PROBLEMS The gear has the angular motion shown

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. C A w=2 rad/s 2 m 0. 5 m 0. 7 m B O a=4 rad/s 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 1 A 10 cm 2 20 cm 37 o w 1=5 rad/s B O 16 cm C

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/s 2 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.

Problem 7 Velocity Analysis v. B b 25 24 7

Velocity Analysis

Velocity Analysis vrel q 3 5 4

Acceleration Analysis a. B b 25 24 7

Acceleration Analysis

Acceleration Analysis

Acceleration Analysis +n +t (arel)n vrel q 3 (arel)t 5 4

PROBLEMS The pin A in the bell crank AOD is guided by the flanges of the collar B, which slides with a constant velocity v. B of 0. 9 m/s along the fixed shaft for an interval of motion. For the position q=30 o determine the acceleration of the plunger CE, whose upper end is positioned by the radial slot in the bell crank. .

v. A Problem 8 Velocity Analysis vrel v. A 30 o v. B=(v. A)x 129. 9 mm 60 o vrel (1)=(2) vrel=-1. 039 m/s vc=2. 079 m/s 30 o

Acceleration Analysis a. A 30 (a. A)n o VB=constant So a. A must be vertical. (a. A)t vrel a. A 60 o 30 o 129. 9 mm

(3)=(4) arel=24. 92 m/s 2 a. C=27. 92 m/s 2

PROBLEMS 1. The uniform 30 -kg bar OB is secured to the accelerating frame in the 30 o position from the horizontal by the hinge at O and roller at A. If the horizontal acceleration of the frame is a=20 m/s 2, compute the force FA on the roller and the x- and y-components of the force supported by the pin at O.

PROBLEMS 2. The block A and attached rod have a combined mass of 60 kg and are confined to move along the 60 o 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.

SOLUTION FBD Kinetic Diagram m. Tax=60 ax x x N 60 o W=60(9. 81) N By FBD of rod KD of rod m 1 ax=20 ax Bx M W 1=20(9. 81) N

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 60 o, the links have an angular acceleration an angular velocity of 6 rad/s 2 and 3 rad/s, respectively. For this instant calculate the magnitudes of the force F and torque M supported by the pin at E.

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.

SOLUTION FBD +n TA KD TB +t +n +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. *

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. C A 60° 24 cm B 10 cm 60° D G Answer: 20 cm

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/s 2, and find the force R on the bar at O just after release.

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 30 o clockwise from the position shown. Neglect any sag of the spring, whose mass is negligible.

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