1. The tie-rod AB exerts the 250 N force on the steering knuckle AO as shown. Replace this force by an equivalent force-couple system at O.

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2 1. The terod AB exerts the 50 N force on the steerng knuckle AO as shown. Replace ths force by an equvalent forcecouple system at O.

3 . The devce shown s part of an automoble seatbackrelease mechansm. The part s subected to the 4 N force exerted at A and a 00 Nmm restorng moment exerted by a hdden torsonal sprng. Determne the yntercept of the lne of acton of the sngle equvalent force.

4 . Under nonunform and slppery road condtons, the four forces shown are exerted on the four drve wheels of the allwheeldrve vehcle. Determne the resultant of ths system and the x and yntercepts of ts lne of acton. Note that the front and rear tracks are equal (. e., ). AB CD

5 4. A 50 N horzontal force s appled to the handle of the ndustral water valve as shown. The force s perpendcular to the vertcal plane contanng lne OA of the handle. Determne the equvalent forcecouple system at pont O.

6 5. Represent the resultant of the force system actng on the ppe assembly by a sngle force at A and a couple.

7 5 N. m 115 N 100 N 6. Two forces and a couple (appled to porton AB) are appled to the car s exhaust system as shown. Replace the gven force system wth an equvalent forcecouple system at D.

8 * Lne MN les n a plane parallel to the horzontal plane * Lne AD les n the xz plane and makes a 7 angle wth the x axs. 7. The drecton cosnes of robot arm AB are cos q x =0.6, cos q y (q y <90 ) and cos q z =0. For arm BC the drecton cosnes are, cos q x =7/9, cos q y =4/9 and cos q z =4/9. A force of magntude F=50 N and a couple of magntude C=7 Nm along the axs BC are appled to the end C of arm BC. Determne the moment about lne AD. Replace the force and couple actng on the robot assembly wth an equvalent forcecouple at pont A.

9 8. The threadng dye s screwed onto the end of the fxed ppe whch s bent through an angle of 0. Replace the two forces by an equvalent force at O and a couple. Fnd and calculate the magntude M of the moment whch tends to screw the ppe nto the fxed block about ts angled axs through O.

10 R F M o 0. 15sn cos 0k 0. k sn cos 0k 0. k Mo 17 85k noc sn 0 cos 0k M M M OC o k 17 85k k Nm

11 tan q 15 8 q 1700 N 500 N y 4 cm 400 N 4 50 cm 0 cm 800 N. m q tan q 8 15 z 50 cm x 50 cm 9. The pulleys and the gear are subected to the loads shown. For these forces, determne the equvalent forcecouple system at pont A.

12 R F R F F F k C F r M k C k k F r k F r k F r k k F r C F r M A A

13 10. In tghtenng a bolt whose center s at pont O, a person exerts a 180 N force on the ratchet handle wth hs rght hand. In addton, wth hs left hand he exerts a 90N force as shown n order to secure the socket onto the bolt head. Determne the equvalent forcecouple system at O. The fnd the pont n the xy plane through whch the lne of acton of the resultant force of the wrench passes.

14 11.

15 Z C F 1 = 0 N F = 75 N F = 40 N C 1 = 60 Nm C = 100 Nm (n yz plane) X B 6 m 7 C 1 A F C F G q y C O 5 E 0 F C = 80 Nm (n plane ABCD) q y > 90 o Y O (0, 0, 0) m A (1, 0, 0) m B (n xz plane) C (1, 8, 0) m E (6, 10, ) m G (10, 4, 4) m 4 m D 1. Replace the system comprsng two forces, two couples and a postve wrench wth an equvalent forcecouple actng at pont O. Then, reduce the system further nto a wrench and determne the coordnates of pont P, of whch the lne of acton of the wrench cuts through the yz plane.

16 Force: Z C F 1 = 0 N F = 75 N F = 40 N C 1 = 60 Nm C = 100 Nm (n yz plane) X 6 m 7 C 1 A F C F G q y C O 5 E 0 F C = 80 Nm (n plane ABCD) q y > 90 o Y B 4 m D cos 45 F 0 cos 60 cos q y 1 cos45 cos60 cos60k k y 60 1 q o

17 Force: Z C F 1 = 0 N F = 75 N F = 40 N C 1 = 60 Nm C = 100 Nm (n yz plane) X 6 m 7 C 1 A F C F G q y C O 5 E 0 F C = 80 Nm (n plane ABCD) q y > 90 o Y O (0, 0, 0) m A (1, 0, 0) m B (n xz plane) C (1, 8, 0) m E (6, 10, ) m G (10, 4, 4) m B 4 m D 1 18 ( 8 0 ) ( 0 8)k F k

18 Force: Z C F 1 = 0 N F = 75 N F = 40 N C 1 = 60 Nm C = 100 Nm (n yz plane) X 6 m 7 C 1 A F C F G q y C O 5 E 0 F C = 80 Nm (n plane ABCD) q y > 90 o Y O (0, 0, 0) m A (1, 0, 0) m B (n xz plane) C (1, 8, 0) m E (6, 10, ) m G (10, 4, 4) m B 4 m D F 40cos 60cos 5 40cos 60 sn 5 40cos 0k k R F k R k nr k R

19 r r r 1 Moment: F1 F F M o r F C k k k 1... k k. k k Z k X 6 m 7 C 1 A F C F G q y C O 5 E C 0 F Y F 1 = 0 N F = 75 N F = 40 N C 1 = 60 Nm C = 100 Nm (n yz plane) C = 80 Nm (n plane ABCD) q y > 90 o O (0, 0, 0) m A (1, 0, 0) m B (n xz plane) C (1, 8, 0) m E (6, 10, ) m G (10, 4, 4) m B 4 m D

20 C1 60 cos45 cos 60 cos 60k 4. 4 C 100 BA BD 6 k 8 4 4k 4k C k Z k C F 1 = 0 N F = 75 N F = 40 N C 1 = 60 Nm C = 100 Nm (n yz plane) C = 80 Nm (n plane ABCD) q y > 90 o O (0, 0, 0) m A (1, 0, 0) m B (n xz plane) C (1, 8, 0) m E (6, 10, ) m G (10, 4, 4) m X B 4 m 6 m 7 D C 1 A F C F G q y C O 5 E 0 F Y

21 Moment: M M o o k k k 4. k k k Equvalent forcecouple system at pont O R k M k o

22 Equvalent forcecouple system at pont O R k M k o Reducton to a wrench n yz plane M M // // M M o // n n R R Postve wrench k k.... k k 1 5 R k M k // M M o 1. 5 z Postve wrench M // k Nm R k O x y

23 The coordnates of pont P, of whch the lne of acton of the wrench cuts through the yz plane: M Mo M // M k y zk k r k k R k 1.95yk 96.5y 1.45z 77.8z k 1.95z z m k 1.95y y 91.7 m M z R k Postve wrench r M // k P(0;91.7;474.66) x O y