Comparative study of four-bar hyperbolic function generation mechanism with four and five accuracy points

Kinematic mechanisms are synthesized for a task. Function generation provides precise displacement at output links that obeys a given functional relations. This article describes the synthesis of four-bar mechanism for the hyperbolic function generation with four and five accuracy point, which is further optimized using least square method. This research is concerned with development of mathematical formulation based on Freudenstein-Chebyshev approximation theory, extended to four- and five-point synthesis function generation problem. The objective function is analyzed for the structural error between the generated function and the desired function. Resulting nonlinear equations are converted into set of linear equations applying the compatibility conditions and are solved using Gauss elimination method. The formulation is proposed for five position synthesis for algebraic and trigonometric function generation problem. Associated structural error is estimated. Comparison of estimated error through the formulation is carried out with the reported errors through graphical method. The error for hyperbolic function is estimated. Attempt is made to minimize the error through simple of least square technique. The results obtained are compared with Freudenstein-Chebyshev approximation method. Three hyperbolic functions, namely sinh(x), cosh(x) and tanh(x), are used to demonstrate the effectiveness of the proposed synthesis method.