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A Short Course in Combinatorial Designs by Anderson, Ian; Honkala, Iiro

By Anderson, Ian; Honkala, Iiro

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Sur les six droites qui peuvent e´ tre les directions de six forces en e´ quilibre. C. R. S´eances Acad. Sci. 52, 1094–1104 (1861) 9. : Singularities and self-motions of a special type of platforms. , Thomas, F. ) Advances in Robot Kinematics: Theory and Applications, pp. 155–164. Springer (2002) 10. : Singularities and self-motions of equiform platforms. Mech. Mach. Theory 36(7), 801–815 (2001) 11. : Parallel manipulators with simple geometrical structure. In: Ceccarelli, M. ) Proc. of the 2nd European Conference on Mechanism Science, pp.

5, the complete subgraph of the cut X3 can be removed, and removal of the subgraph of cut X1 increases the implicit equation count of loops L9 and L8 by one, respectively. Hence, the remaining subgraph consists of loops L7 , L8 and L9 with 4 global inputs and 3 implicit constraints. This yields the correct DoF of 1 for loops L7 , L8 and L9 , and also of the initially removed recursively solvable loops L14 and L15 . Thus it can be seen that the rigidity detection algorithm also correctly determines the mobility of the remaining system.

And the union of these 10 disjoint subsets yields the set of all the m-n FPM architectures. (iii) More than three leg endings which coalesce into one multiple spherical pair yield an hyperstatic substructure3 . , only double or triple spherical pairs are allowed), which implies that the multiplicity, μi , of the ith attachment point (i = 1, . . , k with k ∈ {3, 4, 5, 6}) must belong to the set {1, 2, 3} and satisfy the condition: μ1 + μ2 + · · · + μk = 6. (iv) If two legs share both the endings, they will constitute an hyperstatic substructure.

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