三維空間之機械手臂虛擬實境模擬

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圭寿
5 years ago
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1 VRML Model of 3-D Robot Arm

2 VRML Model of 3-D Robot Arm

3 MATLAB VRML MATLAB Simulink i

4 MATLAB Simulink V-Realm Build Joystick ii

5 Abstract The major purpose of this thesis presents the procedure of VRML modeling of 3-D robot arm in computer. We use virtual reality toolbox of MATLAB7.1 to perform our researchful result. By computing vectors and trigonometric function, we understand the moving track of robot arm. Using many block diagrams to show our program after counting. Last we connect the figure by using V-Realm Build program with Joystick block to control the robot arm. Let robot arm can move any place we want. Before using the toolbox, we must have background knowledge about the motion mode of three domains robot arm and basic block diagram. These will be introduced in our thesis. We really hope that the thesis can provide much useful information on dynamic simulation. iii

6 ...i...ii Abstract...iii...iv...v...viii Joystick VRML VRML iv

7 Data Type Conversion...8 Gain Math Function MATLAB Fcn Mux Dead Zone Saturation Sign Joystick Joystick Joystick VR Sink VR Sink a4+a5 & a θ v

8 4.5 Fcn1(a4) Fcn2(a4) θ Fcn2(a5) Fcn3(a5) a X1(a6) Y1(a6) Z1(a6) Fcn1(a4+a5) a C1 translation &rotation Fcn1(C1 translation) Fcn2(C1 translation) Fcn3(C1 translation) Fcn4(C1 & C4 rotation) Fcn5(C1 & C4 rotation) Fcn6(C1 & C4 rotation) a C2 translation Fcn1(C2 translation) Fcn2(C2 translation) Fcn3(C2 translation) Fcn1(C3 translation) Fcn2(C3 translation) Fcn3(C3 translation)...39 vi

9 4.31 C4 & S2 translation Fcn1(C4 & S2 translation) Fcn2(C4 & S2 translation) Fcn3(C4 & S2 translation) Fcn4(C4 & S2 translation) Fcn5(C4 & S2 translation) Fcn6(C4 & S2 translation) Fcn1(S3 translation) Fcn2(S3 translation) Fcn3(S3 translation) X vii

10 viii

11 1.1 MATLAB Simulink MATLAB Simulink V-Realm Build MATLAB VRML Joystick

13 2.1 XYZ 2.1 X1 Y 1 Z 1 C 1 X2 Y 2 Z 2 C 2 C1 C C C2 1 1 C1X = ( Cco 1 sθ1) cosθ3 2 (2.1) 1 C1 Y = C1 θ1 2 ( sin ) (2.2) 1 C1Z = ( Cco 1 sθ1) sinθ3 2 (2.3) ( ) 1 C2X = Cco 1 sθ1 + ( C2cosθ2) cosθ3 2 (2.4) 3

14 1 C = C + C 2 ( sinθ ) ( sinθ ) 2Y (2.5) ( ) 1 C2Z = Cco 1 sθ1 + ( C2cosθ2) sinθ3 2 (2.6) (2.1) (2.6) C1 C 2 XYZ 2.1 C1 C 2 C1 C θ = tan 4 1 Y X+Z 2 2 (2.7) ( ) X = C cos θ + θ cosθ (2.8) 4

15 ( ) Y = C sin θ + θ (2.9) ( ) Z = C cos θ + θ sinθ (2.10) θ = cos 5 θ = tan X + Y + Z 2 C ( Y-Y1 ) ( X-X ) + ( Z-Z ) (2.11) (2.12) θ = tan 3 1 Z X (2.13) θ3 θ 4 θ 5 θ 6 C1 C 2 1 (2.7) arctan2 tan 360 arctan2 (2.8) (2.9) (2.10) X 1 Y 1 Z 1 (2.12) θ6 +Z -Z C1 C 2 ( sin θ, 0, cosθ ) 3 3 X Y Z 5

16 MATLAB 7.1 Model 3.1 Simulink

17 3.1 A Constant 1 B Demux C Input D Data Type conversion E Gain F Display G Output H Sum I Math Function exp log square conj J MATLAB Fcn u K Integrator L Dead Zone M Saturation N Sign O Mux P Joystick Input Q VR Sink 7

