Nonlinear Mixed Integer-Discrete-Continuous Programming and its Application to Engineering Design Problems

An algorithm for solving nonlinear programming problems containing integer, discrete and continuous variables is presented. Based on a commonly employed optimization algorithm, penalties on integer and/or discrete violations are imposed on the objective function to force the search to converge onto standard values. Examples are included to illustrate the practical use of this algorithm.

A Hybrid Expert System–Nonlinear Programming Approach to Optimal Gear Design

An expert system is developed for optimal spur gear design. Design automation is accomplished by dividing the design variables into different categories, i.e. geometric design variables and non-geometric design variables. The geometric variables are further divided into terms that are related to the gear mathematical model and terms that are determined according to the designer’s experience. By properly developing the mathematical model, numerical optimisation can be used to seek the best solution for a given set of geometric constraints. The process of determining the non-geometric design variables is automated by using symbolic computation. This gear design expert system is built according to the AGMA standards and a survey of gear design experts. The recommendations of gear designers and the information provided by AGMA standards are integrated into knowledge bases and data bases. By providing fast information retrieval and design guidelines, this expert system greatly streamlines the spur gear design process and makes it possible for a novice designer to achieve a reliable design in a short period of time.

Shape Optimization of Robotic Manipulators for Maximum Stiffness and Load Carrying Capacity

Structural optimization can result in robotic arms with significantly improved stiffness and load carrying capacity. The geometrical shape of the manipulator links can be optimized for maximum stiffness-to-weight and strength-to-weight ratios. The problem of stiffening and strengthening a manipulator is solved by optimal redistribution of the available material without increasing the total mass of the manipulator. Since manipulators are programmed to move through a range of postures, thereby creating different loading conditions on the links, a multi-posture design criteria is implemented to provide a more uniform stiffness and strength over the range of possible postures. Finite element based performance criteria are developed which facilitate the simultaneous maximization of specific stiffness and strength. Three application examples on a SCARA class arm illustrate the dramatic potential for simultaneous improvements in specific stiffness and specific strength. The significance of multiple postures on the optimal design, the merits of tapered versus straight link shapes, and the relation of maximum stiffness to maximum strength, are also examined.

Optimum Design of Crown Brakes

The use of crown brakes with heat input from both the inner and outer surfaces has been suggested as a means of improving the performance of frictional brakes. This paper presents an algorithm for the design of the optimal thermal load sharing and configuration of the rotor for brakes with different ratios of inner to outer radius. Several illustrative examples are considered and the results show that significant improvement in the performance and weight of the brake rotor can be achieved by this approach.

The Determination of the Probabilistic Properties of Velocities and Accelerations in Kinematic Chains With Uncertainty

A probabilistic model and methods to determine the means and variances of the velocity and acceleration of stochastically-defined planar pin jointed kinematic chains are presented. The presented model considers the effect of tolerances on link length and radial clearance and uncertainty of pin location as a net effect on the link’s effective length. The determination of the mean values and variances of the output variables requires the calculation of sensitivities of secondary variables with respect to the random variables. It is shown that this computation is straightforward and can be accomplished by a conventional kinematic analysis package. Thus, the concepts of tolerance and clearance have been captured by the model and analysis. The only input data is the nominal linkage model and statistical information. The “effective link length” model is shown to be applicable to both analytical solution and Monte Carlo simulation. The results from both methods are compared. This paper solves the higher-order kinematics problem for the probabilistic design analysis of stochastically defined mechanisms.

Numerical Optimization of Rotor-Bearing Systems

Nonlinear programming techniques are combined with a finite element program for dynamic analysis of rotor-bearing systems. The resulting program provides the means for obtaining optimal designs for improved dynamic performance of a rotor through the automated selection of various design parameters of the rotor-bearing system. Both constrained and unconstrained optimizations are considered. Illustrative examples are presented for the case of optimum placement of critical speeds.

Integrated Optimal Design of Planar Mechanisms Using Fuzzy Theories

A new integrated approach to the design of high speed planar mechanisms is presented. The resulting nonlinear programming formulation combines both the kinematic and dynamic synthesis aspects of mechanism design. The multiobjective optimization techniques presented in this work facilitate the design of a linkage to meet several kinematic and dynamic design criteria. The method can be used for motion, path, and function generation problems. The nonlinear programming formulation also permits the imposition of constraints to eliminate solutions which possess undesirable kinematic and motion characteristics. To model the vague and imprecise information in the problem formulation, the tools of fuzzy set theory have been used. A method of solving the resulting fuzzy multiobjective problem using mathematical programming techniques is presented. The outlined procedure is expected to be useful in situations where doubt arises about the exactness of permissible values, degree of credibility, and correctness of statements and judgements.

Parameter Sensitivity Analysis of a Large-Scale System With Several Components Interacting in Series

Parameter sensitivity for large-scale systems that include several components which interface in series is presented. Large-scale systems can be divided into components or sub-systems to avoid excessive calculations in determining their optimum design. Model Coordination Method of Decomposition (MCMD) is one of the most commonly used methods to solve large-scale engineering optimization problems. In the Model Coordination Method of Decomposition, the vector of coordinating variables can be partitioned into two sub-vectors for systems with several components interacting in series. The first sub-vector consists of those variables that are common among all or most of the elements. The other sub-vector consists of those variables that are common between only two components that are in series. This study focuses on a parameter sensitivity analysis for this special case using MCMD.

Robot Path Planning and Obstacle Avoidance: A Design Optimization Approach

A design optimization approach to robot path planning in a two dimensional workplace is presented. Obstacles are represented as a series of rectangular regions and collision detection is performed by an operation similar to clipping in computer graphics. The feasible design space is approximated by a discrete set of robot arm and gripper positions. Control is applied directly through the angular motion of each link. Feasible positions which are located between the initial and final robot link positions are grouped into stages. A dynamic programming algorithm is applied to locate the best state within each stage which minimizes the overall path length. An example is presented involving a three link planar manipulator. Extensions to three dimensional robot path planning and real time control in a dynamically changing workplace are discussed.

Sizing Design Sensitivity Analysis of Dynamic Frequency Response of Vibrating Structures

Dynamic frequency response of mechanical and structural systems is of interest in design problems that are subjected to harmonically varying external loads caused by the reciprocating power train or other rotating machineries such as motors, fans, compressors, and forging hammers [1]. For example, airplane body and wing structures are subjected to a harmonic load transmitted from the propulsion system. Also, ship vibrations resulting from the propeller and engine excitation can cause noise problem, cracks, fatigue failure of tailshaft, and discomfort to crew. When a machine or any structure oscillates in some form of periodic or random motion, the motion generates alternating pressure waves that propagate from the moving surface at the velocity of sound. For instance, the interior sound pressure in an automobile compartment can occur when the input forces transmitted from road and power train excite the vehicle compartment boundary panels. These motions with frequencies between 20 Hz and 20 KHz stimulate the hearing mechanism of human [2].