In this paper, the effect of some design parameters on the kinematiccharacteristics (displacement, velocity, and acceleration)of the external and internal Geneva Mechanism (GM) has been considered analytically using MATLAB and numerically using SolidWorks program. The parameters, such asthe change of: the drive pin diameter or the width of slot orthe total tolerance, the direction of motion of the pin when it enters or leaves the slot; tangent, above and below to the centerline of the slot, and the number of slots (inside or outside diameter) of the wheel, were taken into account. To compare the results, three, six, and nine slotted external and internal Geneva wheels (GWs) were used for the same crank length and constant drivingangular speed. In order to remove the unwanted non-zero initial and final accelerations or jerks, twocrank-rocker linkages, the first combining with external six-slotGW and the second combining with internal three-slot GW,were suggested and simulated using SolidWorks program.From that, the angularacceleration of the slotted wheelat the specified(initial and final) positions has been eliminated to zero or reduced to small value. Also,the maximum angular velocity and acceleration of the wheel joining the first linkagehas been reduced to about 39.4% and 63.3%, respectively, while in the case of the wheel joining the second linkage, the maximum angular velocity and acceleration has been increasedto about 279.4% and 27.4%, respectively.