FOURTH-ORDER APPROXIMATE SYNTHESIS OF SLIDER-CRANK FUNCTION GENERATORS
Journal of theoretical and applied mechanics · 2025
A new computer-applicable mathematical model for the synthesis of slider-crank mechanisms has been derived, in which the Burmester curves for infinitely close relative positions are generated indirectly using the Carter-Hall circle.The characteristic of the model is that it is linear, easy to implement with any computer program for engineering calculations (eg.MathCAD, MAT-LAB, etc.), and would greatly ease the work of engineers in the synthesis of mechanisms.The mathematical model is composed only of equations of lines, written in Cartesian coordinates, including when determining the kinematic diagrams of slider-crank mechanisms.Introduced an additional condition for achieving a certain value of the pressure angle, of which the reactions of the forces in the kinematic pairs and the force dimensioning of the mechanism depend, which unambiguously determines the kinematic diagrams of the mechanism.Since linear equations lead to a single solution, there is no need to search for additional conditions to determine a technically adequate solution, as when using higher-degree equations.The model greatly facilitates the synthesis of slider-crank mechanisms, generating set functions near a given position.The ease of working with the model and its adequacy with graphical constructions is illustrated with an example of the synthesis of a slider-crank mechanism that generates a function with a fourth-order derivative approximation to the given function.