### Optimization and Systems Theory Seminar

Friday, January 14, 2005, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Mathias Stolpe**

Department of Mathematics

Technical University of Denmark (DTU)

Matematiktorvet, Building 303

DK-2800 Kgs. Lyngby, Denmark

E-mail: M.Stolpe@mat.dtu.dk

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Design of planar articulated mechanisms using branch and bound

In this talk we present an optimization model and a solution method
for optimal design of two-dimensional mechanical mechanisms. The
mechanism design problem is modeled as a nonconvex mixed integer
program which allows the optimal topology and geometry of the
mechanism to be determined simultaneously. The underlying mechanical
analysis model is based on a truss (pin jointed assembly of straight
bars) representation allowing for large displacements. For mechanisms
undergoing large displacement elastic stability is of major
concern. We derive conditions, modeled by nonlinear matrix
inequalities, that guarantee that a stable mechanism is found. The
feasible set of the design problem is described by nonlinear
constraints as well as nonlinear matrix inequalities.
To solve the mechanism design problem a branch and bound method based
on convex relaxations is developed. The relaxations are strengthened
by adding valid inequalities to the feasible set. Encouraging
computational results, which will be presented, indicate that the
branch and bound method can reliably solve mechanism design problems
of realistic size to global optimality.

The talk is based on joint work with Atsushi Kawamoto.

Calendar of seminars

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by Anders Forsgren.
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