Optimal synthesis of function-generating slider-crank mechanism based on a closed-form solution using five design parameters

Abstract

Kinematic dimensional synthesis is one of the essential steps during the process of design. It is classified into three tasks: function generation, path generation, and motion generation. In this paper, a design method is presented to solve the synthesis of the slider-crank mechanism for function generation based on a closed-form solution with five design parameters. The success criterion of a method used for function generation depends on the structural error function within an operational domain of the slider-crank mechanism. The structural error reduction is related to the number of design parameters utilized in mechanism synthesis, and the effective maximum number of design parameters for the slider-crank mechanism is five. In this study, the closed-form synthesis is found using three methods: precision point method, sub-domain method, and galerkin method. The system of equations is reduced to a twelfth-degree univariate polynomial equation, and thus all the available solutions are obtained. The effectiveness of this design method is tested with some examples of commonly used test functions, namely e^x, sin(x), tan(x) and ln(x), using a developed computer program. This design method gives lower structural error than traditional methods in kinematics literature.

Keywords

• Kinematic Synthesis
• Function Generation
• Slider-Crank Mechanism
• Closed-Form Solution

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