A Closed-Form Solution to the Crank Position Corresponding to the Maximum Velocity of the Slider in a Centric Slider-Crank Mechanism

This paper revisits a classical problem in kinematics, specifically determination of the crank position corresponding to the maximum velocity of the slider in the centric slider-crank mechanism. This position is often critical in designing products constructed using the slider-crank mechanism, e.g., industrial sewing machinery, rotary engine systems, etc. In current literature, the numerical, graphical, or approximate closed-form solution to this problem is available. In this paper, an exact closed-form solution is derived. With this new closed-form solution, it is found that there exist significant errors in an approximate closed-form solution which can be found from many machine design text books for a practica1 use.