Comparison between structural and residual error formulations of an optimum design mechanism problem

Summary The model formulation of the objective function is one of the most important steps for solving an optimization problem. Generally, the objective function of an optimal design mechanism problem can be mathematically formulated either with structural or residual errors. In this paper we have conducted some comparisons between the results obtained by the structural and residual error formulations utilized in solving the optimum design of a four-bar linkage. The optimization problem is defined as a nonlinear least-squares problem. The damped Gauss-Newton algorithm is utilized for computing the solution, which ensures a local convergence for almost all nonlinear least-squares problems.

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Sommario La formulazione matematica della funzione obiettivo è uno degli aspetti più delicati nella soluzione di un problema di ottimizzazione. Generalmente la funzione obiettivo di un problema di progettazione ottima di un meccanismo può essere formulata sia mediante l'errore strutturale che residuo. In questo lavoro sono stati eseguiti dei confronti tra i risultati ottenuti mediante le due precedenti formulazioni, in riferimento al problema della progettazione ottima di un quadrilatero articolato. Il problema di ottimizzazione viene definito come un problema nonlineare ai minimi quadrati la cui soluzione numerica è ottenuta mediante l'algoritmo damped di Gauss-Newton.

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This paper was partially discussed at theII Congegno di Meccanica Computazionale, Roma, 1987.     

Study of the microstructure of tetrahydrofuran-3,3 dimethyloxetane copolymers by 13C-NMR spectroscopy.

The microstructure of tetrahydrofuran (A)-3,3 dimethyloxetane (B) copolymers was studied by ¹³C-{¹H}-NMR spectroscopy. Only the methyl carbons corresponding to the 3,3 dimethyloxetane unit appear as a singlet, whereas the other carbons present a more complicated spectral pattern than it would be expected if ? effects were negligible. The assignment of the resonance signals allowed the determination of the values of the probabilities of the different triads, which were in good agreement with those obtained from the reactivity ratios.     

Neutron diffraction structure determination of the high-temperature form of lithium tritantalate,HLiTa3O8

The crystal structure of HLiTa₃O₈ has been reexamined by electron and neutron diffraction techniques. Neutron Weissenberg and electron diffraction photographs show that the space group of the compound isPmmn and notPmma as determined previously by X-ray diffraction techniques. There are eight molecules in the unit cell of lattice parametersa = 16.718(2)A?,b = 7.696(1)A?,c = 8.931(1)A?. These values show that thebaxis of the new cell is doubled with respect to the parameter measured by X-rays. The structural refinement was based on 1074 independent reflections measured on a single crystal with a four-circle neutron diffractometer. The positions of all atoms, including the lithium atoms have been determined. The finalR andwRfactors were 0.036 and 0.035, respectively. The eight lithium cations occupy two sets of4fpositions(x,¼, z)of thePmmn space group. The ordering of four lithium ions over two sets of possible positions (4j) of space groupPmma is responsible for the doubling of theb axis. The other four Li⁺ occupy two sets of positions (2d) of space groupPmma. All lithium ions are surrounded by 12 oxygen atoms arranged as cuboctahedra. The large thermal vibrations found for the lithium atoms and the ionic conductivity of HLiTa₃O₈ at high temperatures are consistent with weak LiO bonding.