Union CollegeMechanical Engineering

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

6 Velocity Analysis

Lecture 13

Union CollegeMechanical Engineering

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

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

Union CollegeMechanical Engineering

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

6.1: Definition - Link in Pure Rotation

Union CollegeMechanical Engineering

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

6.1 Definition - Velocity Difference

Union CollegeMechanical Engineering

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

6.1 Definition - Relative Velocity

Union CollegeMechanical Engineering

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

6.2 Graphical Solution – Joint

q

q

pp

VA

VB

VBA

?√ ?√√ √

Union CollegeMechanical Engineering

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

r

r

6.2 Graphical Solution – Point on link

VA

VC

VCA

? ? √ √ √ √

vCA = (CA)ω3

Union CollegeMechanical Engineering

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

Chap. 6: VELOCITY ANALYSIS

Lecture 11

Instant Centers of Velocityand Centroides

Union CollegeMechanical Engineering

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

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

Union CollegeMechanical Engineering

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

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:

Union CollegeMechanical Engineering

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

Kennedy’s Rule

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

Union CollegeMechanical Engineering

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

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

Union CollegeMechanical Engineering

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

IC’s Can Be At Infinity

V I 34V I 34

The IC of a

Union CollegeMechanical Engineering

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

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.

Union CollegeMechanical Engineering

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

1

24

3Dual Graph

IC’s of a Slider- Crank Linkage

V I 34

V I 23

Union CollegeMechanical Engineering

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

Instant Centers of a Cam and Follower

Finding IC’s using Effective linkage

Union CollegeMechanical Engineering

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

Instant Centers of a Cam and Follower

Finding IC’s without using effective linkage

Union CollegeMechanical Engineering

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

6.4 Velocity Analysis Using IC’s

Union CollegeMechanical Engineering

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

6.4.1 Angular Velocity Ratio

Union CollegeMechanical Engineering

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

6.4.2 Mechanical Advantage

Union CollegeMechanical Engineering

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

6.4.3 Using Instant Center in Linkage Design

The “Hopalong” Chevrolet Vega (c. 1970)

Union CollegeMechanical Engineering

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

6.4.3 Using Instant Center in Linkage Design

The “Hopalong” Chevrolet Vega (c. 1970)