Problem 6-62

1
Problem 6-62

• A carton turnover machine is shown below.

2
Problem 6-62

• At the instant shown, the 15 in link is driven
  clockwise at 5 rad/sec, and decelerating at
• 40 rad/sec2. Determine the instantaneous torque
  required to operate the 15 in arm, and the forces
  at the two lower bearings. The two long links
  closely resemble slender members, made from
  steel, with a width of 1 in and a thickness of
• 0.25 in. The carrier and carton weigh 26 lb and
  its mass moment of inertia, relative to an axis
  through its center, is 2.75 lb in s2.

3
Kinematic Diagram
4
Velocity Analysis
VB w2 rAB (5 rad/s)(15 in) 75 in/s
VC VB gt VC/B
VG3 VB gt VG3/B VC gt VG3/C
5
Velocity Results

• VC 40.4 in/s 680
• VC/B 49.8 in/s
• VX/B 25.6 in/s 56.30
• VX/C 41.5 in/s 310
• VG3 77.7 in/s 490
• VG2 37.5 in/s 300
• VG4 20.2 in/s 680

6
Acceleration Analysis

• anB (75)2/15 375.0 in/s2 60.00

7
Acceleration Analysis
anCgtatC anBgtatBgt anC/BgtatC/B
8
Acceleration Analysis

• atC 250.8 in/s2 68.00

• a4 (250.8)/16 15.68 rad/s2 ccw

• a3 (332.7)/7 47.53 rad/s2 ccw

9
aG3 aBgtanG3/BgtatG3/B aCgt
anG3/CgtatG3/C
10
Inertia Forces Link 2

• Vol2 (16 in)(1 in)(.25 in) 4 in3

• W2 (.283 lb/in3)(4 in3) 1.13 lb

11
Inertia Forces Link 2
FiG2

• a2 40 rad/s2 ccw

15 in

• Assume slender rod

600

• IG2 ¼ (1.13 lb)/(386.4 in/s2)(16 in)2
• 0.19 lb in s2

12
Inertia Forces Link 3

• a3 47.53 rad/s2 ccw

13
Inertia Forces Link 4

• Vol4 (17 in)(1 in)(.25 in) 4.25 in3

• W4 (.283 lb/in3)(4.25 in3) 1.20 lb

14
Inertia Forces Link 4
FiG4

• a4 15.68 rad/s2 ccw

• Assume slender rod

• IG4 ¼ (1.20 lb)/(386.4 in/s2)(17 in)2
• 0.22 lb in s2

15
Free Body Diagrams
16
FBD Link 2
Bx
SFx 0 Ax - Bx FiG2 cos62 0
TiG2
FiG2
By
620
W2
TA
SFy 0 Ay - By FiG2 sin62 - W2 0
600
15 in
7.5
Ax
Ay
17
FBD Link 3
SFx 0 Bx Cx FiG3 cos83 0
SFy 0 By Cy FiG3 sin83 W3 0
SMc 0 W3(3) - Bx(7) - (FiG3 sin83)(3) - (FiG3
cos83)(5) - TiG3 0
18
FBD Link 4
SFx 0 Dx - Cx 0
SFy 0 Dy - Cy FiG4 - W4 0
19
Finally, Solving the Nine Simultaneous
Equations

• Ax -23.3 lbs
• Ay -11.5 lbs
• Bx -22.8 lbs
• By -11.7 lbs

• Cx 17.3 lbs
• Cy -7.2 lbs
• Dx 17.3 lbs
• Dy -6.4 lbs
• TA -394.1 in lbs