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In this paper we propose a new method for generating synthetic handwritten signature images for biometric applications. The procedures we introduce imitate the mechanism of motor equivalence which divides human handwriting into two steps: the working out of an effector independent action plan and its execution via the corresponding neuromuscular path. The action plan is represented as a trajectory on a spatial grid. This contains both the signature text and its flourish, if there is one. The neuromuscular path is simulated by applying a kinematic Kaiser filter to the trajectory plan. The length of the filter depends on the pen speed which is generated using a scalar version of the sigma lognormal model. An ink deposition model, applied pixel by pixel to the pen trajectory, provides realistic static signature images. The lexical and morphological properties of the synthesized signatures as well as the range of the synthesis parameters have been estimated from real databases of real signatures such as the MCYT Off-line and the GPDS960GraySignature corpuses. The performance experiments show that by tuning only four parameters it is possible to generate synthetic identities with different stability and forgers with different skills. Therefore it is possible to create datasets of synthetic signatures with a performance similar to databases of real signatures. Moreover, we can customize the created dataset to produce skilled forgeries or simple forgeries which are easier to detect, depending on what the researcher needs. Perceptual evaluation gives an average confusion of 44.06% between real and synthetic signatures which shows the realism of the synthetic ones. The utility of the synthesized signatures is demonstrated by studying the influence of the pen type and number of users on an automatic signature verifier.