下載本文檔
版權(quán)說明:本文檔由用戶提供并上傳,收益歸屬內(nèi)容提供方,若內(nèi)容存在侵權(quán),請進行舉報或認領(lǐng)
文檔簡介
1、2.4 Kinematic Analysis of a Particle in 3D SpaceInvestigation into the motion of a particle is a simplest yet the most fundamental aspect in kinematics. In this section, we deal with the kinematic equations of a particle P moving in 3D space by using vector notation. Three coordinate systems will be
2、 introduced to describe the curvilinear motion of a particle: They areq Rectangular(Cartesian) Coordinate System ()q Cylindrical Coordinate System()q Spherical Coordinate System() Rectangular (Cartesian) Coordinate System () Consider a particle P moving in 3D space, in the rectangular coordinate sys
3、tem as shown in the figure, its position vector can be given as (1a) the unit vectors of three orthogonal axes. Note that they are constant since all axes have been fixed in space, i.e.,the coordinates of P with respect to.Taking derivatives once and twice with respect time gives the velocity and ac
4、celeration of point P (1b) (1c)Obviously, this is the form which we are very familiar with.Projectile Problem(A classical problem for particle kinematics)An object located at origin of a Cartesian system with its axis upward and axis horizontal as shown, is thrown through the air with an initial vel
5、ocity and an angle about horizontal at , determine the trajectory function of the object. Solution:Initial conditionsPosition: , Velocity: , Acceleration: , ( g-the gravitational acceleration) , , One more integration leads toSubstituting into the above equation finally results inCylindrical Coordin
6、ate System () In the cylindrical coordinates, the position of a particle P can be located by-the radial distance from the -axis- the angle from the -axis to the radial line-the vertical distance from the plane. Define , and as three orthogonal unit vectors in the sense of positive , and directions,
7、respectively. The position vector of P can then be expressed by (2a)In order to achieve the velocity of P, let us rotate , and about with an small angle during an infinitesimal time interval . Then the differentiation of has the form (2b)Since keeps unchanged, . While the small changes in and occur
8、as follows Thus, This will also lead toand thereby (2c)Differentiating Eq.(2c) finally results in the acceleration of P (2d)Sample ProblemDetermine , , and of a RRPR planar mechanism as shown provided that , , , , and have been known. Solution:The polar coordinate system may be used for this problem
9、. The general formulae 2(a), 2(c) and 2(d) are reduced to xyyxxyVelocity Polygon, , Velocity AnalysisSetp1: Establish the polar coordinate system with and being as the unit vectors. The velocity of A in can be expressed by Since is a constant, . ThusStep 2: Establish another polar coordinate system
10、with and being as the unit vectors. The velocity of point A in can be expressed by - the velocity of a fictitious point B on link 3, which is momentarily coincident with the point A. - the sliding velocity of A relative to B along the direction of .Step 3: The velocity of the point A evaluated by us
11、ing these two systems SHOULD BE THE SAME. ThusProjecting onto and , respectively, leads to, Acceleration Polygon Acceleration Analysis Acceleration analysis can be implemented in the same way.Evaluated in Keep in mind that is a constant such that Evaluated inThe acceleration constraint condition givesProjecting the left hand term onto and finally results inSpherical Coordinate SystemWhen a radial distance and two angles are used to specify the position of a particle
溫馨提示
- 1. 本站所有資源如無特殊說明,都需要本地電腦安裝OFFICE2007和PDF閱讀器。圖紙軟件為CAD,CAXA,PROE,UG,SolidWorks等.壓縮文件請下載最新的WinRAR軟件解壓。
- 2. 本站的文檔不包含任何第三方提供的附件圖紙等,如果需要附件,請聯(lián)系上傳者。文件的所有權(quán)益歸上傳用戶所有。
- 3. 本站RAR壓縮包中若帶圖紙,網(wǎng)頁內(nèi)容里面會有圖紙預覽,若沒有圖紙預覽就沒有圖紙。
- 4. 未經(jīng)權(quán)益所有人同意不得將文件中的內(nèi)容挪作商業(yè)或盈利用途。
- 5. 人人文庫網(wǎng)僅提供信息存儲空間,僅對用戶上傳內(nèi)容的表現(xiàn)方式做保護處理,對用戶上傳分享的文檔內(nèi)容本身不做任何修改或編輯,并不能對任何下載內(nèi)容負責。
- 6. 下載文件中如有侵權(quán)或不適當內(nèi)容,請與我們聯(lián)系,我們立即糾正。
- 7. 本站不保證下載資源的準確性、安全性和完整性, 同時也不承擔用戶因使用這些下載資源對自己和他人造成任何形式的傷害或損失。
最新文檔
- 2024智慧城市交通信號控制系統(tǒng)優(yōu)化合同
- 2025年度橙子包裝設計與定制生產(chǎn)合同2篇
- 2025年度環(huán)保設備銷售與服務合同4篇
- 2024版人身損害賠償協(xié)議
- 二零二四年外墻清洗專業(yè)團隊服務合同樣本3篇
- 2024-2025學年高中地理第一章環(huán)境與環(huán)境問題第一節(jié)我們周圍的環(huán)境課時分層作業(yè)含解析新人教版選修6
- 二零二五版城市綜合體土方運輸與臨時堆場租賃合同3篇
- 二零二五年度餐飲業(yè)人力資源派遣合同范本3篇
- 2025年特色小鎮(zhèn)物業(yè)經(jīng)營權(quán)及配套設施合作合同3篇
- 二零二五版科技公司股份交易與稅收籌劃合同3篇
- 上海紐約大學自主招生面試試題綜合素質(zhì)答案技巧
- 辦公家具項目實施方案、供貨方案
- 2022年物流服務師職業(yè)技能競賽理論題庫(含答案)
- ?;钒踩僮饕?guī)程
- 連鎖遺傳和遺傳作圖
- DB63∕T 1885-2020 青海省城鎮(zhèn)老舊小區(qū)綜合改造技術(shù)規(guī)程
- 高邊坡施工危險源辨識及分析
- 中海地產(chǎn)設計管理程序
- 簡譜視唱15942
- 《城鎮(zhèn)燃氣設施運行、維護和搶修安全技術(shù)規(guī)程》(CJJ51-2006)
- 項目付款審核流程(visio流程圖)
評論
0/150
提交評論