AME 352
GRAPHICAL VELOCITY ANALYSIS
5.1 GRAPHICAL VELOCITY ANALYSIS
Simple Exercises
We start this chapter with some simple exercises to ensure that the fundamentals of velocity
analysis using vector algebra are well understood. You may want to review these fundamentals
in Chapter 2 of the notes.
In these exercises take direct measurements from the figures for link lengths and the
magnitudes of the velocity vectors. If it is stated that the angular velocity is known, assume
ω = 1 rad/sec CCW unless it is stated otherwise. Write the position and velocity vector
equations. Construct the velocity equation graphically in order to find the unknown(s).
P.1
Tools: ruler, right angle, protractor, drawing compass
P.2
Known: VA and ω
Determine: VB
Known: VA and VB
A
Determine: ω
A
B
B
VB
VA
VA
P.3
P.4
Known: VA and VB
What do you observe?
A
Determine: ω
Known: VA and ω are known.
Determine: VB , VC and VBC
B
B
VB
V
A
VA
C
A
P.6
P.5
Known: VA and VB
Determine: VC
B
Determine: VB , VC and VBC
V
B
C
VA
Known: VA and ω
A
B
C
A
VA
P.E. Nikravesh
5-1
AME 352
GRAPHICAL VELOCITY ANALYSIS
P.7
P.8
Known: VA and VB
Known: VA and ω
Determine: VC
Determine: VB and VC
What do you observe? Explain!
A
C
B
A
V
A
B
C
V
A
P.9
s
Known: VA , ω and VBA
P.10
s
Known: VA , ω and VBA
s
Assume VBA
= 1 unit/sec positive
s
Assume VBA
= 1 unit/sec negative
Determine: VB and VC
V
A
A
B
Determine: VB and VC
C
Determine: ω and VC
V
A
V
A
B
C
P.12
Known: VA , ω i and ω j
P.11
Known: VA and VB
A
A
B
Assume ω i = 1 rad/sec CCW and ω j = 1
rad/sec CW.
Determine: VB and VC
C
V
B
A
B
(i)
(j)
C
V
A
P.E. Nikravesh
5-2
AME 352
GRAPHICAL VELOCITY ANALYSIS
P.13
(This is not a commonly encountered
situation—the problem is rather difficult to
solve.)
Known: VA and VC
Determine: VB
P.E. Nikravesh
A
B
(i)
(j)
V
A
C
VC
5-3