6 velocity analysis - union...

Union CollegeMechanical Engineering

MER 312: Dynamics and Kinematics (of Mechanisms) / AT

6 Velocity Analysis

Lecture 13



6.1 Definition

DefinitionRate of change of position with timeLinear velocity: V = dR/dt, R position vectorAngular velocity: ω= dθ/dt θ Position angleR and θ are function of time t.

Of a point in pure rotation:Magnitude: V = rωAngle: Perpendicular to radius r



6.1: Definition - Link in Pure Rotation



6.1 Definition - Velocity Difference



6.1 Definition - Relative Velocity



6.2 Graphical Solution – Joint

q

q

pp

VA

VB

VBA

?√ ?√√ √



r

r

6.2 Graphical Solution – Point on link

VA

VC

VCA

? ? √ √ √ √

vCA = (CA)ω3



Chap. 6: VELOCITY ANALYSIS

Lecture 11

Instant Centers of Velocityand Centroides



6.1 Definition of Velocity

DefinitionRate of change of position with timeLinear velocity: V = dR/dtAngular velocity: ω = dθ/dt

Of a point in pure rotation:Magnitude: V = rωAngle: Perpendicular to radius r



6.3 Instant Center of Velocity

DefinitionA point, common to two bodies in a plane, which point has the same instantaneous velocity in each bodyThe number of instant centers C of nbodies in the plane is:



Kennedy’s Rule

Any three bodies in the plane will have exactly three instant centers, and they will lie on the same straight line.



Finding Instant Centers

1

24

I1,3

3Dual GraphI2,4

In a Dual, lines become points, and points become lines.

C = 4 (4 - 1) / 2 = 6



IC’s Can Be At Infinity

V I 34V I 34

The IC of a



IC’s Can Be At Infinity

V I 34V I 34

The IC of a slider joint is at infinity along the line perpendicular to the direction of sliding.



1

24

3Dual Graph

IC’s of a Slider- Crank Linkage

V I 34

V I 23



Instant Centers of a Cam and Follower

Finding IC’s using Effective linkage



Instant Centers of a Cam and Follower

Finding IC’s without using effective linkage



6.4 Velocity Analysis Using IC’s



6.4.1 Angular Velocity Ratio



6.4.2 Mechanical Advantage



6.4.3 Using Instant Center in Linkage Design

The “Hopalong” Chevrolet Vega (c. 1970)

6 velocity analysis - union...

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