上游文通大学 SHANGHAI JIAO TONG UNIVERSITY Kinematic analysis methods Graphical。C Graphical method based on vectors Complex vector method ●Anaytic1 Matrix
Kinematic analysis methods ●Graphical IC Graphical method based on vectors ●Analytical Complex vector method Matrix
上海文通大粤 Space of motion SHANGHAI JIAO TONG UNIVERSITY Curvilinear translation General plane motion Rectilinear translation Rotation about a fixed axis fig16_02.jpg Copyright 2010 Pearson Prentice Hall,Inc
Space of motion
上海文通大粤 SHANGHAI JIAO TONG UNIVERSITY Type of Rigid-Body Plane Motion Example all points in the body (a) move in parallel straight Rectilinear translation lines B Rocket test sled all points move on (b) Curvilinear congruent curves translation B Parallel-link swinging plate all particles in a rigid (c) body move in circular Fixed-axis rotation paths about the axis or rotation Compound pendulum (d) General plane motion B B Connecting rod in a reciprocating engine
all p y oints in the bod y move in parallel straight lines all points move on all points move on congruent curves all particles in a rigid bod y move in circular paths about the axis or rotation
上海文通大粤 Vector manipulations SHANGHAI JIAO TONG UNIVERSITY Scalars Vectors Examples: mass,volume,speed force,velocity Characteristics: It has a magnitude It has a magnitude (positive or negative) and direction Addition rule: Simple arithmetic Parallelogram law Special Notation: None Bold font,a line,an arrow
Vector manipulations Scalars Vectors Examples: mass, volume, speed force, velocity Ch i i I h i d I h i d Characteristics: It has a magnitu de It has a magnitu d e (positive or negative) and direction Addition rule: Simple arithmetic Parallelogram law Special Notation: None Bold font, a line, an arrow
上海文通大粤 Vector manipulations SHANGHAI JIAO TONG UNIVERSITY Vector Magnitude Head Magnitude (terminus) Direction Tail (origin) Vector can be represented Graphically R=R,i+R,J R=R,+jR Analytically R=[R,R,T R-Rei=R(cos0+jsine)
Vector manipulations Vector Head Magnitude Direction Magnitude (terminus) Tail ( ii) V t b td (origin ) Vec tor can be represen t e d Graphically R = + Ri R j R x y R = + jR R = + Ri R j x y Analytically x y j ( i) jθ θ θ [ ] T R = R x y R R e (cos s i n ) j R j θ R = = + θ θ