A Geometrical Solution for the Inverse Kinematics of Three Revolute Manipulators

Points of intersection of a circle and a torus are used to find a solution to the inverse kinematics problem for a three revolute manipulator. Both geometrical and algebraic solution procedures are discussed. The algebraic procedure begins with a third order equation instead of the usual fourth order equation. Since the procedure is basically geometrical it lends itself to a computer implementation which graphically displays each steps in the solution procedure. The potential of this approach for both design and pedagogy is discussed.

A Decomposition Method for Concurrent Design of Mixed Discrete/Continuous Systems

Interest in Concurrent Engineering (CE) has increased as industry looks for more efficient means of product design. Design optimization methods that facilitate the CE approach are an important aspect of current research. Among the methods that have been proposed is the Concurrent Subspace Optimization (CSSO) method, which allows the optimization problem to be decomposed into coupled subproblems. These subproblems may correspond to the different disciplines involved in the design process or to participating organizational design or manufacturing groups. The decomposition allows each discipline to apply their own optimization criteria to the problem. While this method may not be as computationally efficient as other methods, it allows the design process to conform to the departmental divisions that already exist in industry. The method development to date has focused on continuous systems only. However, problems that can not be modeled as continuous systems, such as those involving the placement of active controllers in CSI applications, would benefit from a method that allows the use of discrete parameters. The paper presents a decomposition method (based on CSSO) for the optimal design of mixed discrete/continuous systems. The method is applied to the design of a composite plate for minimum weight, with design variables contributed from sizing variables (continuous) and material combinations (discrete).

Dynamic Binding of Features and Solid Modelers

The work described in this paper investigates the feasibility of standardizing communications between geometric modeling core systems and generic feature-based applications. Since geometric modelers differ in the functionality they provide and feature applications vary in the level of geometric operations they can support internally, a multi-layered communication architecture is proposed. The methodology is analogous to the X-Window standard for graphics. At the lowest level is a library of functions named Geo-lib, which are translated into geometric modeler specific commands. If there was to be a future dynamic interfacing standard, such as STEP-SDAI, these specific calls could be replaced by standard calls, analogous to Geo-Protocol. At the next layer is a library, called Geo-widgets, which are written entirely using Geo-lib functions. At the highest level Geo-Tools, functions used commonly by generic applications. Feature applications can choose to use the library at any level, as necessary. This multi-layered geometric toolkit creates a seamless object oriented bond between the feature application and the geometric modeling core, in such a way that either one could be replaced without requiring any changes to the other.

A Hybrid Shape Optimization Method Based on Implicit Differentiation and Node Removal Techniques

This paper presents a hybrid shape optimal design methodology using an implicit differentiation approach for sensitivity analysis and a node removal technique for shape alteration. The approach presented attempts to overcome the weaknesses inherent in each individual technique. The basic idea is to combine the sensitivity analysis, which forms the analytical basis for the algorithm, and a node removal technique, which grossly modifies the shape without the need for a remeshing after each iteration. The sensitivity analysis is based on the finite element equilibrium equation and the implicit differentiation technique. It examines the effect positional changes of the boundary nodes have on the stress values. Using the sensitivity results, a sequential linear programming algorithm is utilized to determine optimum positions of the boundary nodes. These optimization results are provided as inputs to an algorithm that decides which boundary nodes should be removed. By removing boundary nodes, the boundary elements change to either a triangular or a non-existent type. This shape modification procedure starts from the boundary elements and moves toward the internal elements. Only two iterations of finite element analysis are required to modify one boundary layer. To maintain the structural integrity and the connectivity of the elements in the model, a connectivity check is performed after each iteration. Three design examples are given to illustrate the accuracy and the steps involved in the proposed optimal design methodology.

Computing Equidistant Curves and Surfaces

The problem of computing equidistant curves and surfaces between a point and (i) a parametric curve and (ii) a parametric surface is considered. This problem is important since it can form a basis for further generalizations of the problem, viz., computing equidistant curves and surfaces between a pair of curves and a pair of surfaces. Engineering applications of such equidistant curves and surfaces include fluid flow analysis, mesh generation and shape interrogation.

Optimal Approximation of Real Values Using Rational Numbers With Application to the Kinematic Design of Gearboxes

This article proposes a method for optimally approximating real values with rational numbers. Such requirements arise in the design of various types of gear sets, where integer numbers of gear teeth force individual stage ratios to assume rational values. The kinematic design of an 18-speed gearbox, taken from the literature, is analyzed and solved using the proposed method. The method, called sequential exhaustion, sequentially considers each stage of the gearbox design, exhaustively examining each stage. Examination of 94 solutions leads to a pareto-optimal set containing 11 solutions. Further, although the layout of the gearbox is predefined for the kinematic design problem, certain solutions of the problem exhibit “non-reducing” gear pairs, revealing previously unforeseen changes in the gearbox layout.

On the Finite Screw System of the Third Order Associated With a Revolute-Revolute Chain

The finite displacements of the outermost body of a revolute-revolute chain are investigated. All the possible screws of the finite twists of the outermost body of an R-R chain are shown to form a screw system of the third order. The analytic expression of the screw system is given. The finite screw systems of special configurations of an R-R chain as well as the degenerate forms of the finite 3-system in infinitesimal kinematics and in displacing two points of a body are also discussed.

Optimal Design of Forging Processes With Deformation and Temperature Constraints

This paper presents a systematic methodology for the design of process parameters for nonisothermal forgings. The finite element approach is used for deformation and thermal analyses, and an optimal control strategy is used for the process parameter design. A state-space model is developed for representing the coupled deformation and thermal behavior using rigid viscoplastic formulation. Design constraints on strain-rates and temperature variation are imposed for achieving the desired forging conditions. The linear quadratic regulator (LQR) theory for finite time control is used in designing the ram velocity and initial die temperature. The approach is demonstrated on an axisymmetric disc forging and a plane strain channel section forging, under nonisothermal conditions.

Kinematic Synthesis of an RS-SRR-SS Adjustable Spatial Motion Generator for Three Alternate Tasks

A method is presented for kinematical synthesis of an RS-SRR-SS adjustable spatial motion generator for three alternate tasks. Three separate systems of synthesis equations to exactly generate the first and the last positions for each task are obtained for the R-S by co-plane and constant distance conditions, for the S-R-R by co-plane, constant distance conditions and inversion theory, and for S-S by constant distance condition. Based on these equations, mathematical model for approximately generating the intermediate positions for each task is formulated. This method is characterized by reduction of the unknowns and equations in both exact and approximate syntheses. As a result, computing work is to be decreased obviously.

Optimal Design of Composite Lightweight Rollers

A well-aimed layout of fibre-reinforced lightweight rollers does not only require an efficient structural analysis procedure but also the application of structural optimization methods. Therefore, an analytical procedure is introduced for the calculation of the static behaviour of cylindrical shells subject to axisymmetric and/or nonaxisymmetric loads. In the scope of this procedure, arbitrary, unsymmetrical laminates as well as various boundary conditions will be considered. Basis is the shell theory by Flügge enhanced by anisotropic constitutive equations (material law) in the scope of the classical laminate theory. By means of mathematical optimization procedures we then determine optimal lightweight rollers, using different design and evaluation models. For that purpose, coated and uncoated roller constructions as well as hybrid types made of CFRP/GFRP will be applied. Concluding, we will discuss possible improvements and advantages of anisotropic lightweight rollers in contrast to isotropic ones made of steel or aluminium.