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Another mechanism which solves the problem of
rectilinear motion was described by Hart in 1874. It is
based on a "intertwined parallelogram" shown
left, where AB = CD,
AD = BC .
If O, P, Q are three fixed points on the AB, AD and BC
rods, positioned so that the straight line on which they lie is
parallel to AC, the same will happen in whatever position
of the mechanism, and we will have
OP · OQ = BQ · QC - OA · OB = constant.
Thus if O is fixed, the points P and Q correspond in a
circular inversion and, if P moves on a circumference
passing through O, point Q draws a straight line.
With Hart's mechanism, the study of connecting rod
mechanisms for rectilinear motion has reached the minimum
complexity: it is possible to demonstrate that it is
impossible to solve the problem with less than five rods.
But many mechanisms have been invented for the task,
including the one shown on the left, based on two double
kites, trough which a candle holder can be moved and kept
vertical.
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