﻿1875.] 
  Exact 
  Rectilinear 
  Motion 
  by 
  Linkwurk. 
  573 
  

  

  Draw 
  L 
  perpendicular 
  to 
  A 
  B. 
  

  

  Fig. 
  9. 
  

  

  Then 
  KL=F 
  D'. 
  

  

  Therefore 
  BL=BN+NL=NN', 
  a 
  constant. 
  

   Thus 
  the 
  locus 
  of 
  is 
  the 
  straight 
  line 
  O 
  L 
  perpendicular 
  to 
  A 
  B. 
  

   § 
  10. 
  Now 
  in 
  the 
  last 
  link 
  work 
  make 
  

  

  a=d. 
  

  

  Then 
  B 
  coincides 
  with 
  D', 
  

   D'K=CB, 
  

  

  PO 
  =OK=KD=DC, 
  

   and 
  the 
  linkwork 
  becomes 
  that 
  of 
  M. 
  Peaucellier. 
  

  

  Fig. 
  10. 
  

  

  IV. 
  § 
  11. 
  Taking 
  the 
  fundamental 
  linkage 
  in 
  its 
  most 
  general 
  form, 
  

   fix 
  the 
  point 
  P 
  on 
  a 
  pivot. 
  Now 
  if 
  the 
  bar 
  AB 
  be 
  made 
  to 
  remain 
  

   always 
  parallel 
  to 
  the 
  fixed 
  line 
  P 
  S, 
  since 
  N 
  N' 
  is 
  constant, 
  P' 
  will 
  move 
  

   on 
  the 
  straight 
  line 
  P' 
  L 
  perpendicular 
  to 
  P 
  S. 
  

  

  The 
  parallelism 
  of 
  A 
  B 
  is 
  effected 
  most 
  obviously 
  by 
  adding 
  the 
  bar 
  S 
  T 
  

   equal 
  to 
  P 
  B, 
  P 
  S 
  being 
  equal 
  to 
  B 
  T. 
  Other 
  methods 
  may, 
  however, 
  be 
  

   employed 
  ; 
  for 
  if 
  C 
  A 
  be 
  joined 
  cutting 
  P 
  S 
  in 
  U, 
  U 
  is 
  a 
  fixed 
  point 
  ; 
  and 
  

   if 
  U 
  V 
  be 
  drawn 
  parallel 
  to 
  C 
  D, 
  TJ 
  V 
  is 
  constant 
  and 
  V 
  is 
  a 
  fixed 
  point 
  

   on 
  CD. 
  So 
  if 
  TJ 
  W 
  be 
  drawn 
  paralled 
  to 
  CD, 
  U¥ 
  is 
  constant 
  and 
  W 
  

  

  