\/auto-render.min.js\" onload=\"renderMathInElement(document.body, {\n delimiters: [\n { left: '$$', right: '$$', display: true },\n { left: '$', right: '$', display: false }\n ]\n });\"><\/script>\n\n <style>\n *, *::before, *::after { box-sizing: border-box; margin: 0; padding: 0; }\n\n :root {\n --green: #1a6b3c;\n --green-dark: #0f4a28;\n --green-mid: #2d8a55;\n --green-light: #e8f4ed;\n --green-xlight: #f2faf5;\n --amber: #b45309;\n --amber-light: #fef3c7;\n\n --bg: #ffffff;\n --bg-soft: #f8f9fa;\n --bg-muted: #f1f3f5;\n --border: #e5e7eb;\n --border-mid: #d1d5db;\n\n --text-primary: #111827;\n --text-secondary: #4b5563;\n --text-muted: #9ca3af;\n\n --radius-sm: 6px;\n --radius-md: 8px;\n --radius-lg: 12px;\n --shadow-sm: 0 1px 3px rgba(0,0,0,.06), 0 1px 2px rgba(0,0,0,.04);\n --shadow-md: 0 4px 12px rgba(0,0,0,.08), 0 2px 4px rgba(0,0,0,.04);\n }\n\n body { min-height: 100vh; 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}\n\n .badge {\n display: inline-block;\n font-size: 12px;\n font-weight: 600;\n padding: 2px 8px;\n border-radius: 20px;\n background: var(--green-light);\n color: var(--green-dark);\n }\n\n \/* ============================================================\n RESPONSIVE\n ============================================================ *\/\n @media (max-width: 900px) {\n .article-body { flex-direction: column; padding: 20px 20px 48px; }\n }\n \n \/* Formula blocks *\/\n .formula-block {\n background: var(--bg-soft);\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n padding: 16px 20px;\n margin: 16px 0;\n text-align: center;\n overflow-x: auto;\n }\n .katex { font-size: 1.1em; }\n .formula-block .katex { font-size: 1.25em; }\n .formula-block .katex-display { margin: 0; }\n\n \/* Glossary tooltips *\/\n .glossary-term {\n border-bottom: 1px dotted var(--green);\n color: var(--green);\n font-style: italic;\n cursor: help;\n }\n .glossary-tooltip {\n position: fixed;\n z-index: 9999;\n background: #fff;\n border: 1px solid var(--border-mid);\n border-radius: var(--radius-md);\n box-shadow: var(--shadow-md);\n padding: 10px 14px;\n max-width: 300px;\n font-family: 'Inter', sans-serif;\n font-size: 13px;\n }\n .glossary-tooltip__title {\n font-weight: 600;\n color: var(--text-primary);\n margin-bottom: 4px;\n }\n .glossary-tooltip__def {\n font-size: 12.5px;\n color: var(--text-secondary);\n line-height: 1.6;\n }\n .glossary-tooltip__tag {\n display: inline-block;\n margin-top: 6px;\n font-size: 9px;\n font-weight: 600;\n padding: 2px 7px;\n border-radius: 20px;\n background: var(--green-light);\n color: var(--green-dark);\n text-transform: uppercase;\n letter-spacing: 0.04em;\n }\n\n <\/style>\n<\/head>\n<body>\n\n<div id=\"tt-evolvente\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Involute<\/div>\n <div class=\"glossary-tooltip__def\">Geometric curve defining the tooth flank profile. Generated by unwrapping a straight line that rolls without slipping on a base circle. It ensures a constant transmission ratio even in the presence of small centre-distance errors.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-angolo-di-pressione\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Pressure angle<\/div>\n <div class=\"glossary-tooltip__def\">Angle between the direction of the contact force between mating teeth and the tangent to the pitch circle at the point of contact. The standard value is 20\u00b0.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-gioco-di-flanchi-backlash\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Backlash<\/div>\n <div class=\"glossary-tooltip__def\">Free clearance between the flanks of two mating teeth, measured at the pitch circle. It prevents jamming due to thermal expansion or assembly errors.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-sottotaglio\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Undercut<\/div>\n <div class=\"glossary-tooltip__def\">Unintentional removal of material at the tooth root during profile generation. It occurs with low tooth counts and weakens the root cross-section.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-addendum\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Addendum<\/div>\n <div class=\"glossary-tooltip__def\">Tooth height above the pitch circle. For standard tooth geometry, it equals one module.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-dedendum\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Dedendum<\/div>\n <div class=\"glossary-tooltip__def\">Tooth height below the pitch circle, down to the root circle. For standard tooth geometry, it equals 1.25 modules.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-grado-di-ricoprimento\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Contact ratio<\/div>\n <div class=\"glossary-tooltip__def\">Average number of tooth pairs simultaneously in mesh. Obtained from the ratio of the length of the contact path to the base pitch. A value greater than 1 ensures continuity of motion.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n\n <div class=\"article-page\">\n <div class=\"article-body\">\n <div class=\"article-body__main\"><script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@graph\": [\n {\n \"@type\": \"TechArticle\",\n \"@id\": \"#article\",\n \"headline\": \"Involute profile and pressure angle\",\n \"description\": \"Have you ever disassembled a gear after a failure and found the teeth worn unevenly, with oblique streaks on the flanks? In most cases, the problem isn't the chosen material or the transmitted torque: it's the tooth profile. 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For standard tooth geometry, it equals 1.25 modules.