[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-144166-en":3,"doc-seo-144166-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},144166,1374391974585,"Genevieve","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",6,"Technology","Gears - Gear Law - Complete Study Guidebook","Complete study guidebook for understanding gears through copybook notes, extended explanations, diagrams, and progressively leveled practice questions supported by video resources. Covers key vocabulary and core laws such as the fundamental gear law and gear ratio, including direction rules for gear chains and connections on the same axle or via belts. Explores deeper reasoning with pitch circles, derives speed–torque trade-offs, and explains compound gear trains, gear types, real-world efficiency losses, and idler gear design use.","Gears\nA complete study guidebook\nCopybook notes, extended explanations, diagrams, 20 leveled practice questions, and video resources.\n\u000f\nTable of Contents\n\u0003\u0013TOC \\h \\o \"1-3\"\u0014\n\u0015\u0004\n\u000f\nPart 1 — Notes from the copybook\nThis section reproduces exactly what's in the original notes, organized and formatted clearly.\nKey vocabulary\nRPM — rotations per minute\nT — number of teeth\nThe fundamental gear law\nRPM_A · T_A = RPM_B · T_B\nDirection rules (from the notes)\nNumber of gears in a chain = even → different direction (first and last opposite)\nNumber of gears in a chain = odd → same direction (first and last match)\nGear ratio\nG.T. = T_B / T_A = RPM_A / RPM_B\nWorked example from the notes: T_B = 60, T_A = 20 → ratio = 3. Gear B is 3 times slower.\nConnection rules (from the notes)\nOn the same axle/shaft → same direction, same RPM\nCrossbelt → opposite direction\n\u000f\nPart 2 — Going deeper: what the copybook doesn't cover\nThe notes give you the core formulas — here's the reasoning behind them, plus several important ideas that extend the topic further.\nWhy the gear law works: the pitch circle\nEvery gear has an imaginary circle called the pitch circle, where its teeth effectively make contact with the meshing gear. Because two meshed gears touch at this shared point, the linear (tangential) speed of both pitch circles must be identical — otherwise the teeth would jam or slip.\nv = ω · r   (linear speed = angular speed × radius)\nSince v is the same for both gears at the mesh point, a gear with a smaller radius (fewer teeth) must have a higher angular speed (RPM) to match it. This is the physical reason behind RPM_A · T_A = RPM_B · T_B — teeth count is proportional to radius for gears of the same tooth size (module).\nTorque and the speed–torque trade-off\nGears don't just change speed — they also change torque (turning force), in the opposite direction. Ignoring friction losses, power is conserved across a gear mesh:\nTorque_A · RPM_A ≈ Torque_B · RPM_B  (power in ≈ power out)\nThis means whatever ratio you gain in speed, you lose in torque, and vice versa. A gear train that slows rotation down by a factor of 3 multiplies torque by a factor of about 3 (real systems lose a little to friction, so the real gain is slightly less than the ideal ratio).\nSpeed-increasing gear pair (small drives large-to-small direction reversed) → lower output torque, higher output speed\nSpeed-reducing gear pair (small gear drives a big gear) → higher output torque, lower output speed\nThis is exactly why a car uses a low gear to climb a hill (more torque, less speed) and a high gear to cruise on a highway (less torque, more speed).\nCompound gear trains\nA compound gear train uses two or more gears fixed to the same shaft, so that a chain can achieve a much bigger overall ratio in a small physical space than a single mesh could. The overall ratio of a compound train is the product of each individual stage's ratio:\nOverall ratio = (T_B/T_A) × (T_D/T_C) × ...\nThis is how real gearboxes (car transmissions, watch movements, robotics actuators) achieve large speed reductions — stacking several modest ratios in series rather than needing one impractically huge gear.\nTypes of gears\nThe copybook covers the math of meshing gears in general, but doesn't distinguish between the physical types. The four most common are:\nSpur gears — straight teeth, parallel shafts. Simple, efficient, but can be noisy at high speed.\nBevel gears — cone-shaped teeth, used when shafts intersect (commonly at 90°), such as in hand drills or a car's differential.\nWorm gears — a screw-like \"worm\" drives a toothed wheel, giving very large speed reduction and high torque in a compact space; often self-locking (the wheel can't drive the worm backward).\nRack and pinion — a gear (pinion) meshes with a flat toothed bar (rack), converting rotational motion into straight-line motion — used in steering systems.\nEfficiency in real gear systems\nThe formulas in this guide assume ideal, frictionless gears. Real gear systems lose a ","cbCairvHAtSL6zFT","https://ap.wps.com/l/cbCairvHAtSL6zFT","docx",290986,1,11,"English","en",105,"# Part 1 — Notes from the copybook\n## Key vocabulary and fundamental gear law\n## Direction rules and gear ratio\n## Connection rules\n# Part 2 — Going deeper: what the copybook doesn't cover\n## Why the gear law works: the pitch circle\n## Torque and the speed–torque trade-off\n## Compound gear trains and types of gears\n## Efficiency in real gear systems and idler gears\n# Part 3 — Practice questions (easy → expert)","[{\"question\":\"What is the fundamental gear law and how is gear ratio defined?\",\"answer\":\"The fundamental gear law is RPM_A · T_A = RPM_B · T_B. The gear ratio can be written as G.T. = T_B/T_A = RPM_A/RPM_B, linking teeth counts to speed changes.\"},{\"question\":\"How do direction rules work for gear chains and belts?\",\"answer\":\"For a chain with an even number of gears, the first and last gears rotate in opposite directions; with an odd number, they rotate in the same direction. An uncrossed belt keeps both pulleys turning in the same direction, while a crossbelt reverses direction.\"},{\"question\":\"Why do gears trade off speed and torque, and what does compound gear training change?\",\"answer\":\"In idealized form, power is conserved across a mesh, so Torque_A · RPM_A ≈ Torque_B · RPM_B, meaning speed gains reduce torque. Compound gear trains multiply stage ratios to achieve large overall reduction in limited space.\"}]","Gears - Gear Law - Complete Study Guidebook | DOCX",1787698543,28,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"gears-gear-law-complete-study-guidebook","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/technology/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/gears-gear-law-complete-study-guidebook/144166/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/vnd.openxmlformats-officedocument.wordprocessingml.document","2026-08-25",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the fundamental gear law and how is gear ratio defined?","Question",{"text":75,"@type":76},"The fundamental gear law is RPM_A · T_A = RPM_B · T_B. The gear ratio can be written as G.T. = T_B/T_A = RPM_A/RPM_B, linking teeth counts to speed changes.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How do direction rules work for gear chains and belts?",{"text":80,"@type":76},"For a chain with an even number of gears, the first and last gears rotate in opposite directions; with an odd number, they rotate in the same direction. An uncrossed belt keeps both pulleys turning in the same direction, while a crossbelt reverses direction.",{"name":82,"@type":73,"acceptedAnswer":83},"Why do gears trade off speed and torque, and what does compound gear training change?",{"text":84,"@type":76},"In idealized form, power is conserved across a mesh, so Torque_A · RPM_A ≈ Torque_B · RPM_B, meaning speed gains reduce torque. 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