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

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1.4.3 Combined Singularities Combined singularity occurs when the determinants of both Jx and Jq are zero. At a combined singular configuration, Eqn. (1.1) will degenerate. The moving platform can undergo some infinitesimal motions while all actuators are locked. On the other hand, it can also remain stationary while the actuators undergo some infinitesimal motion. 8
Chapter 2 SCREW KINEMATICS In this thesis, the tool used to derive the kinematic equations is called as the screw theory. In this chapter, the screw theory is explained in detail. 2.1 Definition of a Unit Screw in Space where A screw can be described as a dual vector as in figure 2.1. x P L N e : the unit vector of screw axis Figure 2.1 – A unit screw in space E e + o e : moment of e wrt. the origin of fixed coordinate system w: Clifford operator (w 2 =0) z R o = we (2.1) Equation (2.1) is the definition of a unit screw. Screw algebra is the vector algebra of this dual vector. A screw can be described using three dual coordinates in space as o e Q M y e 9
Page 1 and 2: Kinematic and Dynamic Analysis of S
Page 3 and 4: Research is what I'm doing when I d
Page 5 and 6: ÖZ Bu tez yeni bir tip uzaysal alt
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: −1 where J = J q J x . . . q = J
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 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
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Chapter 6 DISCUSSION AND CONCLUSION
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REFERENCES [1] D. Stewart, A platfo
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[19] Seung-Bok Choi, Dong-Won Park,
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[38] Kotelnikov A. P., Screw calcul
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[60] R. I. Alizade, Investigation o
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A.1.1 CASSoM Source Code Like all v
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in the 'Input Parameters' section.
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pty:=roy+dy; ptz:=roz+dz; end; func
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Figure A.2 - a Screenshot of iMIDAS
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APPENDIX B RECURSIVE SYMBOLIC CALCU
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PP := L1 ← 0 M1 ← 0 N1 ← 1 L2
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Preleminary function definitions In
Page 95 and 96:
C.2 Visual NASTRAN Desktop NASTRAN
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