Partial solutions for selected exercises for the
Instantaneous Center of Zero Velocity
ME274 – Basic Mechanics II
Purdue University
West Lafayette, IN
Partial solutions for seven of the instant center examples are presented here.
Use these to compare with your instant center solutions.
Animations for two of these examples are also posted in the course website.
Review these animations as an aid to better understand the type of motion
exhibited by these mechanisms.
• Use the controller on the QuickTime clip to view individual frames for the
motion.
• As you go through the animations frame-by-frame, try to visualize how the
instant centers for the links of the mechanisms change with position. Use
the locations of the IC’s to help explain the magnitude and direction of the
velocity vectors shown in the animations.
• Try to identify special configurations of the mechanisms such as:
stationary positions of particular links, positions for which a particular link
is in pure translations, limit positions of the mechanisms. Use the concept
of instant centers to try to explain these positions.
If you have questions, do not hesitate to ask me (CMK).
Partial solutions for selected example problems
Example No. 2
ICBC
ωBC
ωAB
vB
ICAB
Example No. 3
ωAB
ωBC
vB
Example No. 5
ICBC
ωBC
5 rad/sec
vC
vB
ωCD
. Example No. 8
ωAB
vB
ωBC
ICBC
Example 10
ICBC is at ∞ since vB is parallel to vC
(perpendiculars to these parallel vectors
cross at ∞). Therefore, BC is
instantaneously in translation; as a result,
BC has zero angular velocity
4 rad/sec
vB
vC
ωCD
Example 11
For this position, the perpendiculars to vB and vC
intersect at infinity. Therefore, the angular
velocity of link BC is zero.
ωAB
ωCD
vB
vC
Example 19
vB
40 mm/sec
ωAB
ICAB