Jose M. del Castillo

The analytical expression of the efficiency of planetary gear trains

Two procedures are presented for obtaining the analytical expression for the efficiency of any planetary gear train. The first employs the speed and torque equations and the concept of virtual gear teeth ratios. The second is based on an relationship between the gearing power and the speed ratio. This relationship, which is satisfied by any spur gear train, allows one to obtain the efficiency expression in a surprisingly simple manner. Two proofs of that relationship are presented.

Propagation of perturbations in dense traffic flow : a model and its implications

A model of the evolution of speed perturbations in dense traffic flow is presented in this work. Traffic volume is assumed to be at capacity and a given vehicle undergoes a temporary speed drop. This speed drop may propagate through the traffic flow until it is either dissipated or causes the stoppage of the traffic flow. The two events are random and occur with a certain probability. The proposed model leads to a set of recurrence equations for the speed drop and its duration. The simulation of those equations allows the estimation of the normalization probability, that is, the probability that the perturbation vanishes. An analytical approximation for the normalization probability is also proposed. The approximation is based on a result from Brownian motion theory. The agreement with the simulation results is fairly good given the simplicity of the approximation. The model and its analytical approximation allows one to conjecture which could be the most important parameters that determine the evolution of the perturbation. The implications of this conjecture are commented and the assumptions of the model are contrasted with related work.

An Automatic Filtering Procedure for Processing Biomechanical Kinematic 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.

Technical and Economic Viability of Automated Highway Systems: Preliminary Analysis

Technical and economic investigations of automated highway systems (AHS) are addressed. It has generally been accepted that such systems show potential to alleviate urban traffic congestion, so most of the AHS research has been focused instead on technical design and implementation issues. It is demonstrated that, despite making a number of assumptions that are favorable to AHS, the actual viable implementation opportunities for AHS are scarce, and that most existing congested urban areas can be disqualified on the basis of at least one criterion developed herein. Technical investigations are described, including realistic estimates of AHS capacity, interfacing with the local street system, and storage issues. Discussion then turns to identifying criteria to help establish the types of urban areas that might be likely candidates for AHS technology. These criteria relate to the nature of the surrounding infrastructure and the traffic demands placed on it, as well as the economic realities of AHS implementation. Certain “boutique” locations where AHS might be beneficial are identified, but it is uncertain whether enough benefit could be realized to make AHS palatable to the general public. AHS technology is not dismissed, but the simple analyses contained herein should warn that much more research into these areas is required before fully informed decision making about the future of AHS technologies can be accomplished.