I.3.4 Problems I.3.1 Find the analytical expression of any point P of the elipsograph mechanism in Figure I.2.53. I.3.2 The following data are given for the four-bar mechanism shown in Figure I.3.16: AB = CD = 0.04 m and AD = BC = 0.09 m. Find the trajectory of the point M located on the link BC for the case (a) BM = MC and (b) MC = 2 BM . B M A 0 D 0 C FIGURE I.3.16 Four-bar mechanism for Problem I.3.2. I.3.3 The planar four-bar mechanism depicted in Figure I.3.17 has dimensions AB = 0.03 m, BC = 0.065 m, CD = 0.05 m, BM = 0.09 m, and CM = 0.12 m. Find the trajectory described by the point M . M D A C B FIGURE I.3.17 Four-bar mechanism for Problem I.3.3. 128 KINEMATIC CHAINS AND MACHINE COMPONENTS DESIGN CD = 0.18 Mechanism for Problem I. BC = 0.3.200 m.20. Determine the positions of the joints and the angles of the links. Find the trajectory of the joint C . The angle of the driver element (link AB) with the horizontal axis is φ = 135◦ .04 m. CF = 0. The following data are given: AB = 0. The following data are given: AB = 0.19. I.450 m.21 has the following dimensions: AB = 40 mm.18 has dimensions AB = 0. The driver link is the rigid link 1 (the element AB). BC = 100 mm.025 m. AD = 150 mm. BC = 0.3. BC = 0.3.3. R4 = 0.3.3. EF = CE . DE = 0.3.07 m. and a = 90 mm.17 m. La = 0. I.400 m. CE = 30 mm.150 m. I. La = 0. and Lb = 0.7 The mechanism shown in Figure I. R1 = 0.12 m.I. CE = 0. and Lc = CD.12 m. CE = 0.350 m. Lb = 0.3. 5 F 6 C 0 3 2 Lb D R R La E 0 A 0 B 1 4 FIGURE I. The angle of driver link 1 with the horizontal axis is φ = φ1 = 45◦ .370 m.5 The planar R-RRR-RRT mechanism considered is depicted in Figure I.4 The mechanism shown in Figure I.350 m. CD = 0. Lc = 0.230 m.03 m. Position Analysis 129 .3.3.150 m.105 m. CD = 0. La = 0. EF = 120 mm. Lb = 0. Find the positions of the joints and the angles of the links.080 m.08 m.300 m.4.040 m.6 The R-RRR-RTT mechanism is shown in Figure I.200 m. y 0 3 0 E 4 F 2 5 1 n A 0 Lc La B φ x Lb C D FIGURE I.5.3. 0 E y La 3 Lb 2 C B φ 1 A 0 0 FIGURE I. 4 x Lc F 0 D 5 130 KINEMATIC CHAINS AND MACHINE COMPONENTS DESIGN .3.19 R-RRR-RRT mechanism for Problem I.20 R-RRR-RTT mechanism for Problem I.3.6.3. 3. BD = 670 mm. BD = 240 mm.3.7. and Lb = 70 mm.3.3.The angle of driver link 1 with the horizontal axis is φ = φ1 = 30◦ . B 1 y n A 0 a 4 F 5 0 FIGURE I. Find the positions of the joints and the angles of the links. DE = 420 mm. The angle of driver link 1 with the horizontal axis is φ = φ1 = 30◦ . and b = 170 mm. 2 C 90 3 D 0 φ x E I. I. BC = 240 mm.8.3. EF = 190 mm. CD = 660 mm. AE = 640 mm. AC = 60 mm.3. La = 300 mm. Find the positions of the joints and the angles of the links.8 The dimensions for the mechanism shown in Figure I. CF = 850 mm.3. Position Analysis 131 . DE = 330 mm. B 1 y 2 φ n F 5 C 4 x 0 D 3 A 0 b E 0 FIGURE I.23 has the dimensions: AB = 120 mm.9 The mechanism in Figure I.22 are: AB = 250 mm.3.22 Mechanism for Problem I.21 Mechanism for Problem