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Some recent developments in path generation have been based on neural network mechanism databases, which instantaneously provide an approximate solution of the synthesis problem. We describe a way to reduce the design space, ensuring that the neural network always yields a consistent crank-rocker mechanism with optimal transmission angle. Moreover, instead of the usual strategy of using Fourier coefficients, we propose a new method based on wavelet descriptors to represent the shape of the path, where the points do not need to be sampled at a constant time interval. Numerical results demonstrate the superiority of this wavelet-based neural network over the Fourier-based network in finding the optimal mechanism. They also show the accuracy of the proposed approach in providing near optimal crank-rocker mechanism solutions for path generation.

A procedure for the enumeration of the graphs of 1-dof planetary gear trains is presented. The planetary gear trains enumerated have a single input shaft and a single output shaft. These gear trains should satisfy certain functional constraints that avoid the existence of idle links. These constraints are derived. The enumeration of the graphs exploits the resulting particular features of the structure of planetary gear trains by proceeding gradually through different levels of that structure. The procedure includes a check for isomorphism among the resulting graphs. Finally, the graphs of the planetary gear trains having up to 9 links are presented. Those graphs containing embedded structures are identified.

A procedure for solving, suboptimally, the traveling salesman problem is presented. The set of points on the traveling salesman tour is distributed over a region having the shape of a circular or ring sector. The procedure is based on an optimal partition of the sector and reduces the tour construction to a sorting problem. Namely, the tour is constructed by visiting the points in radial or angular order depending on the part of the sector on which they are located. The optimal partition is derived by a continuous approximation of the set of points. It is defined by a single parameter and simple analytical expressions for it are obtained. A great number of numerical tests were carried out to evaluate the performance of the procedure. These tests allowed a measure of the difference from the optimum solution that could be obtained for problems up to a few hundred points. The results show that the euclidean length of the tours produced by the partition procedure grows, on average, like AN , where A is the region area and N the number of points. The initial tours are improved by means of the Or’s algorithm and the final tours obtained are nearly as good as those given by more intrincate improvement heuristics. The whole procedure, that is, the tour construction and improvement heuristics, is rather simple to implement on a computer, which makes it very appealing to use in routing software.

The use of the Hodrick-Prescott (HP) filter is presented as an alternative to the traditional digital filtering and spline smoothing methods currently used in biomechanics. In econometrics, HP filtering is a standard tool used to decompose a macroeconomic time series into a nonstationary trend component and a stationary residual component. The use of the HP filter in the present work is based on reasonable assumptions about the jerk and noise components of the raw displacement signal. Its applicability was tested on 4 kinematic signals with different characteristics. Two are well known signals taken from the literature on biomechanical signal filtering, and the other two were acquired with our own motion capture system. The criterion for the selection of cutoff frequency was based on the power spectral density of the raw displacement signals. The results showed the technique to be well suited to filtering biomechanical displacement signals in order to obtain accurate higher derivatives in a simple and systematic way. Namely, the HP filter and the generalized cross-validated quintic spline (GCVSPL) produce similar RMS errors on the first (0.1063 vs. 0.1024 m/s2) and second (23.76 vs. 23.24 rad/s2) signals. The HP filter performs slightly better than GCVSPL on the third (0.209 vs. 0.236 m/s2) and fourth (1.596 vs. 2.315 m/s2) signals.

In biomechanics studies it is necessary to obtain acceleration of certain parts of the body in order to perform dynamical analysis. The motion capture systems introduce systematic measurement errors that appear in the form of high-frequency noise in recorded displacement signals. The noise is dramatically amplified when differentiating displacements to obtain velocities and accelerations. To avoid this phenomenon it is necessary to smooth the displacement signal prior to differentiation. The use of Singular Spectrum Analysis (SSA) is presented in this paper as an alternative to traditional digital filtering methods. SSA decomposes original time series into a number of additive time series each of which can be easily identified as being part of the modulated signal, or as being part of the random noise. An automatic filtering procedure based in SSA is presented in this work. The procedure is applied to two signals to demonstrate its performance.