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

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one meaning of orientation for unit vector k e wrt. plane ( e i, e j ), we describe a new vector n as n = ei × e j → n = ei e j S αij = 1. To determine the direction of vector e k ( α kn = π/2-α ki ) we have: e n = e n C α = C( π / 2 −α ) = Sα k k e k i kn k i ki ki ki ki e e = e e C α = Cα (2.26) k e j = ek e j kj C α = 0 Re-writing equation (2.26) in coordinate form: Lk(MiNj – NiMj) + Mk(NiLj – LiNj) + Nk(LiMj – MiLj) = Sαki LkLi + MkMi + NkNi = Cαki (2.27) LkLj + MkMj + NkNj = 0 Solving the system of linear equations (2.27) for Lk, Mk and Nk using Crammer’s method, ∆=1 and the components of vector ek ( Lk , M k , Nk ) are found as: Lk = (MiNj – NiMj) Sαki + Li Cαki Mk = (NiLj – LiNj) Sαki + Mi Cαki (2.28) Nk = (LiMj – MiLj) Sαki + Ni Cαki Using Kotelnikov - Shtudi transformations on (2.28) to find the equations of screw ~ ~ ~ E k ( Lk , M k , Nk ) we change the form of equation (2.28) to: ~ ~ ~ ~ ~ ~ L = ( M N − M N ) S A + L C A k k i i j j j j i i ki ki i ~ ~ ~ ~ ~ ~ M = ( N L − N L ) S A + M C A (2.29) ~ ~ ~ ~ ~ ~ N = ( L M − L M ) S A + N C A k i j j i From equations (2.29), we can find the components of the moment of unit vector o e k ( Pk , Qk , Rk ) as: Pk = (MiRj + NjQi – NiQj – MjRi – akiLi) Sαki + [(MiNj – NiMj)aki + Pi] Cαki ki i i ki ki ki 22
Qk = (NiPj + LjRi – LiRj – NjPi – akiMi) Sαki + [(NiLj – LiNj)aki + Qi] Cαki Rk = (LiQj + MjPi – MiPj – LjQi – akiNi) Sαki + [(LiMj – MiLj)aki + Ri] Cαki (2.30) Equations (2.28) and (2.30) are called as Recurrent Screw Equations, introduced by R. Alizade [39]. They are called as recurrent because, when we apply them to kinematics they will be used recursively to obtain the solutions, as explained in detail in chapter 4. 23
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 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: ~ ~ ~ ~ ~ ~ Let Ei ( Li , M i, Ni )
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
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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