18 Demux 3.2 input Data Type Conversion MATLAB Joystick Buttons Demux Buttons boolean uint Demux 3.3 Data Type Conversion 8

19 3.4 Gain Math Function 3.5 MATLAB Fcn 3.6 u u () ( ) ( ) ( ) ( ( )) u 1 +u 2 -cos u 3 +sin u 4 (3.1) (3.1) u(1) u(2) u(3) u(4) Mux Demux Dead Zone

20 0,if Dead Zone ( -Dead Zone ),if > Dead Zone (3.2) 3.10 Saturation ± ± Sign Joystick VR Sink 3.5 Math Function 10

21 3.6 MATLAB Fcn 3.7 Mux 11

22 Dead Zone 12

23 3.10 Saturation 3.11 Sign 13

24 3.2 Joystick Joystick 3.12 Axes Button Axes (X,Y) Joystick (X,Y) Axes [1 2] Joystick Axes Demux 3.12 Joystick (X,Y) u(1) u(2) ( ( ) ( )) θ =arctan2 u 2,u 1 (3.3) (X,Y)

25 3.12 Saturation Buttons Button Demux Demux Data Type Conversion Button Z Button Axe Sum Z Joystick Input 3.13 Joystick 15

26 3.14 Joystick Joystick Axes Demux (X,Y) Dead Zone Dead Zone Sign Saturation -1 (X,Y) -1 (X,Y) 16

3.3 VRML VRML MATLAB Toolbox V-Realm Bulid VRML 3.15 3.

27 3.3 VRML VRML MATLAB Toolbox V-Realm Bulid VRML VR Sink VRML translation rotation scale VR Sink VR Sink 17

28 3.4VRML

29 3.2 Height( ) Radius( ) (c1) (c2) (c3) (c4) (s1) 0.2 (s2) 0.2 (s3) 0.2 (s4) 0.2 (cp1) ( ) (cp2) (cp3) (c1) (c2) MATLAB toolbox V-Realm Bulider VR Sink 19

4.1 4.1 MATLAB File New Model 10.0 inf 4.

30 MATLAB File New Model 10.0 inf Joystick VR Sink VR Joystick VR Sink 20

31 Joystick Axes (X,Y) Joystick buttons Z (X,Y,Z) (X,Y,Z) (X,Y,Z) (X,Y,Z) C1 C 2 θ3 θ 4 θ 5 θ 6 a4+a5 & a a4+a5 & a6 21

32 1 θ 4 + θ 5 2 θ 6 θ 4 + θ 5 θ 4 θ5 θ4 4.4 θ4 4.4 In1 Joystick (X,Y,Z) Fcn1 u(1) u(2) u(3) (X,Y,Z) Fcn1(a4) 22

33 4.4 Math function Fcn1 (X,Y,Z) Gain 0.5 arc cos 2 Fcn Fcn2(a4) θ4 a4+a5 & a6 2 θ θ5 23

34 4.7 In1 Joystick (X,Y,Z) Fcn1 Y u(2) Fcn2 (X,Z) Fcn2(a5) (X,Z) Fcn3 Mux θ

35 4.9 Fcn3(a5) θ5 atan2(u(1),u(2)) θ4 θ 5 θ a a6 25

36 In1 θ 3 In2 Joystick (X,Y,Z) In3 a4+a5 X Y Z X X u(1) Y Y u(2) Z Z u(3) X1 Y1 Z X1(a6) 26

37 4.12 Y1(a6) 4.13 Z1(a6) 27

38 X-X1 Y-Y1 Z-Z1 Mux u(1)-u(2) (X-X1)*(X-X1) (Z-Z1)*(Z-Z1) u*u Fcn1 u(1)+u(2) Mux arctan atan2(u(1),u(2)) θ a4 a5 Mux Fcn Fcn1(a4+a5) θ4 θ 5 θ 6 θ3 a3 Z X arctan

39 4.15 a3 C1 translation & rotation C S In1 θ4 θ 5 In2 θ3 Fcn1 C1 X 4.17 Fcn2 C1 Y 4.18 Fcn3 C1 Z 4.19 u(1) θ 4 + θ 5 u(2) θ 3 1 cos θ θ )cos( θ ) (4.1) sin θ θ ) (4.2) + 5 cos θ θ )sin( θ ) (4.3)