\",\n \"inDefinedTermSet\": \"#glossario\"\n },\n {\n \"@type\": \"DefinedTerm\",\n \"@id\": \"#term-grado-di-ricoprimento\",\n \"name\": \"Contact ratio\",\n \"description\": \"Average number of tooth pairs simultaneously in mesh. Obtained from the ratio of the length of the contact path to the base pitch. A value greater than 1 ensures continuity of motion.\",\n \"inDefinedTermSet\": \"#glossario\"\n }\n ]\n }\n ]\n}\n<\/script>\n\n\n\n <h1 class=\"article__title\">Involute profile and pressure angle<\/h1>\n<p class=\"article__subtitle\">Have you ever disassembled a gear after a failure and found the teeth worn unevenly, with oblique streaks on the flanks? In most cases, the problem isn’t the chosen material or the transmitted torque: it’s <strong>the tooth profile<\/strong>. The geometry with which the teeth touch during rotation determines how much load passes from one flank to the other, how much energy is lost to friction, and how long the gear lasts over time.<\/p>\n<h2 class=\"article__h2\" id=\"the-involute-profile-the-industrial-standard\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><circle cx=\"12\" cy=\"12\" r=\"10\"><\/circle><\/svg><\/span>\n The involute profile: the industrial standard\n<\/h2>\n<p class=\"article__p\">The tooth profile defines the geometric shape of the flank, the surface that comes into contact with the tooth of the opposite wheel. The three main profiles are: <dfn id=\"def-evolvente\"><span class=\"glossary-term\" data-tooltip=\"tt-evolvente\" title=\"Geometric curve defining the tooth flank profile. Generated by unwrapping a straight line that rolls without slipping on a base circle. It ensures a constant transmission ratio even in the presence of small centre-distance errors.\">involute<\/span><\/dfn>, cycloid and special profiles. Almost all industrial transmissions use the involute profile, for three concrete reasons: it is produced with simple tools (rack cutters or straight-profile cutters), it tolerates small variations in center distance without altering the transmission ratio, and it maintains continuous contact between the teeth that reduces vibration and noise.<\/p>\n<p class=\"article__p\">The cycloid profile gives better strength at the tooth root, but requires special curved tools and precise center distances: it is used where precision is the main constraint, such as in watchmaking. Special profiles are designed case by case for custom applications, for example in robotics, where the parameters fall outside the standards.<\/p>\n<div class=\"article__table-wrap\">\n<table class=\"article__table\">\n<thead><tr><th>Characteristic<\/th><th>Involute profile<\/th><th>Cycloid profile<\/th><th>Special profiles<\/th><\/tr><\/thead>\n<tbody><tr><td>Constant transmission ratio<\/td><td>Very high<\/td><td>Sensitive to displacements<\/td><td>Constrained by conditions<\/td><\/tr>\n<tr><td>Tool simplicity<\/td><td>Rack cutters\/straight cutters<\/td><td>Special curved tools<\/td><td>Depends on the formulas<\/td><\/tr>\n<tr><td>Tooth root strength<\/td><td>Good (with adequate module)<\/td><td>Better but more costly<\/td><td>Can be balanced<\/td><\/tr>\n<tr><td>Center distance tolerance<\/td><td>High<\/td><td>Low<\/td><td>Medium<\/td><\/tr>\n<tr><td>Typical application<\/td><td>Industrial transmissions<\/td><td>Watchmaking, precision<\/td><td>Custom robotics<\/td><\/tr><\/tbody>\n<\/table>\n<\/div>\n<h2 class=\"article__h2\" id=\"the-pressure-angle\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><circle cx=\"12\" cy=\"12\" r=\"10\"><\/circle><line x1=\"22\" y1=\"12\" x2=\"18\" y2=\"12\"><\/line><line x1=\"6\" y1=\"12\" x2=\"2\" y2=\"12\"><\/line><line x1=\"12\" y1=\"6\" x2=\"12\" y2=\"2\"><\/line><line x1=\"12\" y1=\"22\" x2=\"12\" y2=\"18\"><\/line><\/svg><\/span>\n The pressure angle\n<\/h2>\n<p class=\"article__p\">The <strong><dfn id=\"def-angolo-di-pressione\"><span class=\"glossary-term\" data-tooltip=\"tt-angolo-di-pressione\" title=\"Angle between the direction of the contact force between mating teeth and the tangent to the pitch circle at the point of contact. The standard value is 20\u00b0.\">pressure angle<\/span><\/dfn><\/strong> is the angle between the direction of the contact force between teeth and the tangent to the pitch circle at the contact point. In more direct terms: it determines how much of the force is transmitted usefully (tangential component, which turns the wheel) and how much generates radial thrust on the supports (component that loads bearings and shafts).<\/p>\n<p class=\"article__p\">The standard values are 14.5\u00b0 and 20\u00b0. The 20\u00b0 is the most used in modern designs. If you work with high loads, small-module teeth or moderate speeds, consider 25\u00b0: it widens the tooth base, increases load capacity, but generates greater radial forces on the supports. Keep this in mind when sizing the bearings.<\/p>\n<h2 class=\"article__h2\" id=\"why-the-involute-profile-works-well-with-technopolymer-gears\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10 2v7.527a2 2 0 0 1-.211.896L4.72 20.55a1 1 0 0 0 .9 1.45h12.76a1 1 0 0 0 .9-1.45l-5.069-10.127A2 2 0 0 1 14 9.527V2\"><\/path><path d=\"M8.5 2h7\"><\/path><path d=\"M7 16h10\"><\/path><\/svg><\/span>\n Why the involute profile works well with technopolymer gears\n<\/h2>\n<p class=\"article__p\">Technopolymer gears, such as those in PA, POM-C or PK, offer light weight, corrosion resistance and quiet operation. The involute profile pairs well with these materials for a precise geometric reason: the contact point moves along the line of action, a fixed straight line, which concentrates contact in the pitch-circle zone. At that point, sliding between the flanks is minimal and friction is lower.