Incorporating Epistemic Uncertainty in Robust Design

There are two sorts of uncertainty inherent in engineering design, random uncertainty and epistemic uncertainty. Random, or stochastic, uncertainty deals with the randomness or predictability of an event. It is well understood, easily modelled using classical probability, and ideal for such uncertainties as variations in manufacturing processes or material properties. Epistemic uncertainty deals with our lack of knowledge, our lack of information, and our own and others’ subjectivity concerning design parameters. While there are many methods to incorporate random uncertainty in a design process, there are fewer that consider epistemic uncertainty. There are fewer still that attempt to incorporate both sorts of uncertainty, and those that do usually attempt to model both sorts using the same uncertainty model. Two methods, a range method and a fuzzy sets approach, are proposed to achieve designs that are robust to both epistemic uncertainty and random uncertainty. Both methods incorporate preference aggregation methods to achieve more appropriate trade-offs between performance and variability when considering both sorts of uncertainty. The proposed models for epistemic uncertainty are combined with existing models for stochastic uncertainty in a two-step process. An illustrative example incorporating subjectivity concerning design parameters is presented.

On the Robustness of Exactly Constrained Mechanical Assemblies

In recent years a number of practicing engineers have discussed the virtues of exactly constrained (EC) mechanical assemblies. While found by engineers in industry to have many benefits, EC designs remain somewhat unrecognized by academia. One reason for this minimal exposure may be the lack of a mathematical foundation for such designs. EC designs can be analyzed quite simply by understanding that they are statically determinate. This paper describes the history and current background for EC designs. It also begins to develop the mathematical foundation for EC design based on equations of equilibrium. Finally, it examines a Monte Carlo simulation of the effects of variation on EC assemblies vs. over-constrained assemblies. The EC design assembles 100% of the time, while the over-constrained design assembles only 50% of the time with greater error.

Design of Energy Absorbing Structure Using Topology Optimization With a Multi-Material Model

To accommodate the dual objectives of many engineering applications, one to minimize the mean compliance for the stiffest structure under normal service condition and the other to maximize the strain energy for energy absorption during excessive loadings, topology optimization with a multi-material model is applied to the design of energy absorbing structure in this paper. The effective properties of the three-phase material are derived using a spherical micro-inclusion model. The dual objectives are combined in a ratio formation. Numerical examples from the proposed method are presented and discussed.

Choosing the Optimal Contact Force Distribution for Multi-Limbed Mobile Robots With Three Feet Contact

One of the inherent problems of multi-limbed mobile robotic systems is the problem of multi-contact force distribution; the contact forces and moments at the feet required to support it and those required by its tasks are indeterminate. A new strategy for choosing an optimal solution for the contact force distribution of multi-limbed robots with three feet in contact with the environment in three-dimensional space is presented. The optimal solution is found using a two-step approach: first finding the description of the entire solution space for the contact force distribution for a statically stable stance under friction constraints, and then choosing an optimal solution in this solution space which maximizes the objectives given by the chosen optimization criteria. An incremental strategy of opening up the friction cones is developed to produce the optimal solution which is defined as the one whose foot contact force vector is closest to the surface normal vector for robustness against slipping. The procedure is aided by using the “force space graph” which indicates where this solution is positioned in the solution space to give insight into the quality of the chosen solution and to provide robustness against disturbances. The “margin against slip with contact point priority” approach is also presented which finds an optimal solution with different priorities given to each foot contact point for the case when one foot is more critical than the other. Examples are presented to illustrate certain aspects of the method and ideas for other optimization criteria are discussed.

An Integrated Design Optimization Approach for Quantitative and Qualitative Search Space

Most of the algorithmic engineering design optimisation approaches reported in the literature aims to find the best set of solutions within a quantitative (QT) search space of the given problem while ignoring related qualitative (QL) issues. These QL issues can be very important and by ignoring them in the optimisation search, can have expensive consequences especially for real world problems. This paper presents a new integrated design optimisation approach for QT and QL search space. The proposed solution approach is based on design of experiment methods and fuzzy logic principles for building the required QL models, and evolutionary multi-objective optimisation technique for solving the design problem. The proposed technique was applied to a two objectives rod rolling problem. The results obtained demonstrate that the proposed solution approach can be used to solve real world problems taking into account the related QL evaluation of the design problem.

