THEORYMECHANICS1902Chapter 8 Composite motion of pointsCollege of Mechanical and Vehicle EngineeringWang Xiaojun
College of Mechanical and Vehicle Engineering Wang Xiaojun THEORY MECHANICS Chapter 8 Composite motion of points
Chapter8 Composite motion of points> 8.1 The concepts of absolute motion, relative motion andinvolving motion> 8.2 The velocity synthesis theorem of point> 8.3 The associated motion is the synthesis theorem ofacceleration at translational time points> 8.4 The involved motion is the synthesis theorem ofacceleration at the point of rotation
➢ 8.1 The concepts of absolute motion, relative motion and involving motion ➢ 8.2 The velocity synthesis theorem of point ➢ 8.3 The associated motion is the synthesis theorem of acceleration at translational time points ➢ 8.4 The involved motion is the synthesis theorem of acceleration at the point of rotation Chapter8 Composite motion of points
8.1 The concept of absolute motion relative motioninvolving motionDecomposition and synthesis of motionThemotionofpointP(complex)synthesisDecompositionVThemotionofpointPrelativetothefuselageMotionof fuselage
Decomposition and synthesis of motion The motion of point P (complex) Decomposition synthesis The motion of point P relative to the fuselage Motion of fuselage 8.1 The concept of absolute motion relative motion involving motion
8.1 The concept of absolute motion relative motioninvolving motion1.Twocoordinate systemsStatic system: Coordinate system that consolidatesthe surface of the earthDynamic system: A frame of reference that consolidates an object movingrelativetothesurfaceoftheEarthNote that the coordinate system can beextended indefinitelymotionof2.ThreekindsofsportspointsAbsolute motion: Motion of the moving point relative to the static systemRelative motion:The motion of a moving point relative to an active systemTranslational motion: Motion in a dynamic system as opposed to a staticsystem→Motion of Rigid Body
1. Two coordinate systems Static system: Coordinate system that consolidates the surface of the earth Dynamic system：A frame of reference that consolidates an object moving relative to the surface of the Earth 2. Three kinds of sports Absolute motion: Motion of the moving point relative to the static system Relative motion: The motion of a moving point relative to an active system Translational motion: Motion in a dynamic system as opposed to a static system 8.1 The concept of absolute motion relative motion involving motion motion of points Motion of Rigid Body Note that the coordinate system can be extended indefinitely
8.1 The concept of absolute motion relative motioninvolving motionA point M on the rim1The motion trajectory of M:Mrouletteabsolutemovement②circlerelativemovementMotionin a dynamic system:horizontaltranslationtranslationalmotionx
x x? y? y M o A point M on the rim The motion trajectory of M: ① roulette—absolute movement ②circle—relative movement Motion in a dynamic system: horizontal translation—translational motion 8.1 The concept of absolute motion relative motion involving motion
8.1 The concept of absolute motion relative motioninvolving motionA bridge crane on the factory floor
A bridge crane on the factory floor 8.1 The concept of absolute motion relative motion involving motion
8.1 The concept of absolute motion relative motioninvolvingmotionyx'4Weight A-→A'A1The motion trajectory of point A:V1AAl curve movement - absoluteV1motion - ground observerAStraight up - relative motion0XMotion of the dynamic system:Horizontal translation - implicated motion
A A' Weight A→A' 0 x y 0' x' y' A1 v v1 v1 The motion trajectory of point A: ①AA1 curve movement - absolute motion - ground observer ②Straight up - relative motion 8.1 The concept of absolute motion relative motion involving motion Motion of the dynamic system: Horizontal translation - implicated motion
8.1 The concept of absolute motion relative motioninvolving motion3.Three speeds, three accelerationsAbsolutevelocity and acceleration:The velocity and accelerationofthe moving point relative to the static systemare expressed asv.aaRelative velocity and accelerationThe velocity and acceleration of the moving point relative to the movingsystem are expressed as v,a,Associated velocity and acceleration:Thevelocity and accelerationoftheimplicated pointrelative tothe staticsystem are expressed as ve ae①Atransient②Apoint onadynamic systemThe coincides with the movingpoint
3. Three speeds, three accelerations Absolute velocity and acceleration: ➢ The velocity and acceleration of the moving point relative to the static system are expressed as Relative velocity and acceleration: The velocity and acceleration of the moving point relative to the moving system are expressed as Associated velocity and acceleration: The velocity and acceleration of the implicated point relative to the static system are expressed as 8.1 The concept of absolute motion relative motion involving motion ①A transient ②A point on a dynamic system ③The coincides with the moving pointr v ar a v a a ve ae
8.1 The concept of absolute motion relative motioninvolving motionmovingrelativeabsolutepointvarv.a.(Point)(Point)absoluterelativemotionmotionStaticDynamic<translationalmotionsystemsystem(rigid)Atan instant,theinvolvepointon thev.atransportdynamicsystempointcoincideswiththemoving point
translational motion Static system Dynamic system moving point （rigid） absolute a v r v relative e v transport point involve a a r a e a 8.1 The concept of absolute motion relative motion involving motion At an instant, the point on the dynamic system coincides with the moving point
8.1 The concept of absolute motion relative motioninvolving motion Example1: CAM jacking mechanismMoving point: Point A on rod AB12Dynamic fastening: To fix to the CAMabsolutemotion:vertical curve公relative motion:An arc alongthe rimtransportmotion:The level of translationtransportpoint:A pointon the CAM thatcoincideswithA
Example1：CAM jacking mechanism 8.1 The concept of absolute motion relative motion involving motion 0 v A B O Moving point: Point A on rod AB Dynamic fastening: To fix to the CAM x y x’ y’ absolute motion: relative motion: transport motion: transport point: vertical curve An arc along the rim The level of translation A point on the CAM that coincides with A e v r v a v