Abstract: rigid bar, the sprocket as a rigid polygon, and theroller between any two links as a revolving joint. The system is aclosed kinematic chain of rigid bodies connected by revolvingjoints. The gear constraint is treated as a variable constraint. When thelink meshes with the sprocket, the constraint force between the link and thesprocket is determined by testing. If the force is positive, the constraint is treated asa fixed constraint, otherwise the link leaves the sprocket. Lagrange's equationof motion is solved with Runge-Kutta method. Different driving processes aresimulated and analyzed. The phenomenon of locking is explained, and twotreatments to avoid locking of the system are proposed and analyzed.