I. 10. BC = 260 mm.3.24 are: AB = 100 mm.10 The dimensions for the mechanism shown in Figure I.9.3. AD = 240 mm. 0 F B 1 y 2 n Lb φ x 0 C 3 A 0 5 D 4 E La FIGURE I. EF = 250 mm. and 2 B 1 y φ n A 0 x 0 La 5 F 0 3 D C 4 E FIGURE I. DE = 80 mm.23 Mechanism for Problem I. 132 KINEMATIC CHAINS AND MACHINE COMPONENTS DESIGN . Find the positions of the joints and the angles of the links.24 Mechanism for Problem I.3.3. CD = 140 mm.3.The angle of driver link 1 with the horizontal axis is φ = φ1 = 150◦ . I.3. La = 210 mm. and Lc = 140 mm.3. BC = 160 mm.25 Mechanism for Problem I.3. AC = 240 mm.3. and La = 210 mm. BD = 700 mm.25 has the dimensions: AB = 150 mm. BD = 400 mm. Find the positions of the joints and the angles of the links.12 Figure I.3.11 The mechanism in Figure I.3.15 Figure I. and Lb = 200 mm. The angle of the driver link 1 with the horizontal axis is φ = φ1 = 135◦ . Position Analysis 133 . CD = DE = 180 mm.27 has the dimensions: AB = 100 mm.3.3. CE = 250 mm.3. Find the positions of the joints and the angles of the links.26 shows a mechanism with the following dimensions: AB = 180 mm. I. BC = 650 mm. BD = 700 mm.3. Lb = 150 mm. and Lb = 170 mm. CF = 150 mm. EF = 300 mm. AC = 450 mm. EF = 135 mm. EF = 350 mm. Find the positions of the joints and the angles of the links. La = 370 mm. CD = 400 mm.29 shows a mechanism with the following dimensions: AB = 140 mm. I. The angle of driver link 1 with the horizontal axis is φ = φ1 = 150◦ . I. La = 450 mm.28 shows a mechanism with the following dimensions: AB = 120 mm. and Lc = 700 mm. BC = 450 mm. The angle of driver link 1 with the horizontal axis is φ = φ1 = 120◦ .3.3.3. Find the positions of the joints and the angles of the links. La = 35 mm.3. La = 100 mm.16 Figure I.11. The angle of driver link 1 with the horizontal axis is φ = φ1 = 45◦ . 0 E 5 La Lb 2 3 B 1 y φ A x 4 C D 0 0 n FIGURE I. The angle of driver link 1 with the horizontal axis is φ = φ1 = 120◦ . Find the positions of the joints and the angles of the links. I. Lb = 550 mm. CD = 60 mm. DE = 250 mm.30 shows a mechanism with the following dimensions: AB = 60 mm. I.14 Figure I. I.3. Find the positions of the joints and the angles of the links.La = 20 mm. The angle of driver link 1 with the horizontal axis is φ = φ1 = 150◦ . DE = 180 mm.13 The mechanism in Figure I. The angle of driver link 1 with the horizontal axis is φ = φ1 = 60◦ .3.17 Figure I. AD = 25 mm. and BE = 60 mm. 134 KINEMATIC CHAINS AND MACHINE COMPONENTS DESIGN . BC = 50 mm.27 Mechanism for Problem I.3.2 3 C B 1 y φ n 5 D 0 4 A 0 La x E 0 FIGURE I. Find the positions of the joints and the angles of the links.3. Find the positions of the joints and the angles of the links.26 Mechanism for Problem I.12. Lb = 120 mm.3.13.31 shows a mechanism with the following dimensions: AB = 20 mm.3. I. and Lc = 65 mm. 0 F 5 E La Lb 4 2 3 C D 0 n 0 B 1 y φ A x FIGURE I. The angle of driver link 1 with the horizontal axis is φ = φ1 = 30◦ .3. 3. 