Abstract: Since mechanisms became an independent discipline, mathematics has been playing a key role in the mechanisms research. Especially, as mechanisms is developed into the phase of the advanced mechanisms, the role of mathematics has been getting more and more prominent due to the increasing demand on the self-design and innovation of mechanical equipments. Taking the screw theory and differential manifold, which are the most active mathematic tools used currently in the field of mechanisms, as examples, the key role of modern mathematics in mechanisms research is expounded. By analyzing the research progress and remarkable achievements in the field of mechanisms in China, the positive effect of modern mathematics on the development of mechanisms of China is outlined. The role of mathematics in mechanisms in future is finally expected.

Key words: Degree of freedom, Differential manifold, Mechanisms and robotics, Modern mathematics, Performance index, Screw theory, Type synthesis