Subventions et des contributions :

Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023)

Mechanism synthesis is an important branch of mechanism science that has developed over the last millennium. A mechanism is a collection of interconnected components individually called links. The connection between two adjacent links is a joint. Four-bar linkages are an important class of mechanism that consist of a relatively fixed rigid link to which an input and an output link are attached, typically by rotary, or linear joints. The input and output links are additionally connected to a fourth link which couples the motion of the input to that of the output, forming a closed loop. Four-bar linkages have important applications to function generation (the motions of the input and output links are coordinated according to an algebraic function), rigid body guidance, and trajectory generation. The current approach is to prescribe a finite set of positions and orientations of the coupler, link 4, or a finite set of values for pairs of input and output link angles, and then to use numerical procedures to synthesise the geometry of a linkage that can approximate the desired motions with the least error, but relative to only the prescribed values. This is termed discrete approximate synthesis because of the finite number of discrete specified configurations. What occurs between each configuration is not accounted for and tends to make the design process inefficient. This research program consists of developing a fundamentally new branch of mechanism science, which we call continuous approximate synthesis (CAS). Instead of discrete sets, we propose to use calculus and geometry to expand the finite sets into continuous infinite sets. Because we take into account the entire range of motion, the resulting linkage represents the very best that is viable, performing with the smallest possible error throughout the entire range of motion. The long term goal of this work is to create design tools for any type of rigid mechanical linkage, connected both serially (analogous to a single human arm) or in parallel (analogous to two human arms connected to each other, both at the chest and hands, forming a closed loop), that yields the very best linkage relative to a particular error. There are four short term goals, comprising the focus of this grant application: 1) prove that for planar function generating four-bar linkages, the one which minimises a critical non-linear performance index can be identified by solving a set of linear equations; 2) adapt the results to arbitrary planar and spatial closed loop linkages; 3) extend the results to CAS for rigid body guidance; 4) further extend the results to trajectory generation. The concept of CAS has already received strong support from the Canadian mechanism design community, it is therefore expected that the proposed work will make a significant positive impact on the research and industrial sectors of the mechanism design community both within Canada and internationally.