Balancing methods for mechanisms have been used over the years to extend the lifespan of machinery by reducing vibration, wear, and fatigue on their components. These techniques have grown in effectiveness but also in mathematical complexity. Nowadays most balancing methods use Cartesian coordinates, which generate complex equations involving trigonometric functions that are difficult to simplify. This paper presents the use of natural coordinates to obtain the balancing parameters of a simplified crank-connecting rod-slide mechanism avoiding the use of trigonometric functions. The balancing optimization of the mechanism is carried out by using a stochastic optimization algorithm based on populations allowing to reduce the Shaking Moment (ShM) by 97.76% and the Shaking Force (ShF) by 94.58%.