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

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Figure A.3 – a Screenshot of iMIDAS 78
APPENDIX B RECURSIVE SYMBOLIC CALCULATION ALGORITHMS IN MATHCAD Recurrent equations to be used in kinematic analysis are developed in Chapter 2 and the solution for a six DOF spatial parallel manipulator is given in Chapter 4. We need to find the components of E4 and E5 for each branch, to find their intersection points. Derivation of screw equations using recurrent equations is a straight forward algorithm. However, using computer to develop the equation greatly saves time and minimizes the possibility of making calculation errors. In what follows is the derivation of screw equations from recurrent equation using MathCAD software. B.1 Derivation of Unit Vectors To find the unit vectors of the screws e k ( Lk , M k , Nk ) , we input the two initial unit vectors e1 and e2 as given in Section 4.1.2. The second step is to use a loop to calculate the unit vectors of the unknown screws using equation (2.28). Using MathCAD the algorithm is written as in figure B.1. B.2 Derivation of Moments of Unit Vectors o Deriving the equations for moments of unit vectors ek ( Pk , Qk , Rk ) is more complicated since these depend on e k ( Lk , M k , Nk ) as given in (2.30). To find the unit vector of the screws, we input the two initial screws e1, e ,e2, e . Similarly, a loop is used to calculate the unit o 1 o 2 vectors of the unknown screws using equation (2.30). Using MathCAD, the algorithm is written as in figure B.2. The final results are compiled in (4.1). Note that, MathCAD cannot fully simplify the trigonometric equations, final touches are made manually. 79
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Kinematic and Dynamic Analysis of S
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Research is what I'm doing when I d
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ÖZ Bu tez yeni bir tip uzaysal alt
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Chapter 4 KINEMATIC ANALYSIS ......
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Figure 4.15 - Comparison of results
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Chapter 1 INTRODUCTION The introduc
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Figure 1.4 - The first flight simul
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Generally, the actuators of a seria
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−1 where J = J q J x . . . q = J
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Chapter 2 SCREW KINEMATICS In this
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From equation (2.6) we have; or x z
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Using (2.7) and (2.12), one can fin
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LP + MQ + NR = 0 L 1 2 2 + M 2 1 LP
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Following Crammer’s method, the u
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That’s, the variable angle α ki
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~ ~ ~ ~ ~ ~ Let Ei ( Li , M i, Ni )
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Qk = (NiPj + LjRi - LiRj - NjPi - a
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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: Figure A.2 - a Screenshot of iMIDAS
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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