上海交通大学：《Design & Manufacturing II and Project》课程教学资源（讲义）Lecture 6-3 part II

上游充通大学 SHANGHAI JIAO TONG UNIVERSITY LECTURE 6-IIl Part Il Vector fundamentals for kinematic analysis 漏 e SHANG 1日gG ERSITY

LECTURE 6-III P t II Vector fundamentals for kinematic Par t II Vector fundamentals for kinematic analysis

上游充通大粤 OUTLINE SHANGHAI JIAO TONG UNIVERSITY Why kinematic analysis ®Space of motion Vector manipulations ④Motion as vectors Instantaneous velocity center ME357 Design Manufacturing Il

OUTLINE Wh ki ti l i Why kinematic analysis S pace of motion Vector manipulations Motion as vectors Instantaneous velocity center Instantaneous velocity center ME357 Design & Manufacturing II

上游充通大学 Why kinematic analysis SHANGHAI JIAO TONG UNIVERSITY Why kinematic analysis To analyze the displacement,velocity,and acceleration of the motion to determine the design geometry of the mechanical parts. To determine the motion of a rigid body caused by the forces applied to it. Link 2 angle Link 2 length Link 3 lengthSlot 13 Y-Offset Link 2 54.00 1.64 3.30 -0.26 X-Position of Link 4 11 →Velocity of Link411 Acceleration of Link 4 11 8.0 ×m 10 Vx (m/s] 6.0Ax (m/s*2] 6.0 5.0十 4.0 0.0十 2.0 -5.0 2.01 ts] 0.0 t[s] -10+ 4.0+ t[s] 0.0 5.0 10 15 20 0.0 5.0 10 15 20 0.0 5.0 10 15 20

Why kinematic analysis Why kinematic analysis To analyze the displacement velocity and To analyze the displacement, velocity, and acceleration of the motion to determine the design geometr of the mechanical parts geometry of the mechanical parts. To determine the motion of a rigid body caused by the forces applied to it

上游充通大学 SHANGHAI JIAO TONG UNIVERSITY 国 Displacement analysis 1)to determine the output displacement and check if it meets the requirements. 2)to find the stroke or output workspace. 3)to avoid s space interferences. ④Velocity analysis 1)the basis for further analysis 2)to find the velocity characteristics of the output,then check if it meets the requirements. (such as quick return mechanism...)

Displacement analysis 1) to determine the output displacement and 1) to determine the output displacement and check if it meets the requirements. 2) to find the stroke or output workspace. 3) to avoid space interferences. 3) to avoid space interferences. Velocity analysis 1) the basis for further analysis 2) to find the velocity characteristics of the output, then check if it meets the requirements. output, then check if it meets the requirements. (such as quick return mechanism…)

上游文通大学 SHANGHAI JIAO TONG UNIVERSITY Acceleration analysis 1)to find the inertial forces 2)to determine the dynamic performances of the output

Acceleration analysis 1) to find the inertial forces 1) to find the inertial forces 2) to determine the dynamic performances of the 2) to determine the dynamic performances of the output

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 ƒ Magnitude ƒ Direction Magnitude (terminus) Tail ( ii) V t b td (origin ) Vec tor can be represen t e d ƒ Graphically R = + Ri R j R x y R = + jR R = + Ri R j x y ƒ 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