<\/p>\n<p class=\"article__p\">This is particularly useful with technopolymers, which can deform slightly under load. The involute profile absorbs these deformations better than other profiles, keeping meshing more regular.<\/p>\n<div class=\"infobox infobox--grey\">\n <div class=\"infobox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M14.7 6.3a1 1 0 0 0 0 1.4l1.6 1.6a1 1 0 0 0 1.4 0l3.77-3.77a6 6 0 0 1-7.94 7.94l-6.91 6.91a2.12 2.12 0 0 1-3-3l6.91-6.91a6 6 0 0 1 7.94-7.94l-3.76 3.76z\"><\/path><\/svg>\n Technical note\n <\/div>\n <p class=\"infobox__text\">The friction coefficient in technopolymer\/technopolymer or technopolymer\/metal pairings, such as GF-filled PA on steel, generally falls between 0.2 and 0.5. The use of anti-friction fillers (PTFE, MoS\u2082) shifts the value toward the lower limit. Always check the material supplier’s data, because the coefficient also depends on speed and contact pressure.<\/p>\n<\/div>\n<h2 class=\"article__h2\" id=\"when-to-choose-the-involute-profile\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><polyline points=\"9 11 12 14 22 4\"><\/polyline><path d=\"M21 12v7a2 2 0 0 1-2 2H5a2 2 0 0 1-2-2V5a2 2 0 0 1 2-2h11\"><\/path><\/svg><\/span>\n When to choose the involute profile\n<\/h2>\n<p class=\"article__p\">The involute profile is generally the right choice when:<\/p>\n<ul class=\"article__list\">\n <li>The application involves dry running, without lubrication<\/li>\n <li>The environment is chemically aggressive (paired with high chemical-resistance technopolymers)<\/li>\n <li>Noise is a design constraint (robotics, medical devices, packaging)<\/li>\n <li>You want a self-centering system with minimal <dfn id=\"def-gioco-di-flanchi-backlash\"><span class=\"glossary-term\" data-tooltip=\"tt-gioco-di-flanchi-backlash\" title=\"Free clearance between the flanks of two mating teeth, measured at the pitch circle. It prevents jamming due to thermal expansion or assembly errors.\">backlash<\/span><\/dfn><\/li>\n <li>Speed is medium-high with moderate loads<\/li>\n<\/ul>\n<h2 class=\"article__h2\" id=\"dimensional-accuracy-and-iso-quality\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M21.3 8.7 8.7 21.3c-1 1-2.5 1-3.4 0l-2.6-2.6c-1-1-1-2.5 0-3.4L15.3 2.7c1-1 2.5-1 3.4 0l2.6 2.6c1 1 1 2.5 0 3.4Z\"><\/path><path d=\"m7.5 10.5 2 2\"><\/path><path d=\"m10.5 7.5 2 2\"><\/path><path d=\"m13.5 4.5 2 2\"><\/path><path d=\"m4.5 13.5 2 2\"><\/path><\/svg><\/span>\n Dimensional accuracy and ISO quality\n<\/h2>\n<p class=\"article__p\">The involute profile works well only if it is made well. Standard <strong>ISO 1328-1<\/strong> classifies gear quality on a scale from 0 to 12, where lower values correspond to greater precision.<\/p>\n<p class=\"article__p\">For standard industrial mechanisms, ISO 6-7 (equivalent to AGMA Q8-Q9) is the common reference. For precision automation and medical applications, ISO 4-5 is required.<\/p>\n<div class=\"article__table-wrap\">\n<table class=\"article__table\">\n<thead><tr><th>Machining method<\/th><th>Typical tolerances<\/th><th>Achievable quality<\/th><\/tr><\/thead>\n<tbody><tr><td>CNC on technopolymers<\/td><td>$\\pm0.025-0.05 \\; \\text{mm}$<\/td><td>Q8-Q9<\/td><\/tr>\n<tr><td>Critical CNC<\/td><td>$\\pm0.005-0.01 \\; \\text{mm}$<\/td><td>Q4-Q6<\/td><\/tr>\n<tr><td>Standard injection molding<\/td><td>$\\pm0.05-0.1 \\; \\text{mm}$<\/td><td>Q10-Q12<\/td><\/tr>\n<tr><td>High-precision molding<\/td><td>$\\pm0.02-0.05 \\; \\text{mm}$<\/td><td>Q8-Q10<\/td><\/tr><\/tbody>\n<\/table>\n<\/div>\n<p class=\"article__p\">CNC and injection molding cover different needs. CNC allows tight tolerances on the single part, suited to prototypes, small runs and critical profiles, with a direct effect on backlash (the gap between tooth flanks at rest) and meshing quality. Injection molding is more cost-effective on large volumes and, on reinforced materials, orients the fibers along the tooth geometry to the benefit of strength; keep in mind that shrinkage and thermal deformation affect the final tolerances, to be verified after molding with the same instrumentation as CNC.<\/p>\n<div class=\"warnbox\">\n <div class=\"warnbox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg>\n Warning\n <\/div>\n <p class=\"warnbox__text\">Verifying the involute profile requires dedicated instruments: involute testers, profilometers, coordinate measuring machines (CMM) and optical scanners. A generic diameter measurement is not enough to certify profile quality.<\/p>\n<\/div>\n<h2 class=\"article__h2\" id=\"key-parameters-for-design\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><rect x=\"2\" y=\"2\" width=\"20\" height=\"20\" rx=\"2\" ry=\"2\"><\/rect><line x1=\"8\" y1=\"6\" x2=\"16\" y2=\"6\"><\/line><line x1=\"8\" y1=\"10\" x2=\"14\" y2=\"10\"><\/line><line x1=\"8\" y1=\"14\" x2=\"16\" y2=\"14\"><\/line><line x1=\"8\" y1=\"18\" x2=\"12\" y2=\"18\"><\/line><\/svg><\/span>\n Key parameters for design\n<\/h2>\n<p class=\"article__p\">The module is the parameter that defines tooth size. Two gears can mesh only if they have the same module, exactly like screws and nuts: you don’t mix different sizes. The fundamental relation is: <strong>d = m \u00d7 Z<\/strong>, where d is the pitch-circle diameter, m the module and Z the number of teeth.<\/p>\n<p class=\"article__p\">As a starting point for sizing:<\/p>\n<ul class=\"article__list\">\n <li>Use a 20\u00b0 pressure angle as the default<\/li>\n <li>Switch to 25\u00b0 for high loads, small teeth or moderate speeds<\/li>\n <li>For light-to-medium applications, module from 1 to 5 mm; larger modules for industrial loads<\/li>\n <li>Respect a minimum tooth count of 17 with a 20\u00b0 pressure angle, to avoid <strong><dfn id=\"def-sottotaglio\"><span class=\"glossary-term\" data-tooltip=\"tt-sottotaglio\" title=\"Unintentional removal of material at the tooth root during profile generation. It occurs with low tooth counts and weakens the root cross-section.