Robin Corbett’s straight line drawing machine


The points U and O are fixed, and the framework consists of the black lines. All the joints are free to move. Here is a picture of a Meccano version.
The lengths a, b and c are made so that:
           a
b 		  =   b
c

The pen lives at the point Q.
So the kite PQTR is similar to the kite SRPO.
      \ ÐRPQ   =   ÐOSR   =   ÐRUO
      and if we imagine the kite PQTR being rotated about R so that RP lies along RU, PQ will be lie parallel to UO.

We construct the point V to lie on the line OQ so that the line PV is parallel to UO.
Thus
      ÐQPV   =   ÐPRU   =   ÐUOP   =   ÐVPO
and triangles OVP and QVP are congruent and
      ÐOVP   =   ÐQVP   =   90°   =   ÐQOU

Thus OQ is a straight line perpendicular to UO.