Kinematic and Dynamic Analysis of Spatial Six Degree of Freedom ...

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Platform Position (mm) Platform Orientation (deg) 1000 900 800 700 600 500 400 300 200 100 30 20 10 0 -10 -20 -30 -40 0 X Position Y Position Z Position 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 Input Actuator Displacement (mm) Figure 4.10 - Platform position for manipulator actuated by a single linear actuator Yaw Pitch Roll 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 Input Actuator Displacement (mm) Figure 4.11 - Platform orientation for manipulator actuated by a single linear actuator 48
4.2.4 Results for the Actuation of the First Two Linear Actuators The first two linear actuators correspond to Input( a ) and Input( a ) in figure 4.1. Figures 4.12, 4.13 and 4.14 shows the graphs of the results. For figure 4.12, Eavg = 0.91, %Eavg = 0.18. Platform Centroid Distance (mm) 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0 Optimization Numerical Integration 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 2 35 Input Actuator Displacement (mm) Figure 4.12 - Comparison of results for two actuated linear actuators 4 35 49
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Kinematic and Dynamic Analysis of S
Page 3 and 4:
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Page 5 and 6:
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Page 7 and 8: Chapter 4 KINEMATIC ANALYSIS ......
Page 9 and 10: Figure 4.15 - Comparison of results
Page 11 and 12: Chapter 1 INTRODUCTION The introduc
Page 13 and 14: Figure 1.4 - The first flight simul
Page 15 and 16: Generally, the actuators of a seria
Page 17 and 18: −1 where J = J q J x . . . q = J
Page 19 and 20: Chapter 2 SCREW KINEMATICS In this
Page 21 and 22: From equation (2.6) we have; or x z
Page 23 and 24: Using (2.7) and (2.12), one can fin
Page 25 and 26: LP + MQ + NR = 0 L 1 2 2 + M 2 1 LP
Page 27 and 28: Following Crammer’s method, the u
Page 29 and 30: That’s, the variable angle α ki
Page 31 and 32: ~ ~ ~ ~ ~ ~ Let Ei ( Li , M i, Ni )
Page 33 and 34: Qk = (NiPj + LjRi - LiRj - NjPi - a
Page 35 and 36: The methods reported by F. Freudens
Page 37 and 38: Using equations (3.4) and (3.6), we
Page 39 and 40: Order of a structural group is the
Page 41 and 42: 3.3 Geometrical Structural Synthesi
Page 43 and 44: 3.4 Kinematic Structural Synthesis
Page 45 and 46: Let’s consider a 5 DOF parallel m
Page 47 and 48: Chapter 4 KINEMATIC ANALYSIS Kinema
Page 49 and 50: Figure 4.1 - The six degree of free
Page 51 and 52: v v v P4 = yv N 4 − zv M 4 v v v
Page 53 and 54: The best way of visualizing the dis
Page 55 and 56: 4.2.2 Results for the Actuation of
Page 57: 4.2.3 Results for the Actuation of
Page 61 and 62: 4.2.5 Results for the Actuation of
Page 63 and 64: Figure 4.17 - Corresponding piston
Page 65 and 66: Chapter 5 DYNAMIC ANALYSIS Dynamics
Page 67 and 68: Thus, according to Lagrange, the re
Page 69 and 70: J is the 6x6 Jacobian matrix that
Page 71 and 72: Chapter 6 DISCUSSION AND CONCLUSION
Page 73 and 74: REFERENCES [1] D. Stewart, A platfo
Page 75 and 76: [19] Seung-Bok Choi, Dong-Won Park,
Page 77 and 78: [38] Kotelnikov A. P., Screw calcul
Page 79 and 80: [60] R. I. Alizade, Investigation o
Page 81 and 82: A.1.1 CASSoM Source Code Like all v
Page 83 and 84: in the 'Input Parameters' section.
Page 85 and 86: pty:=roy+dy; ptz:=roz+dz; end; func
Page 87 and 88: Figure A.2 - a Screenshot of iMIDAS
Page 89 and 90: APPENDIX B RECURSIVE SYMBOLIC CALCU
Page 91 and 92: PP := L1 ← 0 M1 ← 0 N1 ← 1 L2
Page 93 and 94: Preleminary function definitions In
Page 95 and 96: C.2 Visual NASTRAN Desktop NASTRAN
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