Page 13 - 6742
P. 13

Velocity of the point B is determined by the next two vector
           equations
                                   V  V  A  V BA ,
                                    B
                                   
                                   V  V O 1  V BO 1 .
                                    B
                We must solve these equations graphically. Let’s draw line
           of velocity V ВА action through the point a, which is perpendicular
           to the link AB. V O 1    0, because the point O 1 is fixed. This point is
           placed  in  the  pole  of  velocities  polygon.  Next  one  draw  line  of
           V BO   action through the pole р v. This line should perpendicular to
              1
           the link О 1В. These both lines will cross and will give wanted the
           point b.
                Determine velocities
                         V BA   ab  V    24 0, 012  0, 288m/s,
                         V B  V BO 1   p  v   56 0, 012  0, 672m/s.
                                       b
                                      v
                Velocity  of  the  point  C  is  determined  by  theorem  of
           similarity. Look at these proportions:
                 O 1 C    p v c  , wherefrom  p  c   p   b  O 1 C    56  70    78 mm.
                 O 1 B   p v b            v      v  O 1 B      50
                Draw  vector  p  c    78 mm  on  the  velocities  polygon  from
           the  pole  in  same  direction  as  the  vector  p   (or  continue  the
                                                        b
                                                       
           vector  p v b  on distance  p v c  p v b    22mm). The point C is gotten
           on  the  velocities  polygon  as  result.  Magnitude  of  this  velocity
           looks like:
                           V    p  c   v   78 0, 012   0, 936m/s.
                             C
                We  need  to  solve  the  vector  equation  for  determination  of
           the point D velocity
                                      V D  V C V  DC .
                Draw straight line through  the point c perpendicular to the
           link  CD  –  direction  of  velocity  V DC.  Further,  draw  vertical  line
           from  the  pole  p   –  it  is  direction  of  the  slider’s  trajectory  of
                            
           motion. We got the point d on intersection.
                Determine velocities
                         V DC    cd      8 0, 012  0, 096m/s,
                                     v
                           V    p v d   v    76 0, 012  0, 912 m/s.
                             D
                Let’s determine angular velocities for links,     7s -1
                                                             1
                                          12
   8   9   10   11   12   13   14   15   16   17   18