{"action":"created","issue":{"url":"https://api.github.com/repos/40223114/2015_g4/issues/6","labels_url":"https://api.github.com/repos/40223114/2015_g4/issues/6/labels{/name}","comments_url":"https://api.github.com/repos/40223114/2015_g4/issues/6/comments","events_url":"https://api.github.com/repos/40223114/2015_g4/issues/6/events","html_url":"https://github.com/40223114/2015_g4/issues/6","id":65356477,"number":6,"title":"完成2D正齒輪繪圖系統","user":{"login":"40223114","id":7484043,"avatar_url":"https://avatars.githubusercontent.com/u/7484043?v=3","gravatar_id":"","url":"https://api.github.com/users/40223114","html_url":"https://github.com/40223114","followers_url":"https://api.github.com/users/40223114/followers","following_url":"https://api.github.com/users/40223114/following{/other_user}","gists_url":"https://api.github.com/users/40223114/gists{/gist_id}","starred_url":"https://api.github.com/users/40223114/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/40223114/subscriptions","organizations_url":"https://api.github.com/users/40223114/orgs","repos_url":"https://api.github.com/users/40223114/repos","events_url":"https://api.github.com/users/40223114/events{/privacy}","received_events_url":"https://api.github.com/users/40223114/received_events","type":"User","site_admin":false},"labels":[{"url":"https://api.github.com/repos/40223114/2015_g4/labels/ready","name":"ready","color":"ededed"}],"state":"open","locked":false,"assignee":null,"milestone":null,"comments":8,"created_at":"2015-03-31T03:34:36Z","updated_at":"2015-04-28T12:34:43Z","closed_at":null,"body":null},"comment":{"url":"https://api.github.com/repos/40223114/2015_g4/issues/comments/97046956","html_url":"https://github.com/40223114/2015_g4/issues/6#issuecomment-97046956","issue_url":"https://api.github.com/repos/40223114/2015_g4/issues/6","id":97046956,"user":{"login":"40223113","id":7483853,"avatar_url":"https://avatars.githubusercontent.com/u/7483853?v=3","gravatar_id":"","url":"https://api.github.com/users/40223113","html_url":"https://github.com/40223113","followers_url":"https://api.github.com/users/40223113/followers","following_url":"https://api.github.com/users/40223113/following{/other_user}","gists_url":"https://api.github.com/users/40223113/gists{/gist_id}","starred_url":"https://api.github.com/users/40223113/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/40223113/subscriptions","organizations_url":"https://api.github.com/users/40223113/orgs","repos_url":"https://api.github.com/users/40223113/repos","events_url":"https://api.github.com/users/40223113/events{/privacy}","received_events_url":"https://api.github.com/users/40223113/received_events","type":"User","site_admin":false},"created_at":"2015-04-28T12:34:43Z","updated_at":"2015-04-28T12:34:43Z","body":"齒輪的功用 :\n1. 變化轉速\n2. 變化轉動方向\n齒輪之模擬 :\n以兩滾圓傳遞動之缺點：\n1. 兩圓各有其轉軸，之間距若些許誤差即難維持永遠接觸磨擦力 也因而失效。\n2. 若裝置超過負載，會兩圓間之摩擦力終將產生打滑。\n3. 若採用彈簧將兩軸緊壓， 雖可達到接觸之目的但此時點應力加大反而增加兩圓接觸面之磨耗；其穩定性亦會降低。\n4. 無法傳遞較大的動力。\n齒輪之優點 :\n1. 速比正確。\n2. 大小動力均可傳達。\n3. 高低速傳動均可。\n4. 變速操作容易。\n5. 占用空間少。\n齒輪之相關術語 :\n節面 (Pitch surface)(Pitch surface) (Pitch surface)(Pitch surface)(Pitch surface)(Pitch surface)(Pitch surface) (Pitch surface) ：虛擬之滾動圓筒 ：虛擬之滾動圓筒 (或錐 )表面，其上可以代換不同輪齒。 