\">undercut<\/span><\/dfn><\/strong> (interference at the tooth base that reduces its strength). If you go below this value, use profile shift<\/li>\n<\/ul>\n<p class=\"article__p\">The standard tooth height has an <dfn id=\"def-addendum\"><span class=\"glossary-term\" data-tooltip=\"tt-addendum\" title=\"Tooth height above the pitch circle. For standard tooth geometry, it equals one module.\">addendum<\/span><\/dfn> equal to the module and a <dfn id=\"def-dedendum\"><span class=\"glossary-term\" data-tooltip=\"tt-dedendum\" title=\"Tooth height below the pitch circle, down to the root circle. For standard tooth geometry, it equals 1.25 modules.\">dedendum<\/span><\/dfn> equal to 1.25 times the module. The fillet at the tooth root must be sized to avoid stress concentrations, especially in technopolymers where fatigue strength is lower than in steels.<\/p>\n<div class=\"infobox infobox--grey\">\n <div class=\"infobox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><line x1=\"9\" y1=\"18\" x2=\"15\" y2=\"18\"><\/line><line x1=\"10\" y1=\"22\" x2=\"14\" y2=\"22\"><\/line><path d=\"M15.09 14c.18-.98.65-1.74 1.41-2.5A4.65 4.65 0 0 0 18 8 6 6 0 0 0 6 8c0 1 .23 2.23 1.5 3.5A4.61 4.61 0 0 1 8.91 14\"><\/path><\/svg>\n From the field\n <\/div>\n <p class=\"infobox__text\"><strong>Always account for moisture absorption when defining backlash.<\/strong> A gear designed with textbook clearances, fitted in a humid environment and subject to cyclic temperature swings, can seize. In our experience, it’s one of the most frequent problems on systems that run correctly in dry tests and then fail in production.<\/p>\n<\/div>\n<h2 class=\"article__h2\" id=\"when-to-modify-the-standard-profile\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><circle cx=\"18\" cy=\"18\" r=\"3\"><\/circle><circle cx=\"6\" cy=\"6\" r=\"3\"><\/circle><path d=\"M13 6h3a2 2 0 0 1 2 2v7\"><\/path><path d=\"M11 18H8a2 2 0 0 1-2-2V9\"><\/path><path d=\"m8 9-2 2 2 2\"><\/path><\/svg><\/span>\n When to modify the standard profile\n<\/h2>\n<p class=\"article__p\">Modifications to the standard profile become necessary in certain specific cases:<\/p>\n<ul class=\"article__list\">\n <li>Tooth count below the minimum (undercut to be avoided with profile shift)<\/li>\n <li>Elastic deformation of the technopolymer under load that alters meshing<\/li>\n <li>Non-standard center distance imposed by the mechanical design<\/li>\n <li>High quietness requirements or <dfn id=\"def-grado-di-ricoprimento\"><span class=\"glossary-term\" data-tooltip=\"tt-grado-di-ricoprimento\" title=\"Average number of tooth pairs simultaneously in mesh. Obtained from the ratio of the length of the contact path to the base pitch. A value greater than 1 ensures continuity of motion.\">contact ratio<\/span><\/dfn> greater than 1.4<\/li>\n<\/ul>\n<p class=\"article__p\">These measures improve the durability, precision and function of technopolymer gears, providing an adequate response even under demanding operating conditions.<\/p>\n<p class=\"article__p\">If you’re designing with CAD, the 3D models of Stagnoli gears are available on <a href=\"https:\/\/www.traceparts.com\/it\/search\/stagnoli?CatalogPath=STAGNOLI%3AF_STAGNOLI\" target=\"_blank\" rel=\"noopener\" class=\"cta-link\">TraceParts<\/a>: you can download the geometry you need directly and integrate it into your project.<\/p>\n<div class=\"infobox\">\n <div class=\"infobox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M4 4h16c1.1 0 2 .9 2 2v12c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V6c0-1.1.9-2 2-2z\"><\/path><polyline points=\"22,6 12,13 2,6\"><\/polyline><\/svg>\n Ask us\n <\/div>\n <p class=\"infobox__text\">If your operating conditions fall outside the standard parameters, or you have doubts about the most suitable profile for your application, <a href=\"https:\/\/shop.stagnoligears.com\/en\/contacts\/\" target=\"_blank\" rel=\"noopener\" class=\"cta-link\">write<\/a> to the technical office: we’ll assess the right configuration together.<\/p>\n<\/div>\n\n <\/div>\n <\/div>\n <\/div>\n\n\n<script>\n (function () {\n var hideTimers = {};\n function positionTooltip(trigger, tooltip) {\n var margin = 8;\n tooltip.style.visibility = 'hidden';\n tooltip.style.top = '-9999px';\n tooltip.style.left = '-9999px';\n tooltip.removeAttribute('hidden');\n var ttRect = tooltip.getBoundingClientRect();\n var trRect = trigger.getBoundingClientRect();\n var vw = window.innerWidth, vh = window.innerHeight;\n var top = trRect.bottom + margin;\n var left = 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time.<\/p>\n","protected":false},"parent":0,"template":"","meta":{"_acf_changed":false},"campo-applicazione":[5453],"categoria-ct":[5442],"class_list":["post-25556","centro-tecnico","type-centro-tecnico","status-publish","hentry","campo-applicazione-geometry","categoria-ct-gear-fundamentals"],"acf":[],"yoast_head":"\n<title>Involute Profile and Pressure Angle | Stagnoli Gears Shop<\/title>\n<meta name=\"description\" content=\"Learn how the involute profile and pressure angle affect gear meshing, load transmission, friction, compatibility and long-term gear durability.