Mechanical error estimation in four-bar hyperbolic function mechanisms with tolerances using modified PDA approach

Four-bar mechanisms play a critical role in mechanical design, especially in function generation applications. They are commonly employed across a wide range of systems, from simple mechanical links to sophisticated biomedical devices. This study analyzes the impact of dimensional tolerances on the performance of four-bar mechanisms synthesized to generate hyperbolic functions with four and five accuracy point synthesis. The hyperbolic functions sinh(x), cosh(x), and tanh(x) are examined for the structural and mechanical errors between the generated and desired function using the modified partial derivative approximation (PDA) method. The graphical technique is used to compare the estimated errors using modified PDA formulation with the reported errors. Mechanical errors were quantified for varying tolerance levels in both four-point and five-point synthesis cases. The mechanical error pattern for tolerance magnitude is present, which is beneficial to tolerance design for error control.