Optimum dimensional synthesis of planar mechanisms with geometric constraints

The paper correctly defines both Euclidean and squared-distance constraints, provides exact gradients/Hessians, highlights the d=0 singularity for the Euclidean form, and presents the KKT/SQP block system. It does not formalize the equivalence of KKT multipliers under constraint rescaling nor discuss constraint qualification at D=0. The model’s solution correctly proves feasible-set equivalence for D>0 and the KKT multiplier scaling at feasibility, and it flags the D=0 degeneracy; however, it overstates the equivalence of the SQP Newton systems by omitting the additional gradient–gradient term that appears in the Lagrangian Hessian for the squared formulation. Hence both are largely correct but each misses key technical nuances.