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Department of Computer Science | Institute of Theoretical Computer Science
Theory of Combinatorial Algorithms
Prof. Emo Welzl
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GCMB'07 16 May 07 Linkages worksheet Definitions: A strut is a fixed length bar A linkage
is: 2d: planar linkages 1. Consider a triangle ABC with A=(0,0), B=(3,0), and lengths AB=3,
BC=4, and CA=5. Where can point C be? (What are the coordinates of C?) 2. Consider a
quadrilateral ABCD with A=(0,0), B=(3,0), and lengths AB=3, BC=4, CD=5, and DA =6. Where
can point C be? 3. How many numbers (degrees of freedom) are needed to specify where in the
plane is a point? ___ two points? ___ three points? ____ a strut? ___ a triangle? ___ two struts
joining three points? ___ 4. Make a few linkages that are rigid in the plane.
Is there a pattern of their number of vertices and edges? 3d: space linkages Consider a triangle
ABC with A=(0,0), B=(3,0), and lengths AB=3, BC=4, and CA =5. Where can point C be? 2.
Consider a quadrilateral ABCD with A=(0,0), B=(3,0), and lengths AB=3, BC=4, CD=5, and
DA =6. Where can point C be? 3. How many numbers (degrees of freedom) are needed to
specify where in space is a point? ___ three points? ___ four points? ____ a strut? ___ a triangle?
___ a tetrahedron? ___ 4. Make a few linkages that are rigid in space. Is there a pattern of their
number of vertices and edges?
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