Affine connection control systems are mechanical control systems that model a wide range of real systems such as robotic legs, hovercrafts, planar rigid bodies, rolling pennies, snakeboards and so on. In 1997 the accessibility and a particular notion of controllability was intrinsically described by A. D. Lewis and R. Murray at points of zero velocity. Here, we present a novel generalization of the description of accessibility algebra for those systems at some points with nonzero velocity as long as the affine connection restricts to the distribution given by the symmetric closure. The results are used to describe the accessibility algebra of different mechanical control systems