Hard Problems

1. The Peaucellier linkage (or Peaucellier-Lipkin linkage)

computes the function



Show this by showing that

a) z and 1 over the conjugate of z both have the same Arg, or angle up from the x-axis.

b) The magnitude (or length) of 1 over the conjugate of z is 1 over the length of z. c) There is a constant number C such that |z||w|=C. Setting C=1 and noting the collinearity of 0, z and w gives that


2.
a) Whenever this function is applied to every point in a line through the origin it gives another a line through the origin.

b) Whenever this function is applied to every point of a circle not through the origin it gives another circle not through the origin.

c) Whenever this function is applied to a circle through the origin it gives a line not through the origin (and vice versa)

I hope you've enjoyed this linkage tutorial. Check out the references page to find more advanced material on linkages.

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