Kinematic Analysis of a Tendon-Driven Hybrid Rigid–Flexible Four-Bar; Application to Optimum Dimensional Synthesis

In design matters, mechanisms with deformable elements are a step behind those with rigid bars, particularly if dimensional synthesis is considered a fundamental part of mechanism design. For the purposes of this work, a hybrid rigid–flexible four-bar mechanism has been chosen, the input bar being a continuum tendon of constant curvature. The coupler curves are noticeably more complex but offer more possibilities than the classical rigid four-bar counterpart. One of the objectives of this work is to completely characterize the coupler curves of this hybrid rigid–flexible mechanism, determining the number and type of circuits as well as constituent branches. Another important aim is to apply optimization techniques to the dimensional synthesis of path generation. Considerable progress in finding the best design solutions can be obtained if all the acquired knowledge about the coupler curves of this hybrid mechanism is integrated into the optimization algorithm.This research was funded by the Spanish government through the Ministerio de Ciencia e Innovación (Project PID2020-116176GB-I00), financed by MCIN/AEI/10.13039/501100011033, and funded by the Departamento de Educación from the Regional Basque Government through Project IT1480-22

Hybrid Optimization Based Mathematical Procedure for Dimensional Synthesis of Slider-Crank Linkage

In this paper, an optimization procedure for path generation synthesis of the slider-crank mechanism will be presented. The proposed approach is based on a hybrid strategy, mixing local and global optimization techniques. Regarding the local optimization scheme, based on the null gradient condition, a novel methodology to solve the resulting non-linear equations is developed. The solving procedure consists of decoupling two subsystems of equations which can be solved separately and following an iterative process. In relation to the global technique, a multi-start method based on a genetic algorithm is implemented. The fitness function incorporated in the genetic algorithm will take as arguments the set of dimensional parameters of the slider-crank mechanism. Several illustrative examples will prove the validity of the proposed optimization methodology, in some cases achieving an even better result compared to mechanisms with a higher number of dimensional parameters, such as the four-bar mechanism or the Watt’s mechanism.The authors wish to acknowledge financial support received from the Spanish government through the Ministerio de Economía y Competitividad (Project DPI2015−67626-P (MINECO/FEDER, UE)), the support for the research group through Project Ref. IT949−16, provided by the Departamento de Educación, Política Lingüística y Cultura from the regional Basque Government, and the Program BIKAINTEK 2020 (Ref. 012-B2/2020) provided by the Departamento de Desarrollo Económico, Sostenibilidad y Medio Ambiente from the regional Basque Government

Optimum dimensional synthesis using GIMSYNT software

Paper presented at The 15th International Federation of Theory of Machines and Mechanisms World Congress is held during June 30 - July 4, 2019 in Krakow, Poland.In the field of mechanism design, optimum dimensional synthesis plays a significant role. Focusing on path generation synthesis, the designer has to find the most adequate mechanism capable of tracing a trajectory as similar as possible to a prescribed one. The objective is obviously clear, but, in many occasions, the methods dealing with optimum synthesis are quite complex and with a lack of transparency. Consequently, students often get lost in the insights of the optimization method and do not comprehend the influence of the different parameters that can be included in the optimization, or important choices such as enhancing the starting mechanism. Thus, they are not qualified to assess the validity of the resulting optimum design. To overcome this lack of knowledge, we propose a didactic optimum dimensional synthesis methodology mainly based on the analytic relations of the mechanism under study and considering the interrelation among synthesis variables. The guidelines of the procedure can be easily programmed and different design criteria can be incorporated. A software named GIMSYNT has been developed with this purpose, focusing on the slider-crank and the four-bar mechanism.The authors wish to acknowledge the financial support received from the Spanish Gov-ernment through the Ministerio de Economía y Competitividad (Project DPI2015-67626-P (MINECO/FEDER, UE)), and the financial support given to the research group, through the project with Ref. IT949-16, given by the Departamento de Educa-ción, Política Lingüística y Cultura of the Regional Government of the Basque Country