This paper introduces a new approach for the synthesis of planar six-bar mechanisms via multi-objective numerical optimisation. Using the input-output relationship of such a mechanism, the structural error is formulated. In addition to the structural error, its derivative is also included in the objectives, leading to results which are comparable in accuracy to the exact methods reported in existing literature, and better than the optimisation-based methods. Also, analytical conditions are derived for the identification of the candidate designs which are free of singularities, mobility or branch defects. The formulation and results are demonstrated in the context of a Stephenson-III mechanism, though these can be generalised to the six-bar mechanisms of other topologies.