Approximate Motion Synthesis of Open and Closed Chains via Parametric Constraint Manifold Fitting: Preliminary Results

In this paper we present a novel dyad dimensional synthesis technique for approximate motion synthesis. The methodology utilizes an analytic representation of the dyad’s constraint manifold that is parameterized by its dimensional synthesis variables. Nonlinear optimization techniques are then employed to minimize the distance from the dyad’s constraint manifold to a finite number of desired locations of the workpiece. The result is an approximate motion dimensional synthesis technique that is applicable to planar, spherical, and spatial dyads. Here, we specifically address the planar RR, spherical RR and spatial CC dyads since these are often found in the kinematic structure of robotic systems and mechanisms. These dyads may be combined serially to form a complex open chain (e.g. a robot) or when connected back to the fixed link they may be joined so as to form one or more closed chains (e.g. a linkage, a parallel mechanism, or a platform). Finally, we present some initial numerical design case studies that demonstrate the utility of the synthesis technique.

Multi-Objective Optimisation of Ship Hull With Distributed Applications

In the context of concurrent engineering, this paper presents a quite innovative approach to the collaborative optimisation process, which couples a multi-objective genetic algorithm with an asynchronous communication tool. To illustrate this methodology, three European companies’ collaboration on the optimisation of a ship hull is described. Our study demonstrates that when multi-objective optimisation is carried out in a distributed manner it can provide a powerful tool for concurrent product design.

Optimizing Optimization for Design Optimization

Design optimization is becoming and increasingly important tool for design. In order to have an impact on the product development process it must permeate all levels of the design in such a way that a holistic view is maintained through all stages of the design. One important area is in the case of optimization based on simulation, which generally requires non-gradient methods and as a consequence direct-search methods is a natural choice. The idea in this paper is to use the design optimization approach in the optimization algorithm itself in order to produce an efficient and robust optimization algorithm. The result is a single performance index to measure the effectiveness of an optimization algorithm, and the COMPLEX-RF optimization algorithm, with optimized parameters.

An Analytical Comparison Between Ball and Crossed Roller Bearings for Utilization in Actuator Modules for Precision Modular Robots

A modular robot system is a collection of actuators, links, and connections that can be arbitrarily assembled into a number of different robot configurations and sequences. High performance modular robots require more than just sophisticated controls. They also need top-quality mechanical components. Bearings in particular must operate well at low speed, have high rotational accuracy, be compact for low weight, and especially be stiff for high positional accuracy. To ensure the successful use of bearings in precision modular robots, knowledge of the bearing properties and requirements are investigated. Background information on various topics such as modular robots, precision modular actuators, and their error sources are described with respect to precision engineering. Extensive literature on thin section bearings is reviewed to examine their use in precision robotic applications. Theoretical studies are performed to calculate bearing stiffness adopting a methodology based on Hertzian theory. This approach is applied to analyze two proposed designs of equivalent-sized crossed roller and four-point bearings, principal bearings used for transmitting all the payload and mass of the robot structure. The maximum deflections and contact stresses for the proposed actuator assembly and loading conditions are estimated and compared including a range of general bearing properties such as friction, cost, and shock resistance.

Internet Based Framework to Perform Automated FEA on User Customized Products

Designing family of products require analysis and evaluation of performance for the entire product family. In the past, products were mainly mass-produced hence the use of CAD/CAE was restricted to developing and analyzing individual products. Since the products offered using a platform approach include a variety of products built upon a common platform, CAD/CAE tools need to be explored further to assist in customization of products according to the customer needs. In this paper we investigate the development of a Product Family FEA (PFFEA) module that can support FEA analysis of user customized product families members. Customer specifications for family members are gathered using the internet, users are allowed to scale and change configurations of products. These specifications are then used to automatically generate 3D solid models of the product and then perform FEA to determine feasibility of the customer specified product. In this paper, development of the PFFEA module is illustrated using a family of lawn trimmer and edger. The PFFEA module uses Pro/E to generate the solid model and ANSYS as the base FEA software.