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/shop.stagnoligears.com\/en\/technical-hub\/involute-profile-and-pressure-angle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Involute Profile and Pressure 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{"id":25556,"date":"2026-06-26T14:27:00","date_gmt":"2026-06-26T12:27:00","guid":{"rendered":"https:\/\/shop.stagnoligears.com\/?post_type=centro-tecnico&p=25556"},"modified":"2026-07-10T14:40:30","modified_gmt":"2026-07-10T12:40:30","slug":"involute-profile-and-pressure-angle","status":"publish","type":"centro-tecnico","link":"https:\/\/shop.stagnoligears.com\/en\/technical-hub\/involute-profile-and-pressure-angle\/","title":{"rendered":"Involute profile and pressure angle"},"content":{"rendered":"\n\n \n \n \n Involute profile and pressure angle<\/title>\n\n <link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n <link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin=\"\">\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=Inter:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\n\n <link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/katex.min.css\">\n <script defer=\"\" src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/katex.min.js\"><\/script>\n <script defer=\"\" src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/contrib\/auto-render.min.js\" onload=\"renderMathInElement(document.body, {\n delimiters: [\n { left: '$$', right: '$$', display: true },\n { left: '$', right: '$', display: false }\n ]\n });\"><\/script>\n\n <style>\n *, *::before, *::after { box-sizing: border-box; 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}\n\n .badge {\n display: inline-block;\n font-size: 12px;\n font-weight: 600;\n padding: 2px 8px;\n border-radius: 20px;\n background: var(--green-light);\n color: var(--green-dark);\n }\n\n \/* ============================================================\n RESPONSIVE\n ============================================================ *\/\n @media (max-width: 900px) {\n .article-body { flex-direction: column; padding: 20px 20px 48px; }\n }\n \n \/* Formula blocks *\/\n .formula-block {\n background: var(--bg-soft);\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n padding: 16px 20px;\n margin: 16px 0;\n text-align: center;\n overflow-x: auto;\n }\n .katex { font-size: 1.1em; }\n .formula-block .katex { font-size: 1.25em; }\n .formula-block .katex-display { margin: 0; }\n\n \/* Glossary tooltips *\/\n .glossary-term {\n border-bottom: 1px dotted var(--green);\n color: var(--green);\n font-style: italic;\n cursor: help;\n }\n .glossary-tooltip {\n position: fixed;\n z-index: 9999;\n background: #fff;\n border: 1px solid var(--border-mid);\n border-radius: var(--radius-md);\n box-shadow: var(--shadow-md);\n padding: 10px 14px;\n max-width: 300px;\n font-family: 'Inter', sans-serif;\n font-size: 13px;\n }\n .glossary-tooltip__title {\n font-weight: 600;\n color: var(--text-primary);\n margin-bottom: 4px;\n }\n .glossary-tooltip__def {\n font-size: 12.5px;\n color: var(--text-secondary);\n line-height: 1.6;\n }\n .glossary-tooltip__tag {\n display: inline-block;\n margin-top: 6px;\n font-size: 9px;\n font-weight: 600;\n padding: 2px 7px;\n border-radius: 20px;\n background: var(--green-light);\n color: var(--green-dark);\n text-transform: uppercase;\n letter-spacing: 0.04em;\n }\n\n <\/style>\n<\/head>\n<body>\n\n<div id=\"tt-evolvente\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Involute<\/div>\n <div class=\"glossary-tooltip__def\">Geometric curve defining the tooth flank profile. Generated by unwrapping a straight line that rolls without slipping on a base circle. It ensures a constant transmission ratio even in the presence of small centre-distance errors.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-angolo-di-pressione\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Pressure angle<\/div>\n <div class=\"glossary-tooltip__def\">Angle between the direction of the contact force between mating teeth and the tangent to the pitch circle at the point of contact. The standard value is 20\u00b0.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-gioco-di-flanchi-backlash\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Backlash<\/div>\n <div class=\"glossary-tooltip__def\">Free clearance between the flanks of two mating teeth, measured at the pitch circle. It prevents jamming due to thermal expansion or assembly errors.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-sottotaglio\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Undercut<\/div>\n <div class=\"glossary-tooltip__def\">Unintentional removal of material at the tooth root during profile generation. It occurs with low tooth counts and weakens the root cross-section.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-addendum\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Addendum<\/div>\n <div class=\"glossary-tooltip__def\">Tooth height above the pitch circle. For standard tooth geometry, it equals one module.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-dedendum\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Dedendum<\/div>\n <div class=\"glossary-tooltip__def\">Tooth height below the pitch circle, down to the root circle. For standard tooth geometry, it equals 1.25 modules.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-grado-di-ricoprimento\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Contact ratio<\/div>\n <div class=\"glossary-tooltip__def\">Average number of tooth pairs simultaneously in mesh. Obtained from the ratio of the length of the contact path to the base pitch. A value greater than 1 ensures continuity of motion.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n\n <div class=\"article-page\">\n <div class=\"article-body\">\n <div class=\"article-body__main\"><script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@graph\": [\n {\n \"@type\": \"TechArticle\",\n \"@id\": \"#article\",\n \"headline\": \"Involute profile and pressure angle\",\n \"description\": \"Have you ever disassembled a gear after a failure and found the teeth worn unevenly, with oblique streaks on the flanks? In most cases, the problem isn't the chosen material or the transmitted torque: it's the tooth profile. 