Theory of Machines

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					Theory of Machines

     Lecture 7
                                 Bell Crank
                                                          OA+AB=OO’+O’B
                                 B                        O’C=O’D+DC
                3                                                                                   
                                                       1  L2 cos 2  L3 cos 3  d  L4 cos( 4   )  0
                                                        2  L2 sin  2  L3 sin  3  L4 sin( 4   )  0
    A                                                   3  L4 ' cos 4  e  L5 cos 5  0
                             4                          4  L4 ' sin  4  S  L5 sin  5  0
                                     C                  5   2   20  20t  1  2t 2  0
        2                                                                       2


O           d       O’                   5                                                      
                                                       1   L2 2 sin  2  L3 3 sin  3  L4 4 sin( 4   )  0
                                                                                
                             e                                                                       
                                                        2  L2 2 cos 2  L3 3 cos 3  L4 4 cos( 4   )  0
                                                       
                                                                                  
                                                          L ' sin   L  sin   0
                                                       3
                                                 S      4  L4 ' 4 cos 4  S  L5 5 cos 5  0
                                                       
                                                                 4 4
                                                                   
                                                                           4
                                                                              
                                                                                 5 5
                                                                                      
                                                                                            5


                                                              
                                                        4   2  20   2t  0
                                                       
                                             D
            1
                                                     q=[2, 3, 4, 5,S]T
                     Cam
                     OA+AB=OD+DB

                     x : e cos  2  r  S1
                     y : e sin  2  S 2
                     d :2    
    2
        A                 3
             r   B
        S1           S2
O
                 D


             1
           Position of a point
             A
                                                3

                                                                B
       2

                                                        4

                                                            C
                                                                    e
O

                                     d
      OB=OC+CB                       q=[2,3,4]T

          x  d  L4 cos 4 
    OB   B   
          yB   e  L4 sin  4 
                                 
                                     B=[d+L4*cos(qq(:,3)),e+L4*sin(qq(:,3))];
             Loop Closure
• Minimum equations
• Quick solution for position, velocity and
  acceleration
• convert generalised coordinate to desired
  coordinate

				
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posted:8/11/2011
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