40 4.16 C1 translation & rotation 4.17 Fcn1(C1 translation) 30

41 4.18 Fcn2(C1 translation) 4.19 Fcn3(C1 translation) 31

42 MUX X Y Z X sin( θ ) Fcn Y Z 3 cos( θ3) Fcn θ 4 + θ pi/2 run pi/2 90 (cylinder1)c1 S1 sphere1 C1 S1 translation C1 translation X Y Z Fcn7 Fcn8 Fcn Fcn4(C1 & C4 rotation) 32

43 4.21 Fcn5(C1 & C4 rotation) 4.22 Fcn6(C1 & C4 rotation) 33

44 θ3 a3 θ3 Z X arctan a3 u(1) X u(2) Z (cylinder2)c C2 translation 34

45 Fcn1 X 4.25 Fcn2 Y 4.26 Fcn3 Z 4.27 C1 C2 θ 6 ( ) cos θ + θ5) + cos( θ6) cos( θ3) (4.4) ( sin θ θ ) sin( θ )) (4.5) ( ) cos θ + θ5) + cos( θ6) sin( θ3) (4.6) 4.25 Fcn1(C2 translation) 35

46 4.26 Fcn2(C2 translation) 4.27 Fcn3(C2 translation) 36

47 u(1) θ 4 + θ 5 u(2) θ6 u(3) θ3 C2 C3 translation C1 C2 C3 C4 C3(cylinder3) C2 θ 3 = 0.35 cos( θ ) cos( θ ) (4.7) 6 3 = 0.35 sin( θ ) (4.8) 6 = 0.35 cos( θ ) sin( θ ) (4.9) C3 translation Fcn Fcn Fcn C2 C3 C2 & C3 rotation θ6 C1 rotation X sin( θ ) Y 0 Z cos( θ )

48 4.28 Fcn1(C3 translation) 4.29 Fcn2(C3 translation) 38

49 4.30 Fcn3(C3 translation) C4 & S2 translation 4.31 input output C4 S2 translation C4(cylinder4) C1 C4 (X,Y,Z) X = (cos( θ + θ ) cos( θ )) cos( θ ) (4.10) = (sin( θ + θ ) sin( θ )) (4.11) = (cos( θ + θ ) cos( θ ))sin( θ ) (4.12)

50 4.31 C4 & S2 translation 4.31 Fcn1 C4 X 4.32 Fcn2 C4 Y 4.33 Fcn3 Z Fcn1(C4 & S2 translation) 40

51 4.33 Fcn2(C4 & S2 translation) 4.34 Fcn3(C4 & S2 translation) 41

52 C1 C2 C3 C4 S2 S2 C2 C4 S2 C2 C2 Fcn4 X 4.35 Fcn5 Y 4.36 Fcn6 Z Fcn4(C4 & S2 translation) 42

53 4.36 Fcn5(C4 & S2 translation) 4.37 Fcn6(C4 & S2 translation) 43

54 C3 C4 S3(sphere3) X = 0.7 cos( θ )cos( θ ) (4.13) 6 3 = 0.7 sin( θ ) (4.14) 6 = 0.7 cos( θ )sin( θ ) (4.15) 6 3 Fcn1 Fcn2 Fcn3 X Y Z Fcn Fcn Fcn u(2) θ 6 u(3) θ Fcn1(S3 translation) 44

55 4.39 Fcn2(S3 translation) 4.40 Fcn3(S3 translation) 45

56 CP1 CP2 CP3 给 X Y Z VR Sink 46

57 4.2 MATLAB V-Realm Builder

58 4.42 New World Transform children rotation translation height radius Rotation Z 1 Z Rotation X 90 48

59 4.44 X C1 VR-Sink VR-Sink VR-Sink

60 4.45 Viewpoint orientation X position (0.5,8,0)

61 4.47 X Y Z 4.48 X Y 1 2 Z

63 X Y Z

64 5.2 MATLAB MATLAB 54

65 5.3 MATLAB Joystick X-Y Z 55

66 [1] Matlab 2003 [2] /Simulink 2001 [3] MATLAB [4] Matlab 6.X 2003 [5] Palm, William J. MATLAB

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