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For standard tooth geometry, it equals 1.25 modules.\",\n \"inDefinedTermSet\": \"#glossario\"\n },\n {\n \"@type\": \"DefinedTerm\",\n \"@id\": \"#term-grado-di-ricoprimento\",\n \"name\": \"Contact ratio\",\n \"description\": \"Average number of tooth pairs simultaneously in mesh. Obtained from the ratio of the length of the contact path to the base pitch. A value greater than 1 ensures continuity of motion.\",\n \"inDefinedTermSet\": \"#glossario\"\n }\n ]\n }\n ]\n}\n<\/script>\n\n\n\n <h1 class=\"article__title\">Involute profile and pressure angle<\/h1>\n<p class=\"article__subtitle\">Have you ever disassembled a gear after a failure and found the teeth worn unevenly, with oblique streaks on the flanks? In most cases, the problem isn’t the chosen material or the transmitted torque: it’s <strong>the tooth profile<\/strong>. The geometry with which the teeth touch during rotation determines how much load passes from one flank to the other, how much energy is lost to friction, and how long the gear lasts over time.<\/p>\n<h2 class=\"article__h2\" id=\"the-involute-profile-the-industrial-standard\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><circle cx=\"12\" cy=\"12\" r=\"10\"><\/circle><\/svg><\/span>\n The involute profile: the industrial standard\n<\/h2>\n<p class=\"article__p\">The tooth profile defines the geometric shape of the flank, the surface that comes into contact with the tooth of the opposite wheel. The three main profiles are: <dfn id=\"def-evolvente\"><span class=\"glossary-term\" data-tooltip=\"tt-evolvente\" title=\"Geometric curve defining the tooth flank profile. Generated by unwrapping a straight line that rolls without slipping on a base circle. It ensures a constant transmission ratio even in the presence of small centre-distance errors.\">involute<\/span><\/dfn>, cycloid and special profiles. Almost all industrial transmissions use the involute profile, for three concrete reasons: it is produced with simple tools (rack cutters or straight-profile cutters), it tolerates small variations in center distance without altering the transmission ratio, and it maintains continuous contact between the teeth that reduces vibration and noise.<\/p>\n<p class=\"article__p\">The cycloid profile gives better strength at the tooth root, but requires special curved tools and precise center distances: it is used where precision is the main constraint, such as in watchmaking. Special profiles are designed case by case for custom applications, for example in robotics, where the parameters fall outside the standards.<\/p>\n<div class=\"article__table-wrap\">\n<table class=\"article__table\">\n<thead><tr><th>Characteristic<\/th><th>Involute profile<\/th><th>Cycloid profile<\/th><th>Special profiles<\/th><\/tr><\/thead>\n<tbody><tr><td>Constant transmission ratio<\/td><td>Very high<\/td><td>Sensitive to displacements<\/td><td>Constrained by conditions<\/td><\/tr>\n<tr><td>Tool simplicity<\/td><td>Rack cutters\/straight cutters<\/td><td>Special curved tools<\/td><td>Depends on the formulas<\/td><\/tr>\n<tr><td>Tooth root strength<\/td><td>Good (with adequate module)<\/td><td>Better but more costly<\/td><td>Can be balanced<\/td><\/tr>\n<tr><td>Center distance tolerance<\/td><td>High<\/td><td>Low<\/td><td>Medium<\/td><\/tr>\n<tr><td>Typical application<\/td><td>Industrial transmissions<\/td><td>Watchmaking, precision<\/td><td>Custom robotics<\/td><\/tr><\/tbody>\n<\/table>\n<\/div>\n<h2 class=\"article__h2\" id=\"the-pressure-angle\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><circle cx=\"12\" cy=\"12\" r=\"10\"><\/circle><line x1=\"22\" y1=\"12\" x2=\"18\" y2=\"12\"><\/line><line x1=\"6\" y1=\"12\" x2=\"2\" y2=\"12\"><\/line><line x1=\"12\" y1=\"6\" x2=\"12\" y2=\"2\"><\/line><line x1=\"12\" y1=\"22\" x2=\"12\" y2=\"18\"><\/line><\/svg><\/span>\n The pressure angle\n<\/h2>\n<p class=\"article__p\">The <strong><dfn id=\"def-angolo-di-pressione\"><span class=\"glossary-term\" data-tooltip=\"tt-angolo-di-pressione\" title=\"Angle between the direction of the contact force between mating teeth and the tangent to the pitch circle at the point of contact. The standard value is 20\u00b0.\">pressure angle<\/span><\/dfn><\/strong> is the angle between the direction of the contact force between teeth and the tangent to the pitch circle at the contact point. In more direct terms: it determines how much of the force is transmitted usefully (tangential component, which turns the wheel) and how much generates radial thrust on the supports (component that loads bearings and shafts).<\/p>\n<p class=\"article__p\">The standard values are 14.5\u00b0 and 20\u00b0. The 20\u00b0 is the most used in modern designs. If you work with high loads, small-module teeth or moderate speeds, consider 25\u00b0: it widens the tooth base, increases load capacity, but generates greater radial forces on the supports. Keep this in mind when sizing the bearings.<\/p>\n<h2 class=\"article__h2\" id=\"why-the-involute-profile-works-well-with-technopolymer-gears\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10 2v7.527a2 2 0 0 1-.211.896L4.72 20.55a1 1 0 0 0 .9 1.45h12.76a1 1 0 0 0 .9-1.45l-5.069-10.127A2 2 0 0 1 14 9.527V2\"><\/path><path d=\"M8.5 2h7\"><\/path><path d=\"M7 16h10\"><\/path><\/svg><\/span>\n Why the involute profile works well with technopolymer gears\n<\/h2>\n<p class=\"article__p\">Technopolymer gears, such as those in PA, POM-C or PK, offer light weight, corrosion resistance and quiet operation. The involute profile pairs well with these materials for a precise geometric reason: the contact point moves along the line of action, a fixed straight line, which concentrates contact in the pitch-circle zone. At that point, sliding between the flanks is minimal and friction is lower.