This paper introduces a new adaptive mixed differential evolution (NAMDE) algorithm for mechanical design optimisation problems. The algorithm uses a self-adaptive mechanism to update the values of mutation and crossover factors. Moreover, elitism is used where the best-found individual in each generation is retained. The performance of NAMDE is evaluated by solving 11 well-known constrained mechanical design problems and two industrial applications. Further, comparison results between NAMDE and other recently published methods, for the first problems, clearly illustrate that the proposed approach is an important alternative to solve current real-world optimisation problems. Besides this, new optimal solutions for some engineering problems are obtained and reported in this paper. For the coupling with a bolted rim problem, the objective function improved by 10%. Whereas for the spur minimisation problem, the final design provides a reduction in gearing mass by 7.5% compared to those published in previous works.