Limited stroke automatic watch winding poses a challenge due to the proof mass range being smaller than the input displacements. Traditionally the proof mass is connected to the mainspring by a linear reduction transmission however this setup only functions effectively for specific accelerations. This paper proposes to use a nonlinear transmission between the proof mass and the mainspring improve the power output. This transmission will us a singularity to have a mechanical advantage of zero in the middle of its motion range, and increasing the further it moves This improves the range in which the automatic winding device can operate especially the lower accelerations. A quasi static model of the system is made to estimate the efficiency of the mechanism for different accelerations which is verified by a demonstrator. These efficiencies combined with a human motion analysis suggest it could increase the energy generated to the mainspring by 52% compared to the linear transmission.