<\/p>\n<p class=\"article__p\">This is particularly useful with technopolymers, which can deform slightly under load. The involute profile absorbs these deformations better than other profiles, keeping meshing more regular.<\/p>\n<div class=\"infobox infobox--grey\">\n <div class=\"infobox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M14.7 6.3a1 1 0 0 0 0 1.4l1.6 1.6a1 1 0 0 0 1.4 0l3.77-3.77a6 6 0 0 1-7.94 7.94l-6.91 6.91a2.12 2.12 0 0 1-3-3l6.91-6.91a6 6 0 0 1 7.94-7.94l-3.76 3.76z\"><\/path><\/svg>\n Technical note\n <\/div>\n <p class=\"infobox__text\">The friction coefficient in technopolymer\/technopolymer or technopolymer\/metal pairings, such as GF-filled PA on steel, generally falls between 0.2 and 0.5. The use of anti-friction fillers (PTFE, MoS\u2082) shifts the value toward the lower limit. Always check the material supplier’s data, because the coefficient also depends on speed and contact pressure.<\/p>\n<\/div>\n<h2 class=\"article__h2\" id=\"when-to-choose-the-involute-profile\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><polyline points=\"9 11 12 14 22 4\"><\/polyline><path d=\"M21 12v7a2 2 0 0 1-2 2H5a2 2 0 0 1-2-2V5a2 2 0 0 1 2-2h11\"><\/path><\/svg><\/span>\n When to choose the involute profile\n<\/h2>\n<p class=\"article__p\">The involute profile is generally the right choice when:<\/p>\n<ul class=\"article__list\">\n <li>The application involves dry running, without lubrication<\/li>\n <li>The environment is chemically aggressive (paired with high chemical-resistance technopolymers)<\/li>\n <li>Noise is a design constraint (robotics, medical devices, packaging)<\/li>\n <li>You want a self-centering system with minimal <dfn id=\"def-gioco-di-flanchi-backlash\"><span class=\"glossary-term\" data-tooltip=\"tt-gioco-di-flanchi-backlash\" title=\"Free clearance between the flanks of two mating teeth, measured at the pitch circle. It prevents jamming due to thermal expansion or assembly errors.\">backlash<\/span><\/dfn><\/li>\n <li>Speed is medium-high with moderate loads<\/li>\n<\/ul>\n<h2 class=\"article__h2\" id=\"dimensional-accuracy-and-iso-quality\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M21.3 8.7 8.7 21.3c-1 1-2.5 1-3.4 0l-2.6-2.6c-1-1-1-2.5 0-3.4L15.3 2.7c1-1 2.5-1 3.4 0l2.6 2.6c1 1 1 2.5 0 3.4Z\"><\/path><path d=\"m7.5 10.5 2 2\"><\/path><path d=\"m10.5 7.5 2 2\"><\/path><path d=\"m13.5 4.5 2 2\"><\/path><path d=\"m4.5 13.5 2 2\"><\/path><\/svg><\/span>\n Dimensional accuracy and ISO quality\n<\/h2>\n<p class=\"article__p\">The involute profile works well only if it is made well. Standard <strong>ISO 1328-1<\/strong> classifies gear quality on a scale from 0 to 12, where lower values correspond to greater precision.<\/p>\n<p class=\"article__p\">For standard industrial mechanisms, ISO 6-7 (equivalent to AGMA Q8-Q9) is the common reference. For precision automation and medical applications, ISO 4-5 is required.<\/p>\n<div class=\"article__table-wrap\">\n<table class=\"article__table\">\n<thead><tr><th>Machining method<\/th><th>Typical tolerances<\/th><th>Achievable quality<\/th><\/tr><\/thead>\n<tbody><tr><td>CNC on technopolymers<\/td><td>$\\pm0.025-0.05 \\; \\text{mm}$<\/td><td>Q8-Q9<\/td><\/tr>\n<tr><td>Critical CNC<\/td><td>$\\pm0.005-0.01 \\; \\text{mm}$<\/td><td>Q4-Q6<\/td><\/tr>\n<tr><td>Standard injection molding<\/td><td>$\\pm0.05-0.1 \\; \\text{mm}$<\/td><td>Q10-Q12<\/td><\/tr>\n<tr><td>High-precision molding<\/td><td>$\\pm0.02-0.05 \\; \\text{mm}$<\/td><td>Q8-Q10<\/td><\/tr><\/tbody>\n<\/table>\n<\/div>\n<p class=\"article__p\">CNC and injection molding cover different needs. CNC allows tight tolerances on the single part, suited to prototypes, small runs and critical profiles, with a direct effect on backlash (the gap between tooth flanks at rest) and meshing quality. Injection molding is more cost-effective on large volumes and, on reinforced materials, orients the fibers along the tooth geometry to the benefit of strength; keep in mind that shrinkage and thermal deformation affect the final tolerances, to be verified after molding with the same instrumentation as CNC.<\/p>\n<div class=\"warnbox\">\n <div class=\"warnbox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg>\n Warning\n <\/div>\n <p class=\"warnbox__text\">Verifying the involute profile requires dedicated instruments: involute testers, profilometers, coordinate measuring machines (CMM) and optical scanners. A generic diameter measurement is not enough to certify profile quality.<\/p>\n<\/div>\n<h2 class=\"article__h2\" id=\"key-parameters-for-design\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><rect x=\"2\" y=\"2\" width=\"20\" height=\"20\" rx=\"2\" ry=\"2\"><\/rect><line x1=\"8\" y1=\"6\" x2=\"16\" y2=\"6\"><\/line><line x1=\"8\" y1=\"10\" x2=\"14\" y2=\"10\"><\/line><line x1=\"8\" y1=\"14\" x2=\"16\" y2=\"14\"><\/line><line x1=\"8\" y1=\"18\" x2=\"12\" y2=\"18\"><\/line><\/svg><\/span>\n Key parameters for design\n<\/h2>\n<p class=\"article__p\">The module is the parameter that defines tooth size. Two gears can mesh only if they have the same module, exactly like screws and nuts: you don’t mix different sizes. The fundamental relation is: <strong>d = m \u00d7 Z<\/strong>, where d is the pitch-circle diameter, m the module and Z the number of teeth.<\/p>\n<p class=\"article__p\">As a starting point for sizing:<\/p>\n<ul class=\"article__list\">\n <li>Use a 20\u00b0 pressure angle as the default<\/li>\n <li>Switch to 25\u00b0 for high loads, small teeth or moderate speeds<\/li>\n <li>For light-to-medium applications, module from 1 to 5 mm; larger modules for industrial loads<\/li>\n <li>Respect a minimum tooth count of 17 with a 20\u00b0 pressure angle, to avoid <strong><dfn id=\"def-sottotaglio\"><span class=\"glossary-term\" data-tooltip=\"tt-sottotaglio\" title=\"Unintentional removal of material at the tooth root during profile generation. It occurs with low tooth counts and weakens the root cross-section.