6 Velocity Analysis - Union...
Transcript of 6 Velocity Analysis - Union...
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)