1. C O B A w=2 rad/s 2 m a=4 rad/s2 PROBLEMS
The gear has the angular motion shown. Determine the angular velocity and angular acceleration of the slotted link BC at this instant. The pin at A is fixed to the gear.
w=2 rad/s
a=4 rad/s2
0.5 m
0.7 m
2 m O B A C

2. PROBLEMS
Link 1, of the plane mechanism shown, rotates about the fixed point O with a constant angular speed of 5 rad/s in the cw direction while slider A, at the end of link 2, moves in the circular slot of link 1. Determine the angular velocity and the angular acceleration of link 2 at the instant represented where BO is perpendicular to OA. The radius of the slot is 10 cm.
Take sin 37=06, cos 37=0.8
37o
10 cm
20 cm A O 2 1
w1=5 rad/s C
16 cm B

3. PROBLEMS
For the instant shown, particle A has a velocity of 12.5 m/s towards point C relative to the disk and this velocity is decreasing at the rate of 7.5 m/s each second. The disk rotates about B with angular velocity w=9 rad/s and angular acceleration a=60 rad/s2 in the directions shown in the figure. The angle b remains constant during the motion. Telescopic link has a velocity of 5 m/s and an acceleration of -2.5 m/s. Determine the absolute velocity and acceleration of point A for the position shown.

4. Problem 7
Velocity Analysis 7 24 25 vB b

5. Velocity Analysis

6. Velocity Analysis 4 3 5
vrel q

7. Acceleration Analysis7 24 25 aB b

8. Acceleration Analysis

9. Acceleration Analysis

10. Acceleration Analysis4 3 5
(arel)t q
vrel +t +n
(arel)n

11. PROBLEMS
The pin A in the bell crank AOD is guided by the flanges of the collar B, which slides with a constant velocity vB of 0.9 m/s along the fixed shaft for an interval of motion. For the position q=30o determine the acceleration of the plunger CE, whose upper end is positioned by the radial slot in the bell crank. .

12. (1)=(2) vrel=-1.039 m/s vc=2.079 m/s
Problem 8
Velocity Analysis vA
vrel vA
vB=(vA)x
30o
129.9 mm
60o
30o
vrel
(1)=(2) vrel= m/s vc=2.079 m/s

13. Acceleration AnalysisaA
60o
30o
vrel
(aA)n
30o
(aA)t aA
VB=constant
So aA must be vertical.
129.9 mm

14. (3)=(4)
arel=24.92 m/s2
aC=27.92 m/s2

15. PROBLEMS
1. The uniform 30-kg bar OB is secured to the accelerating frame in the 30o position from the horizontal by the hinge at O and roller at A. If the horizontal acceleration of the frame is a=20 m/s2, compute the force FA on the roller and the x- and y-components of the force supported by the pin at O.

16. PROBLEMS
2. The block A and attached rod have a combined mass of 60 kg and are confined to move along the 60o guide under the action of the 800 N applied force. The uniform horizontal rod has a mass of 20 kg and is welded to the block at B. Friction in the guide is negligible. Compute the bending moment M exerted by the weld on the rod at B.

17. SOLUTION  FBD Kinetic Diagram mTax=60ax x x N W=60(9.81) N FBD of rod
KD of rod By
m1ax=20ax Bx M
W1=20(9.81) N

18. PROBLEMS
3. The parallelogram linkage shown moves in the vertical plane with the uniform 8 kg bar EF attached to the plate at E by a pin which is welded both to the plate and to the bar. A torque (not shown) is applied to link AB through its lower pin to drive the links in a clockwise direction. When q reaches 60o, the links have an angular acceleration an angular velocity of 6 rad/s2 and 3 rad/s, respectively. For this instant calculate the magnitudes of the force F and torque M supported by the pin at E.

19. PROBLEMS
4. The uniform 100 kg log is supported by the two cables and used as a battering ram. If the log is released from rest in the position shown, calculate the initial tension induced in each cable immediately after release and the corresponding angular acceleration a of the cables.

20.  * * FBD +n KD +n TA TB +t +t W=100(9.81) N
SOLUTION +n
FBD KD +n TA TB  +t +t
W=100(9.81) N
When it starts to move, v=0, w=0 but a≠0 *
Length of the cables
The motion of the log is curvilinear translation. *

21. PROBLEMS
5. An 18 kg triangular plate is supported by cables AB and CD. When the plate is in the position shown, the angular velocity of the cables is 4 rad/s ccw. At this instant, calculate the acceleration of the mass center of the plate and the tension in each of the cables. G
10 cm A B C D
60°
24 cm
20 cm
Answer:

22. PROBLEMS
6. The uniform 8 kg slender bar is hinged about a horizontal axis through O and released from rest in the horizontal position. Determine the distance b from the mass center to O which will result in an initial angular acceleration of 16 rad/s2, and find the force R on the bar at O just after release.

23. PROBLEMS
7. The spring is uncompressed when the uniform slender bar is in the vertical position shown. Determine the initial angular acceleration a of the bar when it is released from rest in a position where the bar has been rotated 30o clockwise from the position shown. Neglect any sag of the spring, whose mass is negligible.

24.  W O G On Ot l Fspring lspring SOLUTION
Unstrecthed length of the spring:
When q=30o , length of the spring:
When q=30o , spring force:
(in compression) W O G +n +t On Ot
30o l
Fspring
60o .
lspring 