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Kinematic synthesis of the mechanism for static balancing of an input torque in three positions

Buśkiewicz Jacek

Archive of Mechanical Engineering

2022

LXIX, nr 4

571--594

The aim of this work is to design the links-spring mechanism for balancing, in the three positions of the operating range, a rotary disc subjected to a torque. An energy-related approach towards the conditions of the mechanical system balance for a discrete number of positions leads to the formulation of a task of searching for a four-bar linkage which guides a coupler point through the prescribed positions, where, at the same time, geometrical conditions (specifying the spring tension) and kinematic conditions (defining the radial component of the tension change rate) are satisfied. The finitely and infinitesimally separated position synthesis is considered, however, only a component of the coupler point velocity is essential. A general method was proposed for determining the four-bar mechanism geometry. Mechanism inversion was applied in order to reduce the number of designed variables and simplify the solution method. The system of complex algebraic equations defines the problem. Linear, symbolic transformations and a systematic search technique are utilized to find multiple local optimal solutions. The problem is solved using Mathematica software.

Optimal synthesis of quick return mechanism as a path generator

Buśkiewicz J.

International Journal of Applied Mechanics and Engineering

2012

Vol. 17, no. 3

753-763

The paper deals with an optimal synthesis of planar mechanisms as path generators. The technique verified in the synthesis of four bar linkages and crank slider mechanisms was successfully applied to a quick return mechanism with prismatic joints. The main idea of the method consists in decreasing the number of the design parameters. The problem was formulated as an optimisation task. The mathematical foundations were presented. An objective function was constructed and minimised in searching for generators of test paths using an evolutionary algorithm. The exemplary solutions were presented and discussed.

Application of genetic algorithm and Fourier coefficients (GA-FC) in mechanism synthesis

Starosta R.

Journal of Theoretical and Applied Mechanics

2008

Vol. 46 nr 2

395-411

The paper concerns synthesis of a four-bar linkage as a curve generator. Fourier coefficients of the curvature are applied to represent a closed curve. A genetic algorithm (GA) was adapted to solve the problem. The proposed method was successfully verified by many examples.

Rozważanym zagadnieniem jest synteza czworoboku przegubowego jako generatora krzywej. Zastosowano nowy sposób reprezentowania krzywej zamkniętej za pomocą współczynników Fouriera. Do rozwiązania zadania został zaadaptowany algorytm genetyczny. Proponowana metoda została z sukcesem przetestowana na przykładach.