\">undercut<\/span><\/dfn><\/strong> (interference at the tooth base that reduces its strength). If you go below this value, use profile shift<\/li>\n<\/ul>\n<p class=\"article__p\">The standard tooth height has an <dfn id=\"def-addendum\"><span class=\"glossary-term\" data-tooltip=\"tt-addendum\" title=\"Tooth height above the pitch circle. For standard tooth geometry, it equals one module.\">addendum<\/span><\/dfn> equal to the module and a <dfn id=\"def-dedendum\"><span class=\"glossary-term\" data-tooltip=\"tt-dedendum\" title=\"Tooth height below the pitch circle, down to the root circle. For standard tooth geometry, it equals 1.25 modules.\">dedendum<\/span><\/dfn> equal to 1.25 times the module. The fillet at the tooth root must be sized to avoid stress concentrations, especially in technopolymers where fatigue strength is lower than in steels.<\/p>\n<div class=\"infobox infobox--grey\">\n <div class=\"infobox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><line x1=\"9\" y1=\"18\" x2=\"15\" y2=\"18\"><\/line><line x1=\"10\" y1=\"22\" x2=\"14\" y2=\"22\"><\/line><path d=\"M15.09 14c.18-.98.65-1.74 1.41-2.5A4.65 4.65 0 0 0 18 8 6 6 0 0 0 6 8c0 1 .23 2.23 1.5 3.5A4.61 4.61 0 0 1 8.91 14\"><\/path><\/svg>\n From the field\n <\/div>\n <p class=\"infobox__text\"><strong>Always account for moisture absorption when defining backlash.<\/strong> A gear designed with textbook clearances, fitted in a humid environment and subject to cyclic temperature swings, can seize. In our experience, it’s one of the most frequent problems on systems that run correctly in dry tests and then fail in production.<\/p>\n<\/div>\n<h2 class=\"article__h2\" id=\"when-to-modify-the-standard-profile\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><circle cx=\"18\" cy=\"18\" r=\"3\"><\/circle><circle cx=\"6\" cy=\"6\" r=\"3\"><\/circle><path d=\"M13 6h3a2 2 0 0 1 2 2v7\"><\/path><path d=\"M11 18H8a2 2 0 0 1-2-2V9\"><\/path><path d=\"m8 9-2 2 2 2\"><\/path><\/svg><\/span>\n When to modify the standard profile\n<\/h2>\n<p class=\"article__p\">Modifications to the standard profile become necessary in certain specific cases:<\/p>\n<ul class=\"article__list\">\n <li>Tooth count below the minimum (undercut to be avoided with profile shift)<\/li>\n <li>Elastic deformation of the technopolymer under load that alters meshing<\/li>\n <li>Non-standard center distance imposed by the mechanical design<\/li>\n <li>High quietness requirements or <dfn id=\"def-grado-di-ricoprimento\"><span class=\"glossary-term\" data-tooltip=\"tt-grado-di-ricoprimento\" title=\"Average number of tooth pairs simultaneously in mesh. Obtained from the ratio of the length of the contact path to the base pitch. A value greater than 1 ensures continuity of motion.\">contact ratio<\/span><\/dfn> greater than 1.4<\/li>\n<\/ul>\n<p class=\"article__p\">These measures improve the durability, precision and function of technopolymer gears, providing an adequate response even under demanding operating conditions.<\/p>\n<p class=\"article__p\">If you’re designing with CAD, the 3D models of Stagnoli gears are available on <a href=\"https:\/\/www.traceparts.com\/it\/search\/stagnoli?CatalogPath=STAGNOLI%3AF_STAGNOLI\" target=\"_blank\" rel=\"noopener\" class=\"cta-link\">TraceParts<\/a>: you can download the geometry you need directly and integrate it into your project.<\/p>\n<div class=\"infobox\">\n <div class=\"infobox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M4 4h16c1.1 0 2 .9 2 2v12c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V6c0-1.1.9-2 2-2z\"><\/path><polyline points=\"22,6 12,13 2,6\"><\/polyline><\/svg>\n Ask us\n <\/div>\n <p class=\"infobox__text\">If your operating conditions fall outside the standard parameters, or you have doubts about the most suitable profile for your application, <a href=\"https:\/\/shop.stagnoligears.com\/en\/contacts\/\" target=\"_blank\" rel=\"noopener\" class=\"cta-link\">write<\/a> to the technical office: we’ll assess the right configuration together.<\/p>\n<\/div>\n\n <\/div>\n <\/div>\n <\/div>\n\n\n<script>\n (function () {\n var hideTimers = {};\n function positionTooltip(trigger, tooltip) {\n var margin = 8;\n tooltip.style.visibility = 'hidden';\n tooltip.style.top = '-9999px';\n tooltip.style.left = '-9999px';\n tooltip.removeAttribute('hidden');\n var ttRect = tooltip.getBoundingClientRect();\n var trRect = trigger.getBoundingClientRect();\n var vw = window.innerWidth, vh = window.innerHeight;\n var top = trRect.bottom + margin;\n var left = 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time.<\/p>\n","protected":false},"parent":0,"template":"","meta":{"_acf_changed":false},"campo-applicazione":[5453],"categoria-ct":[5442],"class_list":["post-25556","centro-tecnico","type-centro-tecnico","status-publish","hentry","campo-applicazione-geometry","categoria-ct-gear-fundamentals"],"acf":[],"yoast_head":"\n<title>Involute Profile and Pressure Angle | Stagnoli Gears Shop<\/title>\n<meta name=\"description\" content=\"Learn how the involute profile and pressure angle affect gear meshing, load transmission, friction, compatibility and long-term gear durability.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/shop.stagnoligears.com\/en\/technical-hub\/involute-profile-and-pressure-angle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Involute Profile and Pressure 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