Figure 1.6. The two roads problem
Exercise 1.11. Consider a linkage made of four unit
necting fixed points located at distance d 4; see figu
a) Find the dimension of the configuration space of thi
b) Let d 3.9. Prove that the configuration space is t
c)* Let d = 1. Prove that the configuration space is th
four handles, that is, a surface of genus 4.
Figure 1.7. A plane linkage
This exercise has convinced you that, although a p
a very simple mechanism, its configuration space may
cated topology. In fact, this topology can be arbitraril
(we do not discuss the exact meaning of this statemen
To conclude this digression, let us mention a very
a line in space, fixed at the origin. The configuration
the real projective plane; see Digression 5.4 for a discuss
is considered in R
n
, then the configuration space is the
space R P
n _ 1
. This space plays a very prominent rol
and topology. Of course, if the line is oriented, then
configuration space is the sphere 5 n - 1 . A
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