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          248                      CAM DESIGN HANDBOOK

             5


             4
                                                               Q*
                              n*
             3
                                                                    P
             P
             2
                                            R*
             1                – dh/dq
                                          S
                                     R
             0
                     n specified

            –1
                              n
            –2


            –3
              0      50     100    150     200    250     300    350    400
                                            q
            FIGURE  8.26.  Design  curves  and  the  specification  of  single-dwell  motion  using  half-cycloidal
            curves.


          EXAMPLE In  this  single-dwell  motion  design  example,  the  objective  is  to  obtain  a
          mechanism with the longest possible dwell in the first half of the cycle while satisfying the
          requirements of good transmission and smoothness of motion. A minimum transmission
          index (r/d) of 0.5 is desired.
          Solution The  design  procedure  begins  with  choosing  (d/a)  equal  to  0.6.  Figure  8.26
          shows the design curves and the specified curve for n in the range 0   q   180°. Since
          n is zero or negative from 30° to 150°, the maximum possible dwell period is 120°. It
          should be noted that the specified n must lie in the area enclosed by the n and n* curves
          to  meet  the  minimum  value  specification  for  (r/d).  To  meet  the  smoothness  of  motion
          requirements, the half-cycloidal motion is specified in the range 0   q   30° and 150°
            q   180°. This ensures that the second derivative of n (i.e., the jerk) is also smooth. In
          Fig. 8.26
                                 PQ* = half-cycloidal motion
                                 Q*R = dwell portion
                                 RS = half-cycloidal motion.
          The motion in the second half of the cycle is obtained by reflecting n about the -(dh/dq)
          curve. Therefore, it retains the smoothness at the transition points. The segment SR*Q*P
          corresponds to this part of the motion as seen in Fig. 8.26. The n curve is then used to
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