初论现代数学在机构学研究中的作用与影响

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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 modem 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 modem mathematics on the development of mechanisms of China is outlined. The role of mathematics in mechanisms in future is finally expected.自机构学成为一门独立的学科以来,数学一直在机构学研究中发挥着重要作用。特别是当机构学发展到现代机构学阶段,对装备的自主创新设计要求越来越高,数学的作用也变得越来越突出。以当前机构学应用领域最为活跃的数学工具――旋量理论和微分流形为例,阐述现代数学在机构学研究中所起的作用。结合中国机构学的研究进展及标志性成果,简述现代数学对中国机构学发展的积极影响。展望数学在未来机构学研究中的重要地位与潜在影响。