Many engineering sectors are challenged by multi-objective optimization problems. Even if the idea behind these problems is simple and well established, the implementation of any procedure to solve them is not a trivial task. The use of evolutionary algorithms to find candidate solutions is widespread. Usually they supply a discrete picture of the non-dominated solutions, a Pareto set. Although it is very interesting to know the non-dominated solutions, an additional criterion is needed to select one solution to be deployed. To better support the design process, this paper presents a new method of solving non-linear multi-objective optimization problems by adding a control function that will guide the optimization process over the Pareto set that does not need to be found explicitly. The proposed methodology differs from the classical methods that combine the objective functions in a single scale, and is based on a unique run of non-linear single-objective optimizers.

/pdf/a-new-method-for-decision-making-in-multi-objective-2srhnau0u8.pdf

A new method for decision making in multi-objective optimization problems

A roller rack pinion (RRP) system, which consists of a rack-bar and a cam pinion, transforms a rotation motion into linear motion. The rack-bar has a series of roller train and meshes with the cam pinion. First, the exact tooth profile of the cam pinion and the non-undercut condition to satisfy the required performance have been proposed with the introduction of the profile shift coefficient. Then, the load stress factors are investigated under the variation of the shape design parameters to predict the gear surface fatigue limit which is strongly related to the gear noise and vibration at the contact patch. The results show that the pitting life can be extended significantly with the increase of the profile shift coefficient.

Contact surface fatigue life for roller rack pinion system

The multiobjective optimization of Slide-o-Cam is reported in this paper. Slide-o-Cam is a cam mechanism with multiple rollers mounted on a common translating follower. This trans- mission provides pure-rolling motion, thereby reducing the fric- tion of rack-and-pinions and linear drives. A Pareto frontier is obtainedby means of multiobjective optimization. This optimiza- tion is based on three objective functions: (i) the pressure angle, which is a suitable performance index for the transmission be- cause it determines the amount of force transmitted to the load vs. that transmitted to the machine frame; (ii) the Hertz pressure used to evaluate the stresses produced on the contact surface be- tween cam and roller; and (iii) the size of the mechanism, char- acterized by the number of cams and their width.

/pdf/the-multiobjective-optimization-of-a-prismatic-drive-kwi45jwrht.pdf

The Multiobjective Optimization of a Prismatic Drive

Optimization and a reliability analysis of a cam-roller follower mechanism

Parallel Kinematics Machines (PKMs) have attracted attention for their high speed, good accuracy, low mass/inertia properties and high structural stiffness.They are attractive for the innovative machine-tool architectures. However, practicalutilizations for the potential benefits require an extensive and efficient analysis of their structure, kinematics and dynamics. Conventional design techniques may be used for a trivial design of PKMs with a limited capability of considering the performance measures and constraints. A multiobjective optimization approach, on the other hand, can be used to consider a set of optimal trade-off solutions (called Pareto set) between the conflicting design objectives, to better understand the complex design problems. Three separate but inter-linked design optimization issues of parallel manipulators are addressed in this dissertation. Firstly, a multiobjective optimization problem is proposed for the dimensional synthesis of parallel manipulators, in order to determine their optimum structural and geometric parameters. The proposed approach is applied to the optimum design of a three-degree-of-freedom planar parallel manipulator. Secondly, the issue of the actuators selection based on the kinematic and dynamic models of the manipulators is discussed. The process focuses on the kinematic and dynamic analysis of the Orthoglide 5-axis, a spatial PKM developed for high speed operations. The analysis is carried out firstly for the 2-DOF spherical wrist of the Orthoglide 5-axis and then for the 3-DOF translational parallel manipulator, the Orthoglide 3-axis. Some test trajectories are used to analyze the results and a procedure for motors selection is proposed. The last part deals with the optimal path placement of parallel manipulators. Mono- and multi-objective path placement optimization problems for PKMs based on energy consumption, actuators torques and shaking forces are introduced. Accordingly, a methodology is provided to determine the optimal location of a given test path withinthe workspace of a PKM to optimize some objective functions subject to the geometric, kinematic and dynamic constraints of the PKM. The proposed methodology is applied to the Orthoglide 3-axis as an illustrative example.

https://hal.archives-ouvertes.fr/tel-01390055/document

Multiobjective Optimization of Parallel Robots and Optimal Path Placement

The design of a mechanical transmission taking into account the transmitted forces is reported in this paper. This transmission is based on Slide-o-Cam, a cam mechanism with multiple rollers mounted on a common translating follower. The design of Slide-o-Cam, a transmission intended to produce a sliding motion from a turning drive, or vice versa, was reported elsewhere. This transmission provides pure-rolling motion, thereby reducing the friction of rack-and-pinions and linear drives. The pressure angle is a relevant performance index for this transmission because it determines the amount of force transmitted to the load vs. that transmitted to the machine frame. To assess the transmission capability of the mechanism, the Hertz formula is introduced to calculate the stresses on the rollers and on the cams. The final transmission is intended to replace the current ball-screws in the Orthoglide, a three-DOF parallel robot for the production of translational motions, currently under development for machining applications at Ecole Centrale de Nantes.

https://hal.archives-ouvertes.fr/hal-00144820/document

The Optimization of a Novel Prismatic Drive

The multiobjective optimization of Slide-o-Cam is reported in this paper. Slide-o-Cam is a cam mechanism with multiple rollers mounted on a common translating follower. This transmission provides pure-rolling motion, thereby reducing the friction of rack-and-pinions and linear drives. A Pareto frontier is obtained by means of multiobjective optimization. This optimization is based on three objective functions: (i) the pressure angle, which is a suitable performance index for the transmission because it determines the amount of force transmitted to the load vs. that transmitted to the machine frame; (ii) the Hertz pressure used to evaluate the stresses produced on the contact surface between cam and roller; and (iii) the size of the mechanism, characterized by the number of cams and their width.

Emilie Bouyer

Papers

The Optimization of a Novel Prismatic Drive

The Multiobjective Optimization of a Prismatic Drive

The Optimization of a Novel Prismatic Drive

The Multiobjective Optimization of a Prismatic Drive