3 D La Lb x Position Analysis 135 .3.14.15.3.3.29 Mechanism for Problem I. 5 F 4 E 0 2 C Lc B 1 y φ n A 0 FIGURE I.E 4 5 F 0 3 D Lc 0 2 B 1 y φ n Lb A 0 C La x FIGURE I.28 Mechanism for Problem I. 17.La F 3 B 1 y n A 0 φ x 2 Lc 4 D E 0 5 C Lb FIGURE I.30 Mechanism for Problem I. B 1 y φ n A 0 4 x 5 D 0 2 E C 3 0 FIGURE I.3.31 Mechanism for Problem I.16. .3.3.3. BC = 300 mm.3.3. and Lc = 100 mm.33 Mechanism for Problem I.18 The dimensions of the mechanism shown in Figure I.19 The dimensions of the mechanism shown in Figure I.3.I.3. CD = 280 mm. Lb = 200 mm. AC = 220 mm. CE = 850 mm. DE = 200 mm. Position Analysis 137 . Find the positions of the joints and the angles of the links.19.18.32 are: AB = 150 mm. 2 La 5 E 4 0 D C 0 n A 0 3 y φ x 1 B FIGURE I.33 are: AB = 150 mm.32 Mechanism for Problem I. CD = 330 mm. La 0 y φ x Lb 5 I. and La = 230 mm.3.3. The angle of driver link 1 with the horizontal axis is φ = φ1 = 60◦ . La = 350 mm. EF = 1200 mm.3.3. BE = 600 mm. Find the positions of the joints and the angles of the links. The angle of driver link 1 with the horizontal axis is φ = φ1 = 120◦ . C 3 D 2 B Lc E 1 n A 0 4 F 0 FIGURE I. 20 The dimensions of the mechanism shown in Figure I. AC = 200 mm. The angle of driver link 1 with the horizontal axis is φ = φ1 = 45◦ .I. and b = 450 mm. 138 KINEMATIC CHAINS AND MACHINE COMPONENTS DESIGN . Find the positions of the joints and the angles of the links.3. and DE = 500 mm.3.20. B 1 y n A 0 φ x 2 D 3 90 C 0 4 5 E 0 FIGURE I. CD = 200 mm.3.34 Mechanism for Problem I. The angle of driver link 1 with F G E 0 5 D 4 0 b y n 1 φ x B 2 A 0 3 C 0 FIGURE I. CD = 380 mm.3.35 Mechanism for Problem I. I. AC = 60 mm.3.3.3.21 The dimensions of the mechanism shown in Figure I.35 are: AB = 120 mm.21.34 are: AB = 200 mm.3. 36 Mechanism for Problem I.23. AC = 280 mm. and DE = 220 mm.36 are: AB = 160 mm.3.3.3. The angle of driver link 1 with the horizontal axis is φ = φ1 = 30◦ . I.23 The dimensions of the mechanism shown in Figure I. Find the positions of the joints and the angles of the links.22 The dimensions of the mechanism shown in Figure I.3. 2 B 3 0 C D 1 n 4 5 y φ A 0 x FIGURE I.3. E 5 C 3 0 4 Position Analysis 139 .22. BD = La = 470 mm.3. I.37 Mechanism for Problem I.37 are: AB = 100 mm.the horizontal axis is φ = φ1 = 30◦ . The angle of driver link 1 with the horizontal axis is φ = φ1 = 30◦ . Find the positions of the joints and the angles of the links. AC = 90 mm. Find the positions of the joints and the angles of the links. and CD = 160 mm.3.3. La B 2 1 y n A 0 φ x 0 D FIGURE I. 38 are: AB = 250 mm. 2 φ D x 0 3 1 n A 140 KINEMATIC CHAINS AND MACHINE COMPONENTS DESIGN . AD = 700 mm.3. F 0 4 C G B 5 y E 0 0 a FIGURE I.3.3.38 Mechanism for Problem I. Find the positions of the joints and the angles of the links.24 The dimensions of the mechanism shown in Figure I.24. and a = 650 mm. The angle of driver link 1 with the horizontal axis is φ = φ1 = 145◦ .I.3. BC = 300 mm.