Mathematical Modelling of Displacement of a Slider-Crank Mechanism for a Pick and Place Robot Arm: An Agorithmic Approach

This paper used a computational approach to perform a displacement analysis of the slider crank mechanism. This work created new kinematic response models for the slider crank mechanism. With its use of trigonometric and inverse trigonometric functions, the Akozietic mathematical method is a new mathematical technique that may be applied to the kinematic study of intricate mechanisms like the four-bar mechanism (slider crank). The Akozietic mathematical technique for a four-bar mechanism uses the equilibrium conditions of the forces in the mechanism to generate basic mathematical models that allow user-written computer programs in Matlab and other programming languages. It can be observed from the displacement profile that the maximum position reached by the slider is obtained when the crank angle is at 0° or 360° and the position gradually reduces till it gets to the midpoint at 180° before gradually increasing again. Upon comparing the spreadsheet and the novel mathematical approach for mechanism analysis (Akozietic) with standard numerical solutions performed in Mathematica revealed that the new mathematical process developed in this study performed better than the other two existing methods of kinematic analysis.