Chapter 7, Problem 7.94P

The link lengths and the values of 02, W2, and y for some inverted fourbar crank- slider linkages are defined in the following table. The general linkage configuration and terminology are shown in the figure. For row a, what is the value of acceleration at point A, if we use the analytical vector loop method? Row Link 1 Link 2 Link 4y 02 W2 a2 6 12 4 9030 10-25 7 19 13 3 16 18 13 18 12 15 la b С d e If 02 002 10 5 14 18 Y 18 O 128.48 in/sec2 O 672.505 in/sec2 O 206.155 in/sec2 O 46.138 in/sec2 03 7585-15-40 4545 24 30 6025-5020 3075-45-5 90150100-65 RB B 04 fter 04 X

The link lengths and the value of 2 and offset for some fourbar crank-slide linkages are defined in Table 1. The linkage configuration and terminology are shown in Figure 1. For the rows assigned, find (a) all possible solutions for angle and slider position d by vector loop method. (b) the transmission angle corresponding to angle 83. (Hint: Treat the vector R4 as virtual rocker) Show your work in details: vector loop, vector equations, solution procedure. Table 1 Row a b с offset 02 Link 2 1.4 3 5 A R2 0₂ Link 3 4 8 20 slider axis. R3 Link 3 R₂ d R₁ Figure 1. 0₁ Offset 1 2 -5 С B R4 T 84 X Q2 45° -30° 225°

Problem 1 The link lengths, coupler point location, and the values of 02, w2, and a2 for the samefourbar linkages as used for position and velocity analysis in Chapters 4 and 6 areredefined in Table P7-1, which is the same as Table P6-1 (p. 371). The generallinkage configuration and terminology are shown in Figure P7-1. For the row(i) assigned, draw the linkage to scale and find the accelerations of points A and B. Then calculate a3 and a4 and the acceleration of point P. All steps of calculations must detailed and clear

Problem 1 The link lengths, coupler point location, and the values of 02, w2, and a2 for the samefourbar linkages as used for position and velocity analysis in Chapters 4 and 6 areredefined in Table P7-1, which is the same as Table P6-1 (p. 371). The generallinkage configuration and terminology are shown in Figure P7-1. For the row(i) assigned, draw the linkage to scale and find the accelerations of points A and B. Then calculate a3 and a4 and the acceleration of point P. All steps of calculations must detailed and clear RPA 04 02 04 FIGURE P7-1 TABLE P7-1 Data for Problems 7-3, 7-4 and 7-11t Row Link 1 Link 2 Link 3 Link 4 02 02 a2 Rpa d3 i 4 5 2 80 25 - 25 80

Consider the figure as shown below. O-XoYoZo is the reference frame and O-X₁Y₁Z₁ is the frame attached to the tool. Sketch the tool position after each intermediate position of the operation of the tool about the reference frame: roll π/2(rotate about Zo), pitch -T/2(rotate about Yo), yaw π/2(rotate about Xo). Please write the final rotation matrix expression. ZI,Zo XI,Xo Yı, Yo

A general fourbar linkage configuration and its notation are shown in Figure below. The link lengths, coupler point location, and the values of 02 and w2 for the same fourbar linkages as used for position analysis in Chapter 4 are redefined in Table below. For the row c, draw the linkage to scale and Using an analytical method calculate w3 and w4 and find the velocity of point P. find the velocities of the pin joints A and. RPA Y B 4 03 04 02 1 02 FIGURE P6-1 Configuration and terminology for the pin-jointed fourbar linkage of Problems 6-4 to 6-5 TABLE P6-1 Data for Problems 6-4 to 6-5† Row Link 1 Link 2 Link 3 Link 4 02 Rpa 83 02 a 2 7 9. 30 10 30 7 9. 8 85 -12 9 25 3 10 8 45 -15 10 80

A general fourbar linkage configuration and its notation are shown in Figure below. The link lengths, coupler point location, and the values of 02 and w2 for the same fourbar linkages as used for position analysis in Chapter 4 are redefined in Table below. For the row c, draw the linkage to scale and Using an analytical method calculate w3 and w4 and find the velocity of point P. find the velocities of the pin joints A and. RPA AY 2 04 02 04 FIGURE P6-1 Configuration and terminology for the pin-Jointed fourbar linkage of Problems 6-4 to 6-5 TABLE P6-1 Data for Problems 6-4 to 6-5† Row Link 1 Link 2 Link 3 Link 4 02 02 Rpa 83 6. 2 7 30 10 6. 30 b. 9 3 8 85 -12 9. 25 10 6. 8 45 -15 10 80 O73

Q3) You have been provided with following types of kinematic links. Can Type of link Numbers Binary 8 Ternary 3 Quaternary 2 Can you form a kinematic chain by selecting suitable number of links from the available quantity as indicated in the table above? Justify your answer. Note; (please provide an answer that is based on the Mechanics of Machines 1 handout MIME 3220)

For the 3-DOF Industrial manipulator arm as shown in Figure 3, determine the joint displacements for known position and orientation of the end of the arm point. 0. 0. Y1A Y2 A Y3 X2 X3 21 22 23 Yo xo Figure 3. 3 DOF RRR Industrial manipulator arm The link transformation matrices are given by C3 -S3 0 a3C3 S3 C3 1 C2 -S2 0 a,C2 C1 S1 -S1 -C1 d1 S2 C2 2T3 %3D T2 1 1 1 1 1 S1 C\C2a3+C1a2 C1C2C3 – C1S2S3 -C¡C2S3 – C1S2S3 S,C2C3 – S1S2S3 -SĄC2S3 – S1 S2C3 -C1 SịC2a3+ Sja2 Szaz + d1 1 OT3 = = °T, 'T2 ?T3 S½C3 + C2S3 - S2S3 + C2C3