An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one, and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher and Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer/discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.

Why does a sheet of water flowing over an initially featureless surface spontaneously form a river network? To address this question, we construct a simple model which enables us to examine the shape and stability of individual river channels. We compare predictions for the geometry of fluvial channels with experimental data. In addition, we construct a lattice model which allows us to look at large-scale features of river networks and calculate their scaling relations. PACS numbers: 68.70.4-w, 92.40.Fb, 92.40.GcIf fractals are the geometry of nature, one must still ask how nature produces them. Branched river networks are among nature's most common patterns, spontaneously producing structure over a huge range of length scales [lj. At the heart of this problem is the question of why and how individual river channels are formed. This Letter presents a nonlinear model which describes the evolution of an arbitrary initial landscape covered by a distribution of water, and has the goal of understanding instabilities which lead to the coalescence of the water into channels and, later, river networks. Rivers have been studied extensively by a wide variety of researchers with an equally wide variety of techniques and goals. Geomorphologists have found scaling relationships among various combinations of basin statistics from field data, such as drainage density and branching ratios [2]. Hydrologists have likewise extracted power laws for channel parameters such as width, depth, velocity, and slope as functions of total channel discharge [3]. Other investigators have examined the shape [4-6] of individual equilibrium channels in erodible material while somehave constructed models for the evolution of an entire drainage network [7-9]. However, we are unaware of a previous approach which predicts the shapes spontaneously formed when water flows over an initially featureless surface and allows one to answer questions about selection and stability. We differ from previous authors because we do not try to find closed equations for height of soil alone; we treat water explicitly as well. The aim is to find the simplest model which reveals the essential features of river formation. We pose our model in terms of two scalar fields, b(x,y,t) and d(x,y,t), where b(x,y,t) is the height of soil above some arbitrary horizontal level, dix,y,t)is the depth of water flowing over the soil, x and y are spatial coordinates, and / is time. It will be convenient to introduce an auxiliary field s(x,yj)=b(x,yj) + d(x,yj) which defines the overall surface of the land plus water. The time evolution of the system is given by

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads. Because of this fact, traditional methods of deflection analysis do not apply. Since the nonlinearities introduced by these large deflections make the system comprising such members difficult to solve, parametric deflection approximations are deemed helpful in the analysis and synthesis of compliant mechanisms. This is accomplished by representing the compliant mechanism as a pseudo-rigid-body model. A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms. In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads. A numerical integration technique using quadrature formulae has been employed to solve the large deflection Bernoulli-Euler beam equation for the tip deflection. Implementation of this scheme is simpler than the elliptic integral formulation and provides very accurate results. An example for the synthesis of a compliant mechanism using the proposed model is also presented.

An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher & Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer / discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.

A general method of optimal design of planar mechanisms is presented here called Selective Precision Synthesis (SPS for short), suitable for path, motion or function generation, with different arbitrary limits of accuracy at various discrete positions. It was found that the method yields fundamentally stable solutions: while in closed-form synthesis, small changes in prescribed values often result in very different solutions or no solutions at all, in SPS small perturbations in problem specifications often produce only small variations in the synthesized linkage dimensions. Such stability is rarely found in Burmester theory and other synthesis techniques. Applying nonlinear programming and introducing the dyadic construction of mechanisms, the SPS technique is applicable to the synthesis of most planar mechanisms including four-bar, five-bar, multi-loop, multi-degree of freedom and adjustable mechanisms. Also, dyadic construction simplifies the optimization process and renders the method readily manageable in interactive computer-aided design. The SPS digital computer programs for batch and tele-processing are made available to interested readers.

This paper introduces a symbolic notation for describing two degree-of-freedom spur planetary gear trains with the configuration of two central gears, one carrier or arm, and at least one planet gear. This simple notation is then used to write the kinematic equation of motion for this type of planetary gear train without the need to develop any intermediate equations. It is also shown that, there are exactly 22 basic spur planetary gear trains with this configuration and not 34 as Levai [1] previously found. These 22 planetary gear trains are illustrated along with their symbolic notation and kinematic equation of motion.

The Tetrahedron-Tetrahedron truss (or TT truss for short) has exceptional stability, stiffness, and load-carrying capabilities. Because of this fact, the TT truss is well suited for use as a variable geometry truss manipulator (VGTM) by appropriately choosing certain links whose variable lengths can be controlled. Since the TT truss is composed of n-cells, its applications include the retrieval of equipment, bridges over and around obstacles, and applications which utilize collapsible programmable structures capable of relatively large displacements. In this paper an actuation scheme and the general solution to the forward and inverse kinematics problems for an n-celled TT truss are presented. Numerical examples are also presented.

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