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Nine-bar structure. The univariate polynomial of degree 16 of this system can be computed in general! It can be used 1.to find the maximum number of real.

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Presentation on theme: "Nine-bar structure. The univariate polynomial of degree 16 of this system can be computed in general! It can be used 1.to find the maximum number of real."— Presentation transcript:

1 Nine-bar structure

2 The univariate polynomial of degree 16 of this system can be computed in general! It can be used 1.to find the maximum number of real solutions 2.To find all exceptional mechanisms D. Walter et.al. 2007

3 Dixon‘s mechanisms Theorem: Dixon‘s mechanisms are the only movable 9-bar structures

4 Nine-bar structure (3-D version)

5

6 Methods to generate the polynomials 1.Parameter elimination (implicitation) 2.Geometric properties of the mechanism

7 Left and right translations on S 6 2

8

9 Direct Kinematics of Stewart-Gough Platforms

10

11

12

13 Singularity

14 Workspace and singularities of 3-R robots

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