Computation of Spatial Displacements From Geometric Features

This paper develops the theoretical foundation for computations of spatial displacements from the simple geometric features of points, lines, planes and their combinations. Using an oriented projective three space with a Clifford Algebra, all these three features are handled in a similar fashion. Furthermore, issues related to uniqueness of computations and minimal number of required features are discussed. It is shown that contrary to the common intuition, specification of a minimum of four points (planes) or three lines (each pair being non-planar) are necessary for computation of a unique displacement. Only when the sense of the orientations of these features are specified then the minimal number of required features reduces to three for points and planes and two for lines. The results, in addition to their theoretical interest in computational geometry of motion, have application in robot calibration.

Quantifying Design Feasibility Using Probabilistic Feasibility Analysis

Engineered products are designed for manufacture using nominal values and tolerances. As such, finished products will more or less satisfy design specifications depending on the actual materials and manufacturing processes used. Design feasibility, therefore, depends on how these variations impact specified constraints. Probabilistic feasibility analysis can be used to extend conventional feasibility analysis. By using moment matching and simulation, the probability of points occurring in the design space can be evaluated. The resulting values establish the limits of feasibility and the amount of feasibility in between. The nature of variation in mechanical design is introduced along with concepts of variation propagation in functions of random variables. Moment matching methods are applied to illustrative cases consisting of deterministic and probabilistic constraint equations, resulting in three dimensional feasibility mappings of each design space.

Automated Design of Optimum Belt Drives

The paper describes a belt design package which works from within a commercial Computer Aided Design and Drafting package (AutoCAD) environment and utilizes FORTRAN programs for design and selection of lowest weight components for the drive system. The components used in the process are available as stock items in U.S.A. The relevant information on these products is stored in commercial database management systems such as EXCEL and LOTUS 1-2-3. Output from the package consists of scaled drawing and tabular specifications.

Representing Tolerance and Assembly Information in a Feature-Based Design Environment

This paper describes a strategy for representing tolerance information and assembly information in a feature-based design environment. The concept of designing with features is extended to incorporate the specification of tolerance information. This allows appropriate tolerancing strategies to be provided within the feature definitions themselves. Thus a closer connection is formed between features and the functional intent implicit in their use. The concept of designing with features is also extended to incorporate the specification of assembly information, through the use of assembly features which provide a high-level user interface for the creation and modeling of assemblies, and which handle the identification and creation of mating relations between components. Several examples of component and assembly design using this extended feature-based approach are presented.

Optimal Design With a Monomial-Based Version of Newton’s Method

A monomial-based method for solving systems of algebraic nonlinear equations is presented. The method uses the arithmetic-geometric mean inequality to construct a system of monomial equations that approximates the system of nonlinear equations. This “monomial method” is closely related to Newton’s method, yet exhibits many special properties not shared by Newton’s method that enhance performance. These special properties are discussed in relation to engineering design optimization.

Direct Optimization of Multi-Degree-of-Freedom Mechanisms for Near Time Optimal Motions Along Specified Paths

A design method for selecting system parameters of multi-degree-of-freedom mechanisms for near minimum time motions along specified paths is presented. The time optimization problem is approximated by a simple curve fitting procedure that fits, what we call, the acceleration lines to the given path. The approximate cost function is explicit in the design parameters, facilitating the formulation of the design problem as a constrained optimization. Examples for optimizing the dimensions of a five-bar planar mechanism demonstrate close correlation between the approximate and the exact solutions and better computational efficiency than the previous unconstrained optimization methods.

A Geometry Based Method of Integrated Engineering Analysis and Optimization

An integrated geometry based method of analysis and optimization is presented. The significance of geometry based analysis and optimization methods are discussed. A hierarchical integer based data structure, used to define and manipulate geometry, is presented. Many features of the integer based data structure are given. Shapes are shown to represent the fundamental geometry. Variables of shapes are constrained and related to each other so that a reduced set of design variables result. These design variables are used to pose both analysis and optimization problems. Heuristics are used to simplify the integrated geometry specification, analysis and optimization procedures. The resulting engineering environment concurrently poses analysis and optimization problems during geometry generation, leading to an integrated geometry based method of analysis and optimization.

A Study of Hydroformed Bellows, Applying a Finite Element Method: Relationship of Bellows Dimensions, Shape, Spring Rate and Stress

The spring rate of hydroformed bellows are generally calculated by shell theory or energy theory. In both cases, the calculation model of the bellows will be simplified and the thickness of the bellows convolutions will be assumed as a uniform thickness plate. It is often found that calculated solutions differ from experimental spring rates and stresses since the outside thickness of the bellows is different to the inside thickness. In this paper a finite element method (FEM) is applied to obtain the spring rate and stress of bellows. The calculated spring rates are almost the same as those of experimental data and indicate that the spring rate value is very sensitive to the ratio of OD thickness and ID thickness. The design diagrams for spring rate and maximum shear stress reflecting OD and ID thickness ratio are therefore presented.

An Automatic Approach to Handling Inequality Constraints in an Interactive Design Environment

A general mechanical design can be characterized by a set of equality and inequality constraints. Constraint Management algorithms have been successfully applied for the satisfaction of equality constraints. The goal of this paper is to extend the ideas of constraint management to handle inequality constraints. Past research shows that the handling of inequality constraints has been restricted to optimization and symbolic frameworks. As opposed to the traditional optimization schemes in which all the inequality constraints are converted to equalities, our approach introduces slack variables for only those inequalities that are active at that particular stage of the design process. The basic premise governing the algorithm presented in this paper is to satisfy a set of inequality constraints while deviating as little as possible from the given design specifications. An occurrence matrix formulation is used to represent both the equality and inequality constraints that govern the design. A linear model of the design, based on sensitivity computations, is used to automate the procedure. The work is illustrated for the classical weldment design problem.

Numerical Analysis of the Kinematic Working Capability of Mechanisms

An approach to numerical analysis of the kinematic dexterity of mechanisms is presented. Dextrous workspace problems are defined and illustrated. Composite workspaces are introduced to characterize both positioning and orienting capabilities of mechanisms. Using the composite workspace, numerical techniques for dextrous workspace analysis are presented. A numerical formulation and computer implementation that incorporates computer graphics and a numerical algorithm for solving systems of nonlinear equations are presented. Examples are given to illustrate the techniques developed.