表面，其上可以代換不同輪齒。\n節圓 (Pitch circle)(Pitch circle) (Pitch circle)(Pitch circle)(Pitch circle)(Pitch circle)(Pitch circle)(Pitch circle)(Pitch circle) ：節面之正剖，代表齒輪虛擬圓。\n齒冠圓 (Addendum circle)(Addendum circle) (Addendum circle)(Addendum circle) (Addendum circle)(Addendum circle)(Addendum circle)(Addendum circle)(Addendum circle)(Addendum circle) (Addendum circle)(Addendum circle) (Addendum circle)：齒端所構成之圓，在輪正剖面。\n齒根圓 (root or dedendum circle)(root or dedendum circle)(root or dedendum circle)(root or dedendum circle)(root or dedendum circle)(root or dedendum circle)(root or dedendum circle)(root or dedendum circle)(root or dedendum circle)(root or dedendum circle)(root or dedendum circle)(root or dedendum circle)(root or dedendum circle) (root or dedendum circle)(root or dedendum circle)(root or dedendum circle) (root or dedendum circle)(root or dedendum circle) (root or dedendum circle)(root or dedendum circle) ：齒間所構成之圓，在輪正剖面。 ：齒間所構成之圓，在輪正剖面。\n齒冠 (Addendum)(Addendum) (Addendum)(Addendum) (Addendum)(Addendum)(Addendum) ： 節圓與齒冠間之徑向距離。 節圓與齒冠間之徑向距離。\n齒根 (Dedendum)(Dedendum)(Dedendum) (Dedendum)(Dedendum)(Dedendum)(Dedendum)(Dedendum) ： 節圓與齒根間之徑向距離。\n間隙 (Clearance)(Clearance) (Clearance) (Clearance)(Clearance) ： 某齒輪之根與搭配冠間距離 。\n齒面 (Face of tooth)(Face of tooth)(Face of tooth) (Face of tooth)(Face of tooth)(Face of tooth)(Face of tooth)(Face of tooth)(Face of tooth)(Face of tooth)(Face of tooth)(Face of tooth)： 在節面以外部份之齒。\n齒腹 (Flank of tooth)(Flank of tooth) (Flank of tooth)(Flank of tooth)(Flank of tooth)(Flank of tooth)(Flank of tooth)(Flank of tooth)(Flank of tooth)(Flank of tooth)(Flank of tooth)(Flank of tooth)(Flank of tooth)：在節面以內部份之齒。 ：在節面以內部份之齒。\n弧線齒厚 (Circular thickness )((Circular thickness )( (Circular thickness )((Circular thickness )((Circular thickness )( (Circular thickness )((Circular thickness )((Circular thickness )( (Circular thickness )((Circular thickness )((Circular thickness )( (Circular thickness )((Circular thickness )(亦稱齒厚 tooth thickness) tooth thickness) tooth thickness) tooth thickness) tooth thickness) tooth thickness) tooth thickness) tooth thickness) tooth thickness) tooth thickness) tooth thickness) tooth thickness) tooth thickness) tooth thickness) ： 齒在節圓上之厚度，它 齒在節圓上之厚度，它 齒在節圓上之厚度，它 齒在節圓上之厚度，它 是弧長，不直線度。\n齒間 (Tooth space)(Tooth space)(Tooth space)(Tooth space)(Tooth space)(Tooth space)(Tooth space)(Tooth space) (Tooth space) ： 在節圓上相鄰兩齒之距離。 在節圓上相鄰兩齒之距離。\n齒隙 (Backlash)(Backlash)(Backlash) (Backlash) (Backlash)：某齒輪圓周厚度與搭配之間差。 ：某齒輪圓周厚度與搭配之間差。 \n內圓角 (Fillet )(Fillet ) (Fillet )(Fillet )(Fillet )：齒與根圓連接面之最小半徑。 \n小齒輪 (Pinion)(Pinion) (Pinion) (Pinion)： 任何相配齒輪之最小，而較大者稱為。 任何相配齒輪之最小，而較大者稱為。 \n基圓 (Base circle)(Base circle)(Base circle) (Base circle)(Base circle) (Base circle)(Base circle) ：:虛擬圓，用以產生漸開線形成齒。 \n速度比 (Velocity ratio)(Velocity ratio)(Velocity ratio) (Velocity ratio)(Velocity ratio) (Velocity ratio) (Velocity ratio)(Velocity ratio)(Velocity ratio) ： 單位時間內，驅動 單位時間內，驅動 單位時間內，驅動 (或輸入 )齒輪 與被動(輸出 )之迴轉\n數比。 \n節點 (Pitch point)(Pitch point) (Pitch point)(Pitch point)(Pitch point)(Pitch point)(Pitch point) (Pitch point)(Pitch point)： 一對相配齒輪之節圓切點。 一對相配齒輪之節圓切點。 \n共切線 (Common tangent)(Common tangent) (Common tangent)(Common tangent)(Common tangent)(Common tangent) (Common tangent)(Common tangent)(Common tangent)(Common tangent)(Common tangent)：節點處與圓相切之線。 \n作用線 (Line of action)(Line of action) (Line of action) (Line of action)(Line of action)(Line of action)(Line of action) (Line of action) (Line of action)(Line of action)： 相配齒輪之面接觸點法線。 \n接觸線 (Path of contact)(Path of contact)(Path of contact)(Path of contact)(Path of contact)(Path of contact)(Path of contact)(Path of contact)(Path of contact)(Path of contact)(Path of contact)(Path of contact)(Path of contact)(Path of contact) (Path of contact)： 相配齒輪外形接 觸點之軌跡。 \n壓力角 (Pressure angle )(Pressure angle ) (Pressure angle ) (Pressure angle )(Pressure angle ) (Pressure angle )(Pressure angle )(Pressure angle ) (Pressure angle )：節圓之共切線 與通過齒接觸點法交角。亦即作用：節圓之共切線 與通過齒接觸點法交角。亦即作用：節圓之共切線 與通過齒接觸點法交角。亦即作用：節圓之共切線 與通過齒接觸點法交角。亦即作用：節圓之共切線 與通過齒接觸點法交角。亦即作用與共同切線之交角。 \n周節 (Circular pitch) Pc(Circular pitch) Pc (Circular pitch) Pc(Circular pitch) Pc(Circular pitch) Pc (Circular pitch) Pc(Circular pitch) Pc(Circular pitch) Pc(Circular pitch) Pc(Circular pitch) Pc(Circular pitch) Pc(Circular pitch) Pc(Circular pitch) Pc(Circular pitch) Pc： 齒寬度與間，在節圓上量取。 \n徑節 (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: (Diametral pitch) Pd: 節徑上每吋之齒數。 輪應為整\n模數 (Module) m(Module) m(Module) m(Module) m(Module) m(Module) m(Module) m (Module) m： 節徑除以齒數。公厘表示；為之倒，要注意單 節徑除以齒數。公厘表示；為之倒，要注意單 位不一樣。\n周節 與徑:\n•周節 Pc 等於節圓周除以齒數 N\n•徑節 Pd 為齒數除以節徑 為齒數除以節徑 D Pc = πD / N D Pc = πD / N D Pc = πD / N D Pc = πD / N D Pc = πD / N D Pc = πD / N D Pc = πD / N D Pc = πD / N D Pc = πD / N D Pc = πD / N D Pc = πD / N D Pc = πD / N Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π Pd = N /D Pc π 國際 SI 公制使用模數 m，其定義： m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π m = Dp/N (mm) Pc π\n漸開線之特性 :\n1. 因為連線 AB 沿圓周環繞，距離 BK BK 等於弧長 AB 。\n2. 任何時間此線運動之瞬心應位於切該圓上。\n3. 漸開線上任意點之法均與 基圓相切。由於漸開曲線之第二特性，該點運 基圓相切。由於漸開曲線之第二特性，該點運 基圓相切。由於漸開曲線之第二特性，該點運 基圓相切。由於漸開曲線之第二特性，該點運 基圓相切。由於漸開曲線之第二特性，該點運 動為垂 直於線上任何點，故曲軌跡亦應垂該。\n4. 基圓內部並無漸開曲線。\n擺線 齒形曲:\n1. 正擺線（ 正擺線（ cycloidcycloidcycloidcycloid ） :一圓在直線上滾動，該的 一圓在直線上滾動，該的 一圓在直線上滾動，該的 圓周上任一點所形成的軌跡， 稱為正擺線， 簡稱擺線，用於製造齒條面及腹之曲。\n2. 外擺線（ 外擺線（ epicycloid epicycloid epicycloidepicycloidepicycloid ）:將滾圓在另一節的外側動，則周上任點所 將滾圓在另一節的外側動，則周上任點所 將滾圓在另一節的外側動，則周上任點所 將滾圓在另一節的外側動，則周上任點所 將滾圓在另一節的外側動，則周上任點所 形成的軌跡，稱為外擺線用於製造齒輪面曲。\n3. 內擺線（ hypocycloidhypocycloid hypocycloidhypocycloidhypocycloidhypocycloid ）:將滾圓在另一節之內側動，則周上任點 之軌跡，稱為內擺線用於製造齒輪腹曲。\n接觸比 :\n接觸比 (Contact ratio)(Contact ratio) (Contact ratio)(Contact ratio) (Contact ratio)(Contact ratio)(Contact ratio)(Contact ratio)(Contact ratio) 為同一時間內有多少對 為同一時間內有多少對 牙齒同時相互嚙合。對數愈多，表 示各對牙齒所承受的負荷較輕 ，力量之傳遞也愈為均勻；對數少，齒牙負 力量之傳遞也愈為均勻；對數少，齒牙負 力量之傳遞也愈為均勻；對數少，齒牙負 力量之傳遞也愈為均勻；對數少，齒牙負 力量之傳遞也愈為均勻；對數少，齒牙負 力量之傳遞也愈為均勻；對數少，齒牙負 荷相 對愈重，若接觸比小於 對愈重，若接觸比小於 對愈重，若接觸比小於 1，即表示在某些時候可能沒有齒牙配對一般之接觸比應 ，即表示在某些時候可能沒有齒牙配對一般之接觸比應 不小於 1.2 ，亦即 ，亦即 80% 的時間 是兩對牙齒共同協力作業，而約有 是兩對牙齒共同協力作業，而約有 是兩對牙齒共同協力作業，而約有 20% 20%的時間，僅 的時間，僅 的時間，僅 有一對負責傳遞的工作。\n避免干涉的方法 :\n1. 內切齒腹 \n2. 增加齒輪直徑或使用較小形，以數。 \n3. 減少齒冠，或切除形太高的部份。 \n4. 增加兩齒輪之中心矩，或其壓力角\n齒輪之標準 : \n1. 其壓力角必須相同。 \n2. 其徑節必須相同。 \n3. 兩齒輪必須具有相同的冠及根。 \n4. 齒厚必須等於周節之一半。"}}