Kinematic Design of Machinery
MECH 417
Lecture (10)
Acceleration Analysis
MECH 417 Mechanical Eng., UAEU
Reading Material
Chapter 7, sections 7.1 to 7.7
Related Course Outcome
3. Analyze position, velocity and acceleration of planar
mechanisms
Session topics:
–Definition of acceleration
–Graphical acceleration analysis
–Analytical acceleration analysis
–Human tolerance of acceleration
–Jerk
Definition of Acceleration
MECH 417 Mechanical Eng., UAEU
•Acceleration is
the rate of change in velocity with respect to time
•Assume point Pis on a link and the GCS is placed at a pivot A (A
is fixed). For given , =
•As per the definition
P
Y
X
A
VPA
RP
θ
a
=
=()
=()
+ ()
= + =
APA(t)
APA(n)
Definition of Acceleration
MECH 417 Mechanical Eng., UAEU
•Now, assume that point Ais moving with a given acceleration.
=+
P
y
x
A
θ
α
ω
Y
XAA
APA(t)
•The absolute velocity of point Pis then defined by
AP
APA(n)
=+()+()
Graphical Acceleration Analysis
•Given linkage configuration & α2, find α3and α4.
(note: position and velocity analysis are completed at this point. This
means, θ2, θ3, θ4, ω2, ω3and ω4, are known).
The acceleration equation is
MECH 417 Mechanical Eng., UAEU
ω2
X
θ2
α2
Y
A
C
B
AA(n)
AA(t)
ABA(t)
AB(n)
ABA(n)
()+()=()+()+()+()
=+
AB(t)
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