Geometric errors directly affect the position of the end-effector of a Parallel Kinematic Manipulator (PKM), thus reducing its positioning accuracy. However, the tasks that are performed by PKMs, such as high-precision machining using a kinematic model with nominal values, are affected by machine errors that are not taken into account. Therefore, it is important to make an accurate determination of a machine's error factors to obtain an accurate error model. Identifying the most crucial geometric errors and determining a method to control them is key in improving the accuracy of PKMs. To achieve this objective, a new method of sensitivity analysis, allowing the crucial geometric errors for parallel and serial manipulators to be identified, is proposed. A new dimensionless sensitivity index, based on the definition of a Local Sensitivity Index (LSI), is used to perform this analysis. The geometric error modeling is performed by deriving the position vector of the end-effector of the PKM. To test the efficiency of the proposed method, the main sources of PAR2 PKM errors are identified. The results show that 33.3% of the error components (main errors) from all error sources can be improved, to achieve a 51.8% improvement in the accuracy of the position error. These results indicate that the error sensitivity analysis method is quite effective, and can significantly contribute to improving the accuracy of a PKM.