자유물체도(free body diagram) -...
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자유물체도(Free Body Diagram)
금오공대기계시스템공학과
오충석 ([email protected])
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(권장) 학습과정: 반복학습Practice makes perfect!
Units
Forces
MomentsFree Body Diagram
Applications
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Contents
자유물체도란?
FBD 그리는방법
기계요소들의특징
기초적인 FBD 그려보기
기초적인 FBD보충하기
FBD 교정하기
평지와경사로의자동차
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자유물체도(FBD)란?
정의
상호작용하고있는전체계 (system)로부터 “관심의대상”이되는부분만을분리시켜그린그림
FBD의예
400 N
Ry
o
1.5 m x
전체계 (entire system) 관심의 대상 (지렛대)
[Ref: Statics by Boresi]
300 N
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자유물체도그리는방법(CID)
1) 문제에적합한좌표(Coordinates)설정a. 직각좌표계: x-y-z (linear-linear-linear)
b. 원통좌표계: r-φ-z (linear-angular-linear)
c. 구면좌표계: r-φ-θ (linear-angular-angular)
http://web.mit.edu/6.013_book/www/chapter5/5.10.html
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2) 관심대상을전체시스템으로부터분리(Isolation)시켜나타냄실제와같은상태가되도록해야함
실제와똑같은형상으로그릴필요없음
다양한구성요소들의특징을알고있으면유리함
직관력이요구되는단계
많은문제풀이가요구되는단계
3) 모든힘,모멘트, 치수등표시(Display)작용/반작용힘&모멘트
힘&모멘트작용점까지의거리
단위, 벡터표시사용, 칼라펜사용권장
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기초적인 FBD 그려보기
Plane Truss (평면트러스)가정: Wtruss << P, 무마찰핀
Reactive forces
Applied force
6 Pin 4 Rocker
x
y
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Cantilever Beam (외팔보)
7 Fixed
x
y
8 Gravity
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Beam (보)가정: A점은매끄러운면, B 점은무마찰핀, 보의질량 m
2 SmoothSurface
6 Pin
8 Gravityx
y
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Rigid System of Interconnected Bodies(내부적으로연결되어있는강체시스템)가정: 마찰무시
6 Pin
8 Gravity
4 Roller
x
y합력 고려
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Dan O’Brien미국의 10종경기선수
1992 바르셀로나, 1996 애틀랜타올림픽금메달
포환의 FBD
참고: Boresi
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기초적인 FBD 보충하기
Bell Crank(벨크랭크)가정: 무마찰핀
1 Cable
6 Pin
8 Gravity
x
y
Ay
Ax
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Control lever applying torque to shaft at O(O점의축에토크를가하는손잡이)유마찰핀
6 Pin
M
x
y
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Boom OA, of negligible mass compared with mass m. Boom hinged at O and supported by hoisting cable at B. (O점에서핀, B점에서케이블에의해지지되는질량을무시할수있는붐 OA)
8 Gravity
1 Cable
6 Pin
x
y
Oy
Ox
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Uniform crate of mass m leaning against smooth vertical wall and supported on a rough horizontal surface. (매끈한수직벽과거친수평면에놓인질량 m인상자)
2 SmoothSurface
2 Rough Surface
8 Gravity
Bxx
y
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Loaded bracket supported by pin connection at Aand fixed pin in smooth slot at B. (매끄러운슬롯과고정핀으로지지되는브라켓)
6 Pin
5 Slider
Ay
Ax
x
y
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FBD 교정하기
Lawn roller of mass m being pushed up incline θ(경사각 θ인경사면으로밀어올려지고있는질량 m인잔디롤러)
3 Rough Surface
8 Gravity
μN
mg
x
y
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Pry bar lifting body A having smooth horizontal surface. Bar rests on horizontal rough surface.(거핀수평면상에서매끄러운표면을갖는물체 A를들어올리는쇠지레)
3 Rough Surface
2 SmoothSurface
x
y
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Uniform pole of mass m being hoisted into position by winch. Horizontal supporting surface notched to prevent slipping of pole. (수평면상의노치에의해지지되고윈치에의해들어올려지는질량m인장대)
1 Cable
6 Pin
8 Gravity
x
y
X
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Supporting angle bracket for frame. Pin joints.(구조물지지용 ‘ㄱ”자브라켓 AB)
6 Pin
6 Pin
x
y
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Bend rod welded to support at A and subjected to two forces and a couple. (두힘과하나의모멘트를받으면서 A점에용접되어있는봉)
Ax
M7 Fixed
x
y
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평지와경사로의자동차
평지
작용력: 중력 ( W = mg )
반작용력: 수직항력 ( N )
W = N이면움직이지않음→정적평형